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Robot Mechanisms
and Mechanical
Devices Illustrated
Paul E
...
All rights reserved
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Except as permitted under the United States Copyright Act of 1976, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written permission of the
publisher
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trademarked name, we use names in an editorial fashion only, and to the benefit of the trademark owner, with no intention
of infringement of the trademark
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McGraw-Hill eBooks are available at special quantity discounts to use as premiums and sales promotions, or for use in corporate training programs
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com or (212) 904-4069
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(“McGraw-Hill”) and its licensors reserve all rights in
and to the work
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Except as permitted under the Copyright Act of 1976 and the
right to store and retrieve one copy of the work, you may not decompile, disassemble, reverse engineer, reproduce, modify,
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without McGraw-Hill’s prior consent
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DOI: 10
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For more information about this title, click here
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Click here for Terms of Use
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Rotary Servomotors
Coil Assembly Heat Dissipation
Stepper Motors
Permanent-Magnet (PM) Stepper Motors
Variable Reluctance Stepper Motors
Hybrid Stepper Motors
Stepper Motor Applications
DC and AC Motor Linear Actuators
Stepper-Motor Based Linear Actuators
Servosystem Feedback Sensors
Rotary Encoders
Incremental Encoders
Absolute Encoders
Linear Encoders
Magnetic Encoders
Resolvers
Tachometers
Linear Variable Differential Transformers (LVDTs)
Linear Velocity Transducers (LVTs)
Angular Displacement Transducers (ATDs)
Inductosyns
Laser Interferometers
Precision Multiturn Potentiometers
Solenoids and Their Applications
Solenoids: An Economical Choice for Linear or Rotary Motion
Technical Considerations
Open-Frame Solenoids
C-Frame Solenoids
Box-Frame Solenoids
Tubular Solenoids
Rotary Solenoids
Rotary Actuators
Actuator Count
Debugging
Reliability
Cost
Chapter 2
Belts
Indirect Power Transfer Devices
34
35
36
37
37
38
38
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40
41
42
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43
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53
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55
57
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60
60
62
63
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63
64
64
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67
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68
68
69
72
Contents
Flat Belts
O-Ring Belts
V-Belts
Timing Belts
Smoother Drive Without Gears
Plastic-and-Cable Chain
Chain
Ladder Chain
Roller Chain
Rack and Pinion Chain Drive
Timing or Silent Chain
Friction Drives
Cone Drive Needs No Gears Or Pulleys
Gears
Gear Terminology
Gear Dynamics Terminology
Gear Classification
Worm Gears
Worm Gear with Hydrostatic Engagement
Controlled Differential Drives
Twin-Motor Planetary Gears Provide Safety Plus Dual-Speed
Harmonic-Drive Speed Reducers
Advantages and Disadvantages
Flexible Face-Gears Make Efficient High-Reduction Drives
High-Speed Gearheads Improve Small Servo Performance
Simplify the Mounting
Cost-Effective Addition
Chapter 3
Direct Power Transfer Devices
Couplings
Methods for Coupling Rotating Shafts
Ten Universal Shaft Couplings
Hooke’s Joints
Constant-Velocity Couplings
Coupling of Parallel Shafts
Ten Different Splined Connections
Cylindrical Splines
Face Splines
Torque Limiters
Ten Torque-Limiters
One Time Use Torque Limiting
73
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75
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79
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107
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121
121
125
vii
viii
Contents
Chapter 4
Wheeled Vehicle Suspensions and Drivetrains
Wheeled Mobility Systems
Why Not Springs?
Shifting the Center of Gravity
Wheel Size
Three-Wheeled Layouts
Four-Wheeled Layouts
All-Terrain Vehicle with Self-Righting and Pose Control
Six-Wheeled Layouts
Eight-Wheeled Layouts
Chapter 5
Steering History
Steering Basics
The Next Step Up
Chapter 7
130
130
131
134
136
141
144
150
155
Tracked Vehicle Suspensions and Drive Trains 161
Steering Tracked Vehicles
Various Track Construction Methods
Track Shapes
Track Suspension Systems
Track System Layouts
One-Track Drive Train
Two-Tracked Drive Trains
Two-Tracked Drive Trains with Separate Steering Systems
Four-Tracked Drive Trains
Six-Tracked Drive Trains
Chapter 6
127
167
168
171
174
178
178
179
180
181
184
187
190
193
Walkers
199
Leg Actuators
Leg Geometries
Walking Techniques
Wave Walking
Independent Leg Walking
Frame Walking
Roller-Walkers
Flexible Legs
202
203
208
208
208
211
214
214
Contents
Chapter 8
Pipe Crawlers and Other Special Cases
Horizontal Crawlers
Vertical Crawlers
Traction Techniques for Vertical Pipe Crawlers
Wheeled Vertical Pipe Crawlers
Tracked Crawlers
Other Pipe Crawlers
External Pipe Vehicles
Snakes
Chapter 9
Comparing Locomotion Methods
What Is Mobility?
The Mobility System
Size
Efficiency
The Environment
Thermal
Ground Cover
Topography
Obstacles
Complexity
Speed and Cost
The Mobility Index Comparison Method
The Practical Method
Explain All This Using the Algebraic Method
Chapter 10
Manipulator Geometries
Positioning, Orienting, How Many Degrees of Freedom?
E-Chain
Slider Crank
Arm Geometries
Cartesian or Rectangular
Cylindrical
Polar or Spherical
The Wrist
Grippers
Passive Parallel Jaw Using Cross Tie
Passive Capture Joint with Three Degrees of Freedom
217
220
221
222
223
224
224
226
226
227
229
229
230
231
232
232
233
233
234
235
235
236
236
237
239
241
243
243
245
246
247
248
250
252
255
256
ix
x
Contents
Industrial Robots
Industrial Robot Advantages
Trends in Industrial Robots
Industrial Robot Characteristics
Chapter 11
Proprioceptive and Environmental Sensing
Mechanisms and Devices
Industrial Limit Switches
Layouts
Combination Trip (Sense) and Hard Stop
By-Pass Layouts
Reversed Bump
Bumper Geometries and Suspensions
Simple Bumper Suspension Devices
Three Link Planar
Tension Spring Star
Torsion Swing Arm
Horizontal Loose Footed Leaf Spring
Sliding Front Pivot
Suspension Devices to Detect Motions in All Three Planes
Conclusion
Index
258
259
259
261
263
270
276
277
278
279
280
282
283
284
284
285
286
287
289
291
Introduction
T
his book is meant to be interesting, helpful, and educational to hobbyists, students, educators, and midlevel engineers studying or
designing mobile robots that do real work
...
e
...
Making a
vehicle that can autonomously drive around, both indoors and out,
seems, at first, like a simple thing
...
Unfortunately, soon after these first attempts, the designer will find
the robot getting stuck on what seem to be innocuous objects or bumps,
held captive under a chair or fallen tree trunk, incapable of doing anything useful, or with a manipulator that crushes every beer can it tries to
pick up
...
This book provides
that knowledge with the aid of hundreds of sketches showing drive layouts and manipulator geometries and their work envelope
...
Interspersed throughout the book are unusual mechanisms and devices, included to entice the reader to think outside the box
...
Building, designing, and working with practical mobile robots
requires knowledge in three major engineering fields: mechanical, electrical, and software
...
Click here for Terms of Use
...
While there are books describing the electric circuits
used in robots, and books that teach the software and control code for
robots, there are few that are focused entirely on the mechanisms and
mechanical devices used in mobile robots
...
It is written in laymen’s language and filled with sketches so novices and those not trained in
mechanical engineering can acquire some understanding of this interesting field
...
Since mobile robots
are being called on to perform more and more complex and practical
tasks, and many are now carrying one or even two manipulators, this
book has a section on manipulators and grippers for mobile robots
...
Autonomous robots place special demands on their mobility system
because of the unstructured and highly varied environment the robot
might drive through, and the fact that even the best sensors are poor in
comparison to a human’s ability to see, feel, and balance
...
In many cases, the microprocessor controlling the robot will only be telling the mobility system “go over there”
without regard to what lays directly in that path
...
In contrast, a human driver has very acute sensors: eyes for seeing
things and ranging distances, force sensors to sense acceleration, and
balance to sense levelness
...
) mobility system (wheels, suspension, and steering) and uses those many and powerful sensors to
guide that mobility system’s efforts to traverse difficult terrain
...
For these reasons, mobility systems on mobile robots can be both simpler and more complex than those found in automobiles
...
It feels right to a human, and it is well suited to higher
speed travel, but a robot doesn’t care about feeling right, not yet, at least!
The best mobility system for a robot to have is one that effectively
accomplishes the required task, without regard to how well a human
could use it
...
First, the term robot itself has unfortunately come to
have at least three different meanings
...
Colin Angle, CEO of iRobot Corp
...
In the manufacturing industry, however, the word robot means a
reprogrammable stationary manipulator with few, if any sensors, commonly found in large industrial manufacturing plants
...
This form of robot usually
has a microprocessor on it to aid in controlling the vehicle itself, perform
some autonomous or automatic tasks, and aid in controlling the manipulator if one is onboard
...
Robot and
mobile robot are used interchangeably throughout the book
...
Therefore, autonomous robot means a self-controlled, selfpowered, mobile vehicle that makes its own decisions based on inputs
from sensors
...
The more common form of mobile robot today
is semiautonomous, where the robot has some sensors and acts partially
on its own, but there is always a human in the control loop through a
radio link or tether
...
Specific
vehicles in this book that do not use sensors to make decisions are
labeled telerobotic or teleoperated to differentiate them from
autonomous robots
...
Another word, which gets a lot of use in the robot world, is mobility
...
Chapter Nine focuses entirely on comparing drive
systems’ mobility based on a wide range of common obstacles found in
xiii
xiv
Introduction
outdoor and indoor environments, some of which can be any size (like
rocks), others that cannot (like stair cases)
...
While
hydraulic power can be the answer when very compact actuators or
high power density motors are required, it is potentially more dangerous, and definitely messier, to work with than electrically powered
devices
...
There are many texts on hydraulic power and its uses
...
, published by Womack Education
Publications
...
These tools include 3D design tools like SolidWorks and Pro-Engineer
and also new ways to produce prototypes of the mechanisms themselves
...
NEW PROCESSES EXPAND CHOICES
FOR RAPID PROTOTYPING
New concepts in rapid prototyping (RP) have made it possible to build
many different kinds of 3D prototype models faster and cheaper than by
traditional methods
...
Rapid-prototyping techniques make use
of computer programs derived from computer-aided design (CAD)
drawings of the object
...
They can be passed around a conference
table and will be especially valuable during discussions among product
design team members, manufacturing managers, prospective suppliers,
and customers
...
Rapid prototyping models
can be made by the owners of proprietary equipment, or the work can be
contracted out to various RP centers, some of which are owned by the RP
equipment manufacturers
...
New and improved RP methods are being introduced regularly, so the RP field is in a state of change, expanding the
range of designer choices
...
If design flaws
or omissions are discovered, changes can be made in the source CAD
program and a replacement model can be produced quickly to verify that
the corrections or improvements have been made
...
Most of the RP technologies are additive; that is, the model is made
automatically by building up contoured laminations sequentially from
materials such as photopolymers, extruded or beaded plastic, and even
paper until they reach the desired height
...
By contrast, a subtractive RP
process involves milling the model from a block of soft material, typically plastic or aluminum, on a computer-controlled milling machine
with commands from a CAD-derived program
...
Thermoplastic systems are based on procedures for successively melting and fusing solid
filaments or beads of wax or plastic in layers, which harden in the air to
form the finished object
...
The first commercial RP process introduced was stereolithography in
1987, followed by a succession of others
...
They have become multinational businesses through branch
offices, affiliates, and franchises
...
Some processes are not effective in making large models, and each
process results in a model with a different finish
...
xv
xvi
Introduction
Rapid prototyping is now also seen as an integral part of the even
larger but not well defined rapid tooling (RT) market
...
Some concept modeling equipment, also called 3D or office printers,
are self-contained desktop or benchtop manufacturing units small
enough and inexpensive enough to permit prototype fabrication to be
done in an office environment
...
Computer-Aided Design Preparation
The RP process begins when the object is drawn on the screen of a CAD
workstation or personal computer to provide the digital data base
...
The thickness of the “slices” can
range from 0
...
5 in
...
06 to 13 mm) depending on the RP
process selected
...
The digitized data then guides a laser, X-Y table, optics, or other
apparatus that actually builds the model in a process comparable to
building a high-rise building one story at a time
...
Prototyping Choices
All of the commercial RP methods depend on computers, but four of
them depend on laser beams to cut or fuse each lamination, or provide
enough heat to sinter or melt certain kinds of materials
...
Introduction
xvii
Stereolithography (SL)
The stereolithographic (SL) process is performed on the equipment
shown in Figure 1
...
The
SL equipment is located in a sealed chamber to prevent the escape of
fumes from the resin vat
...
The UV laser
beam is focused on an X-Y mirror in a computer-controlled beam-shaping and scanning system so that it draws the outline of the lowest crosssection layer of the object being built on the film of photopolymer resin
...
The laser beam can harden the layer down to a depth of 0
...
0300
in
...
06 to 0
...
The laser beam scans at speeds up to 350 in
...
The photopolymer not scanned by the laser beam remains a liquid
...
When
model surface finish is important, layer thicknesses are set for 0
...
(0
...
The table is then submerged under computer control to the specified
depth so that the next layer of liquid polymer flows over the first hardened layer
...
Figure 1 Stereolithography (SL):
A computer-controlled
neon–helium ultraviolet light
(UV)–emitting laser outlines each
layer of a 3D model in a thin liquid film of UV-curable photopolymer on a platform submerged a
vat of the resin
...
” The platform
is then lowered into the liquid to
a depth equal to layer thickness,
and the process is repeated for
each layer until the 3D model is
complete
...
The model is them removed for
finishing
...
Without support, parts of the model can sag or break off before
the polymer has fully set
...
Each scan of the laser forms
support layers where necessary while forming the layers of the model
...
The SL process leaves the model only partially polymerized, with only about half of its fully cured strength
...
The UV completes
the hardening or curing of the liquid polymer by linking its molecules in
chainlike formations
...
Polymers
such as urethane acrylate resins can be milled, drilled, bored, and tapped,
and their outer surfaces can be polished, painted, or coated with sprayedon metal
...
Resins can be formulated
to solidify under either UV or visible light
...
3D Systems of
Valencia, California, is a company that manufactures stereolithography
equipment for its proprietary SLA process
...
The SLA process can build a model within a volume
measuring 10 × 7
...
(25 × 19 × 20 cm)
...
62 in
...
Aaroflex, Inc
...
Solid Ground Curing (SGC)
Solid ground curing (SGC) (or the “solider process”) is a multistep inline process that is diagrammed in Figure 2
...
An electron gun writes a charge pattern of the photomask
on a clear glass plate, and opaque toner is transferred electrostatically to
the plate to form the photolithographic pattern in a xerographic process
...
Liquid photopolymer is applied to the work platform to form a
layer, and the platform is moved under the photomask and a strong UV source that
defines and hardens the layer
...
After
the wax is cooled, excess polymer and wax are milled off to form the first “slice
...
Masking and
layer formation are repeated with the platform being lowered and moved back and forth
under the stations until the 3D model is complete
...
The photomask is then moved to the exposure station, where it is aligned
over a work platform and under a collimated UV lamp
...
The platform is then moved left to the exposure station, where
the UV lamp is then turned on and a shutter is opened for a few seconds
to expose the resin layer to the mask pattern
...
The platform is then moved back to the right to the wiper station,
where all of resin that was not exposed to UV is removed and discarded
...
The wax is hardened at the next station by
pressing it against a cooling plate
...
The platform piece is then returned to the resin application station, where it is lowered a depth equal to the thickness of the
next layer and more resin is applied
...
The
complete cycle is repeated, and this will continue until the 3D model
encased in the wax matrix is completed
...
After the prototype is removed from the process equipment, the wax is
either melted away or dissolved in a washing chamber similar to a dishwasher
...
The SGC process is similar to drop on demand inkjet plotting, a
method that relies on a dual inkjet subsystem that travels on a precision
X-Y drive carriage and deposits both thermoplastic and wax materials
onto the build platform under CAD program control
...
Cubital America Inc
...
Selective Laser Sintering (SLS)
Selective laser sintering (SLS) is another RP process similar to stereolithography (SL)
...
The prototype is fabricated in a cylinder with
a piston, which acts as a moving platform, and it is positioned next to a
cylinder filled with preheated powder
...
Just before it is applied, the powder is heated further until its temperature is just below its melting point
When the laser beam scans the thin layer of powder under the control
of the optical scanner system, it raises the temperature of the powder
even further until it melts or sinters and flows together to form a solid
layer in a pattern obtained from the CAD data
...
The process is repeated, with
each layer being fused to the underlying layer, until the 3D prototype is
completed
...
No
final curing is required, but because the objects are sintered they are
porous
...
The powder layer is then scanned by a
computer-controlled carbon dioxide infrared laser that defines the layer and melts the
powder to solidify it
...
It is then removed and finished
...
surfaces, and it can be smoothed by various manual or machine grinding
or melting processes
...
Many different powdered materials have been used in the SLS
process, including polycarbonate, nylon, and investment casting wax
...
One
advantage of the SLS process is that materials such as polycarbonate and
nylon are strong and stable enough to permit the model to be used in limited functional and environmental testing
...
SLS process equipment is enclosed in a nitrogen-filled chamber that is
sealed and maintained at a temperature just below the melting point of
the powder
...
The SLS process was developed at the University of Texas at Austin,
and it has been licensed by the DTM Corporation of Austin, Texas
...
Another company participating in SLS is EOS GmbH of Germany
...
The carbon-dioxide
laser beam, directed by an optical system under CAD data control, cuts
cross-sectional outlines of the prototype in the layers of paper, which are
bonded to previous layers to become the prototype
...
The laser beam cuts the outline
of each lamination and cross-hatches the waste material within and
around the lamination to make it easier to remove after the prototype is
completed
...
Finally, a heated roller applies pressure to bond the adhesive coating on each layer cut from the paper to the
previous layer
...
When all the layers have been cut and bonded, the excess cross-hatched material in the
Figure 4 Laminated Object Manufacturing (LOM): Adhesive-backed paper is fed across
an elevator platform and a computer-controlled carbon dioxide infrared-emitting laser
cuts the outline of a layer of the 3D model and cross-hatches the unused paper
...
When all the layers have been cut and
bonded, the cross-hatched material is removed to expose the finished model
...
Introduction
form of stacked segments is removed to reveal the finished 3D model
...
Using inexpensive, solid-sheet materials makes the 3D LOM models
more resistant to deformity and less expensive to produce than models
made by other processes, its developers say
...
The objects made by LOM can be larger than those made
by most other RP processes—up to 30 × 20 × 20 in
...
The LOM process is limited by the ability of the laser to cut through
the generally thicker lamination materials and the additional work that
must be done to seal and finish the model’s inner and outer surfaces
...
Helysys Corporation, Torrance, California, manufactures the LOM2030H LOM equipment
...
Other companies offering equipment for building prototypes from
paper laminations are the Schroff Development Corporation, Mission,
Kansas, and CAM-LEM, Inc
...
Fused Deposition Modeling (FDM)
The Fused Deposition Modeling (FDM) process, diagrammed in Figure 5,
forms prototypes from melted thermoplastic filament
...
070 in
...
78 mm), is fed into a temperaturecontrolled FDM extrusion head where it is heated to a semi-liquid state
...
Successive laminations ranging in thickness from 0
...
030 in
...
05 to 0
...
010 to 0
...
(0
...
1 mm) adhere to each by thermal fusion to form the 3D model
...
These supports can easily be removed in a later secondary
operation
...
Four different kinds of inert, nontoxic filament
materials are being used in FDM: ABS polymer (acrylonitrile butadiene
styrene), high-impact-strength ABS (ABSi), investment casting wax, and
xxiii
xxiv
Introduction
Figure 5 Fused Deposition Modeling (FDM): Filaments of thermoplastic are unwound
from a spool, passed through a heated extrusion nozzle mounted on a computercontrolled X-Y table, and deposited on the fixtureless platform
...
The hot filament
bonds to the layer below it and hardens
...
The
completed object is removed and smoothed to improve its finish
...
These materials melt at temperatures between 180 and 220ºF
(82 and 104ºC)
...
The company offers four different systems
...
(20 × 20
× 20 cm), and it prints models from square polyester wafers that are
stacked in cassettes
...
01in
...
25-mm)–diameter hole at a controlled rate
...
Stratasys also offers four systems that use spooled material
...
(26 × 26 × 41 cm)
...
(46 × 46 × 61 cm), and the FDM Quantum
system, which builds models up to 24 × 20 × 24 in
...
All of these systems can be used in an office environment
...
The
Introduction
water-soluble supports are formed by a separate extrusion head, and they
can be washed away after the model is complete
...
The powder supply cylinder is filled with starch and
cellulose powder, which is delivered to the work platform by elevating a
delivery piston
...
A multichannel inkjet head sprays a water-based liquid adhesive onto the surface
of the powder to bond it in the shape of a horizontal layer of the model
...
Liquid adhesive is then
sprayed on the powder to form the contours of the layer
...
This procedure is repeated until the 3D model is complete
...
xxv
xxvi
Introduction
ton
...
Any loose
excess powder is brushed away, and wax is coated on the inner and outer
surfaces of the model to improve its strength
...
One of those firms, the Z Corporation of
Somerville, Massachusetts, uses the original MIT process to form 3D
models
...
Soligen Technologies has
modified the 3DP process to make ceramic molds for investment casting
...
Direct-Shell Production Casting (DSPC)
The Direct Shell Production Casting (DSPC) process, diagrammed in
Figure 7, is similar to the 3DP process except that it is focused on forming molds or shells rather than 3D models
...
As in the
3DP process, DSPC begins with a CAD file of the desired prototype
...
Ceramic powder is
spread by roller over the surface of a movable piston that is recessed to the depth of a single layer
...
The
next layer is bonded to the first by the binder
...
The mold can be used to cast a prototype
...
Introduction
Two specialized kinds of equipment are needed for DSPC: a dedicated
computer called a shell-design unit (SDU) and a shell- or moldprocessing unit (SPU)
...
SDU software also modifies the original design dimensions in the CAD file to compensate for ceramic
shrinkage
...
The movable platform in DSPC is the piston within the build cylinder
...
Then a thin layer of fine aluminum oxide (alumina) powder is spread by roller over the platform, and a fine jet of colloidal silica is sprayed precisely onto the powder surface to bond it in the
shape of a single mold layer
...
The excess powder is then removed, and
the mold is fired to convert the bonded powder to monolithic ceramic
...
After the molten metal has cooled, the ceramic shell and any cores or
gating are broken away from the prototype
...
DSPC is a proprietary process of Soligen Technologies, Northridge,
California
...
Ballistic Particle Manufacturing (BPM)
There are several different names for the Ballistic Particle Manufacturing (BPM) process, diagrammed in Figure 8
...
The molten plastic used to form the model
and the hot wax for supporting overhangs or indentations are kept in
heated tanks above the build station and delivered to computercontrolled jet heads through thermally insulated tubing
...
The droplets are deposited only where directed, and they harden
rapidly as they leave the jet heads
...
Particles that are removed by the
cutter are vacuumed away and deposited in a collector
...
After each layer has been deposited, a stripe of each material is
deposited on a narrow strip of paper for thickness measurement by opti-
xxvii
xxviii Introduction
Figure 8 Ballistic Particle Manufacturing (BPM): Heated plastic and wax are deposited
on a movable work platform by a computer-controlled X-Y table to form each layer
...
The platform is lowered and the
next layer is applied
...
A fault
detection system determines the quality and thickness of the wax and plastic layers and
directs rework if a fault is found
...
cal detectors
...
However, if a clot is detected in either nozzle, a jet cleaning
cycle is initiated to clear it
...
After the 3D model is completed, the wax material
is either melted from the object by radiant heat or dissolved away in a hot
water wash
...
With this RP method, a slower process that yields
a 3D model with a superior finish is traded off against faster processes
that require later manual finishing
...
It offers the ModelMaker II processing equipment, which
produces 3D models with this method
...
Directed Light Fabrication (DLF)
The Directed Light Fabrication (DLF) process, diagrammed in Figure 9,
uses a neodymium YAG (Nd:YAG) laser to fuse powdered metals to
build 3D models that are more durable than models made from paper or
plastics
...
The technique is also called Direct-Metal Fusing,
Laser Sintering, and Laser Engineered Net Shaping (LENS)
...
DLF is an outgrowth of nuclear weapons research at the Los Alamos
National Laboratory (LANL), Los Alamos, New Mexico, and it is still in
the development stage
...
The heat from the laser beam melts the metal powder to form thin layers of a
3D model or prototype
...
Powdered aluminum, copper, stainless steel, and other metals have been fused to make
prototypes as well as practical tools or parts that are furnace-fired to increase their bond
strength
...
A system that would regulate and mix metal powder to modify the properties of the prototype is also being investigated
...
Protypes made by this method
have proven to be durable and they have shown close dimensional tolerances
...
At the same time, practical commercial processes have been improved
...
This discussion is limited to two techniques, SDM and Mold SDM, that have shown commercial promise
...
This process, diagrammed in Figure 10, forms successive layers of
metal on a platform without masking, and is also called solid free- form
(SFF) fabrication
...
The first steps in manufacturing a part by SDM are to reorganize or
destructure the CAD data into slices or layers of optimum thickness that
will maintain the correct 3D contours of the outer surfaces of the part and
then decide on the sequence for depositing the primary and supporting
materials to build the object
...
The work is then
moved to a machining station (b), where a computer-controlled milling
machine or grinder removes deposited metal to shape the first layer of
the part
...
The work
is then transferred back to the deposition station (a) for simultaneous
deposition of primary metal for the next layer and sacrificial support
Introduction
Figure 10 Shape Deposition Manufacturing (SDM): Functional metal parts or tools can
be formed in layers by repeating three basic steps repetitively until the part is completed
...
They retain their heat long enough to remelt the
underlying metal on impact to form strong metallurgical interlayer bonds
...
The sacrificial metal supports
any undercut features
...
metal
...
This SDM cycle is
repeated until the part is finished, and then the sacrificial metal is etched
away with acid
...
The metal droplets in microcasting are large enough
(1 to 3 mm in diameter) to retain their heat longer than the 50-mm
droplets formed by conventional thermal spraying
...
This process overcame the low adhesion and low
mechanical strength problems encountered with conventional thermal
metal spraying
...
The SDM laboratory has produced custom-made functional mechanical parts and has embedded prefabricated mechanical parts, electronic
components, electronic circuits, and sensors in the metal layers during
the SDM process
...
Mold SDM
The Rapid Prototyping Laboratory at Stanford University, Palo Alto,
California, has developed its own version of SDM, called Mold SDM,
for building layered molds for casting ceramics and polymers
...
The wax
occupies the same position as the sacrificial support metal in SDM, and
water-soluble photopolymer sacrificial support material occupies and
supports the mold cavity
...
No machining is performed in this process
...
The actual processing
begins at Figure 11(a), which shows the results of repetitive cycles of the
deposition of wax for the mold and sacrificial photopolymer in each
layer to occupy the mold cavity and support it
...
After the mold and support structures are
built up, the work is moved to a station (b) where the photopolymer is
removed by dissolving it in water
...
It can be any compatible castable
material
...
The wax mold is then removed (d) by melting it, releasing the “green”
ceramic part for furnace firing
...
Mold SDM has been expanded into making parts from a variety of
polymer materials, and it has also been used to make preassembled
mechanisms, both in polymer and ceramic materials
...
” This old design philosophy is far easier to use with the aid of RP
tools
...
UV energy solidifies the photopolymer
...
Materials
such as polymers and ceramics can be cast in the wax mold
...
The wax mold is then removed by heat or a hot liquid bath and the green
ceramic part released (d)
...
Popsicle sticks, crazy glue, hot glue, shirt cardboard, packing tape, clay,
or one of the many construction toy sets, etc
...
There’s
nothing like holding the thing in your hand, even in a crude form, to see
if it has any chance of working as originally conceived
...
Start simple and test ideas one at a time,
then assemble those pieces into subassemblies and test those
...
Design the mobility system
to handle more difficult terrain because there will always be obstacles that
will cause problems even in what appears to be a simple environment
...
Trial and error is the best method in many fields of design, and is
especially so for robots
...
Mobile robots are inherently complex devices with many interactions within themselves and with their environment
...
There is nothing like seeing an autonomous robot happily driving around, doing some useful task
completely on its own
...
Acknowledgments
T
his book would not even have been considered and would never have
been completed without the encouragement and support of my loving wife, Victoria
...
In addition to the support of my wife, I would like to thank Joe Jones
for his input, criticism, and support
...
Thanks also goes to Lee Sword, Chi Won, Tim Ohm,
and Scott Miller for input on many of the ideas and layouts
...
And, lastly, thanks to my extended family, especially my Dad and Jenny for their encouragement and patience
...
Click here for Terms of Use
...
Chapter 1
Motor and Motion
Control Systems
Copyright © 2003 by The McGraw-Hill Companies, Inc
...
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...
The system might also contain other components such as one or
more belt-, ballscrew-, or leadscrew-driven linear guides or axis stages
...
All of the components of a motion control system must work together
seamlessly to perform their assigned functions
...
Figure 1-1
illustrates a typical multiaxis X-Y-Z motion platform that includes the
three linear axes required to move a load, tool, or end effector precisely
through three degrees of freedom
...
3
4
Chapter 1
Motor and Motion Control Systems
Figure 1-2 The right-handed
coordinate system showing six
degrees of freedom
...
Motion control systems today can be found in such diverse applications as materials handling equipment, machine tool centers, chemical
and pharmaceutical process lines, inspection stations, robots, and injection molding machines
...
• Quicker changeovers for higher flexibility and easier product customizing
...
• Simpler system design for easier installation, programming, and
training
...
• Cleaner, quieter operation without oil or air leakage
...
This discussion of motion control is limited to
electric-powered systems
...
An open-loop system does not require that measurements of any output
variables be made to produce error-correcting signals; by contrast, a
closed-loop system requires one or more feedback sensors that measure
and respond to errors in output variables
...
Feedback sensors
provide the electronic signals for correcting deviations from the desired
input commands
...
Each motor in a servosystem requires its own feedback sensors, typically encoders, resolvers, or tachometers that close loops around the
motor and load
...
A velocity control loop, as shown in block diagram Figure 1-4, typically
contains a tachometer that is able to detect changes in motor speed
...
These signals are sent
Figure 1-3 Block diagram of a
basic closed-loop control system
...
to the motion controller so that it can compute a corrective signal for the
amplifier to keep motor speed within those preset limits despite load
changes
...
These sensors generate error signals that
are sent to the motion controller, which produces a corrective signal for
amplifier
...
Most position control
closed-loop systems also include a velocity-control loop
...
Three examples of feedback sensors mounted on the ballscrew
mechanism that can provide position feedback are shown in Figure 1-7:
(a) is a rotary optical encoder mounted on the motor housing with its shaft
coupled to the motor shaft; (b) is an optical linear encoder with its gradu-
Figure 1-5 Block diagram of a
position-control system
...
ated scale mounted on the base of the mechanism; and (c) is the less commonly used but more
accurate and expensive laser interferometer
...
An error signal from the circuit is
sent to the motion controller, which computes a
corrective signal for the motor amplifier to keep
motor current, and hence torque, constant
...
Trapezoidal Velocity Profile
If a motion control system is to achieve smooth,
high-speed motion without overstressing the ser-
Figure 1-7 Examples of position feedback sensors installed
on a ballscrew-driven slide mechanism: (a) rotary encoder,
(b) linear encoder, and (c) laser interferometer
...
vomotor, the motion controller must command the motor amplifier to
ramp up motor velocity gradually until it reaches the desired speed and
then ramp it down gradually until it stops after the task is complete
...
The trapezoidal profile, shown in Figure 1-8, is widely used because it
accelerates motor velocity along a positive linear “up-ramp” until the
desired constant velocity is reached
...
Amplifier current and output
voltage reach maximum values during acceleration, then step down to
lower values during constant velocity and switch to negative values during deceleration
...
All three of these techniques can be combined to form proportionalintegral-derivative (PID) control
...
• In integral control the signal driving the motor equals the time integral of the difference between the input command and the measured
actual output
...
• In proportional-integral-derivative (PID) control the signal that
drives the motor equals the weighted sum of the difference, the time
integral of the difference, and the time derivative of the difference
between the input command and the measured actual output
...
This system does not need feedback sensors because load
Figure 1-9 Block diagram of
an open-loop motion control
system
...
Because load position is not continuously sampled by a feedback
sensor (as in a closed-loop servosystem), load positioning accuracy is
lower and position errors (commonly called step errors) accumulate over
time
...
Kinds of Controlled Motion
There are five different kinds of motion control: point-to-point, sequencing, speed, torque, and incremental
...
This is done at a constant speed, with
both velocity and distance monitored by the motion controller
...
X-Y tables and milling machines position their loads by multiaxis point-to-point control
...
Speed control is the control of the velocity of the motor or actuator in
a system
...
Incremental motion control is the simultaneous control of two or
more variables such as load location, motor speed, or torque
...
There are three kinds of interpolation: linear, circular, and contouring
...
The motion controller must determine the speed of each axis so that
it can coordinate their movements
...
The path can lie in one plane or be three dimensional
...
It
requires that the motion controller modify load acceleration while it is in
transit
...
Contouring is the path followed by the load, tool, or end- effector
under the coordinated control of two or more axes
...
Load speed is determined
along the trajectory, and it can be constant except during starting and
stopping
...
Electronic gearing is the control by software of one or more
axes to impart motion to a load, tool, or end effector that simulates the
speed changes that can be performed by actual gears
...
Mechanical Components
The mechanical components in a motion control system can be more
influential in the design of the system than the electronic circuitry used
to control it
...
Mechanical actuators convert a motor’s rotary motion into linear
motion
...
Method selection is based on the relative costs of the alternatives
and consideration for the possible effects of backlash
...
Figure 1-10 Leadscrew drive: As
the leadscrew rotates, the load is
translated in the axial direction of
the screw
...
Figure 1-12 Worm-drive systems can provide high speed
and high torque
...
The linear stage supports the mass of the load to be actuated
and assures smooth, straight-line motion while minimizing friction
...
The motor turns the ballscrew, and its
rotary motion is translated into the linear motion that moves the carriage
and load by the stage’s bolt nut
...
As shown in Figure 1-7, these stages can be equipped with sensors such
as a rotary or linear encoder or a laser interferometer for feedback
...
This method ignores
Figure 1-13 Ballscrew-driven
single-axis slide mechanism translates rotary motion into linear
motion
...
the tolerance, wear, and compliance in the mechanical components
between the carriage and the position encoder that can cause deviations
between the desired and true positions
...
Other kinds of single-axis stages include those containing antifriction
rolling elements such as recirculating and nonrecirculating balls or
rollers, sliding (friction contact) units, air-bearing units, hydrostatic units,
and magnetic levitation (Maglev) units
...
Some
models being offered are 3
...
2 m) long and include a carriage for
mounting loads
...
8 ft/s (3 m/s)
...
The resolution of this type of
stage with a noncontact linear encoder can be as fine as 20 nm and accuracy can be ±1 µm
...
3 nm resolution and submicron accuracy if a laser interferometer is installed
...
Some manufacturers claim ±1 arc-s per 100 mm as the
limits for each of these characteristics
...
The important attributes of all these stages are their dynamic and
static friction, rigidity, stiffness, straightness, flatness, smoothness, and
load capacity
...
14
Chapter 1
Motor and Motion Control Systems
Figure 1-15 Flexible shaft couplings adjust for and accommodate parallel misalignment (a)
and angular misalignment
between rotating shafts (b)
...
Misalignments can
be 9º angular or 1⁄4 in
...
Helical couplings (b) prevent
backlash and can operate at constant velocity with misalignment
and be run at high speed
...
A properly designed base or host
machine will be highly damped and act as a compliant barrier to isolate
the motion system from its environment and minimize the impact of
external disturbances
...
A high static mass to reciprocating
mass ratio can also prevent the motion control system from exciting its
host structure to harmful resonance
...
For
example, a flexible shaft coupling, as shown in Figure 1-15, will compensate for minor parallel (a) and angular (b) misalignment between
rotating shafts
...
The bellows configuration (a) is acceptable for light-duty applications where misalign-
Chapter 1
Motor and Motion Control Systems
ments can be as great as 9º angular or 1⁄4 in
...
By contrast, helical
couplings (b) prevent backlash at constant velocity with some misalignment, and they can also be run at high speed
...
Electronic System Components
The motion controller is the “brain” of the motion control system and
performs all of the required computations for motion path planning,
servo-loop closure, and sequence execution
...
The motion controller produces a
low-power motor command signal in either a digital or analog format for
the motor driver or amplifier
...
Added to that are the decreasing
cost of more advanced semiconductor and disk memories
...
The motion controller is the most critical component in the system
because of its dependence on software
...
However, making field changes can be costly in terms of lost productivity
...
Also to be considered are the system’s multitasking capabilities, the
number of input/output (I/O) ports required, and the need for such features as linear and circular interpolation and electronic gearing and camming
...
Motor Selection
The most popular motors for motion control systems are stepping or stepper motors and permanent-magnet (PM) DC brush-type and brushless DC
servomotors
...
These motors are indexed or partially
rotated by digital pulses that turn their rotors a fixed fraction or a revolution where they will be clamped securely by their inherent holding torque
...
However, a feedback loop can improve the positioning accuracy of a
stepper motor without incurring the higher costs of a complete servosystem
...
Brush and brushless PM DC servomotors are usually selected for
applications that require more precise positioning
...
Brush-type permanent-magnet (PM) DC servomotors have wound
armatures or rotors that rotate within the magnetic field produced by a
PM stator
...
These
motors are quite mature, and modern versions can provide very high performance for very low cost
...
The disk-type
armature of the pancake-frame motor, for example, has its mass concentrated close to the motor’s faceplate permitting a short, flat cylindrical
housing
...
The brush-type DC motor with a cup-type armature also offers lower
weight and inertia than conventional DC servomotors
...
However, any servomotor with brush commutation can be unsuitable
for some applications due to the electromagnetic interference (EMI)
caused by brush arcing or the possibility that the arcing can ignite nearby
flammable fluids, airborne dust, or vapor, posing a fire or explosion hazard
...
In addition, motor brushes wear down and leave a gritty residue that can
contaminate nearby sensitive instruments or precisely ground surfaces
...
Also, brushes must be replaced periodically, causing unproductive downtime
...
Built as insideout DC motors, typical brushless motors have PM rotors and wound stator coils
...
The HEDs are
wired to power transistor switching circuitry, which is mounted externally
in separate modules for some motors but is mounted internally on circuit
cards in other motors
...
Brushless DC motors exhibit low rotor inertia and lower winding thermal resistance than brush-type motors because their high-efficiency magnets permit the use of shorter rotors with smaller diameters
...
Nevertheless, brushless motors still cost more than comparably rated
brush-type motors (although that price gap continues to narrow) and their
installation adds to overall motion control system cost and complexity
...
The linear motor, another drive alternative, can move the load
directly, eliminating the need for intermediate motion translation mechanism
...
Essentially rotary motors that have been sliced open and unrolled,
they have many of the characteristics of conventional motors
...
If increased performance is
17
18
Chapter 1
Motor and Motion Control Systems
Table 1-1 Stepping and Permanent-Magnet DC Servomotors
Compared
...
Linear motors must operate in closed feedback loops, and they typically require more costly feedback sensors than rotary motors
...
Moreover, their
applications are also limited because of their inability to dissipate heat as
readily as rotary motors with metal frames and cooling fins, and the
exposed magnetic fields of some models can attract loose ferrous
objects, creating a safety hazard
...
A drive circuit for a stepper
motor can be fairly simple because it needs only several power transistors to sequentially energize the motor phases according to the number
of digital step pulses received from the motion controller
...
Servodrive amplifiers for brush and brushless motors typically receive
analog voltages of ±10-VDC signals from the motion controller
...
When amplified, the
signals control both the direction and magnitude of the current in the
Chapter 1
Motor and Motion Control Systems
motor windings
...
Pulse-width modulated amplifiers predominate because they are more
efficient than linear amplifiers and can provide up to 100 W
...
When the power transistors are
switched on (on state), they saturate, but when they are off, no current is
drawn
...
Because of their higher operating frequencies, the magnetic components in PWM amplifiers can be smaller and
lighter than those in linear amplifiers
...
By contrast, the power transistors in linear amplifiers are continuously
in the on state although output power requirements can be varied
...
However, linear
amplifiers permit smoother motor operation, a requirement for some sensitive motion control systems
...
Moreover, these amplifiers generate less
EMI than PWM amplifiers, so they do not require the same degree of filtering
...
Feedback Sensors
Position feedback is the most common requirement in closed-loop
motion control systems, and the most popular sensor for providing this
information is the rotary optical encoder
...
They
generate either sine waves or pulses that can be counted by the motion
controller to determine the motor or load position and direction of travel
at any time to permit precise positioning
...
Absolute rotary optical encoders produce binary words for the
motion controller that provide precise position information
...
Linear optical encoders, by contrast, produce pulses that are proportional to the actual linear distance of load movement
...
Tachometers are generators that provide analog signals that are
directly proportional to motor shaft speed
...
After
tachometer output is converted to a digital format by the motion controller, a feedback signal is generated for the driver to keep motor speed
within preset limits
...
Less common are the more accurate laser interferometers
...
Installation and Operation of the System
The design and implementation of a cost-effective motion-control system require a high degree of expertise on the part of the person or persons responsible for system integration
...
Each servosystem (and
many stepper systems) must be tuned (stabilized) to the load and environmental conditions
...
Moreover, operators must be properly trained in
formal classes or, at the very least, must have a clear understanding of
the information in the manufacturers’ technical manuals gained by careful reading
...
These
include both conventional rotary and linear alternating current (AC) and
direct current (DC) motors
...
The most popular servomotors are permanent magnet (PM) rotary DC
servomotors that have been adapted from conventional PM DC motors
...
The brush-type PM DC servomotors include those with wound rotors
and those with lighter weight, lower inertia cup- and disk coil-type armatures
...
Some motion control systems are driven by two-part linear servomotors that move along tracks or ways
...
Linear
motors require closed loops for their operation, and provision must be
made to accommodate the back-and-forth movement of the attached data
and power cable
...
Increased position accuracy can be
obtained by enclosing the motors in control loops
...
While they share many of the characteristics of conventional rotary
series, shunt, and compound-wound brush-type DC motors, PM DC servomotors increased in popularity with the introduction of stronger
ceramic and rare-earth magnets made from such materials as
neodymium–iron–boron and the fact that these motors can be driven easily by microprocessor-based controllers
...
Because there are both brush-type and
brushless DC servomotors, the term DC motor implies that it is brushtype or requires mechanical commutation unless it is modified by the
term brushless
...
They are
lightweight, low-inertia armatures that permit the motors to accelerate
faster than the heavier conventional wound armatures
...
than earlier generation comparably rated DC motors with alnico (aluminum–nickel–cobalt or AlNiCo) magnets
...
Brush-Type PM DC Servomotors
The design feature that distinguishes the brush-type PM DC servomotor, as
shown in Figure 1-17, from other brush-type DC motors is the use of a permanent-magnet field to replace the wound field
...
Permanent-magnet DC motors, like all other mechanically commutated
DC motors, are energized through brushes and a multisegment commutator
...
These
linear characteristics conveniently describe the full range of motor perform-
Chapter 1
Motor and Motion Control Systems
23
Figure 1-18 A typical family of
speed/torque curves for a permanent-magnet DC servomotor at
different voltage inputs, with
voltage increasing from left to
right (V1 to V5)
...
It can be seen that both speed and torque increase linearly with
applied voltage, indicated in the diagram as increasing from V1 to V5
...
When the motor is powered, the opposite polarities of the energized
windings and the stator magnets attract, and the rotor rotates to align
itself with the stator
...
This sequence continues as long as power is applied, keeping the rotor in
continuous motion
...
If the connections of a PM DC motor are reversed, the motor
will change direction, but it might not operate as efficiently in the
reversed direction
...
This nonferrous
laminated disk is made as a copper stamping bonded between
epoxy–glass insulated layers and fastened to an axial shaft
...
bell, which completes the magnetic circuit
...
These motors are also called pancake motors because they are housed
in cases with thin, flat form factors whose diameters exceed their
lengths, suggesting pancakes
...
The flat
motor case concentrates the motor’s center of mass close to the mounting
plate, permitting it to be easily surface mounted
...
Their disk-type motor form
factor has made these motors popular as axis drivers for industrial robots
where space is limited
...
Consequently, these motors are usually limited to applications where the motor can be run under controlled
conditions and a shorter duty cycle allows enough time for armature heat
buildup to be dissipated
...
servo applications
...
A cutaway view
of this class of servomotor is illustrated in Figure1-20
...
This permits the motor to accelerate rapidly for the quick response required in
many motion-control applications
...
The magnetic field from the stationary magnets is completed through the cup-type armature and a stationary ferrous cylindrical core connected to the motor frame
...
Springbrushes commutate these motors
...
The cup type armature is rigidly fastened to the
shaft by a disk at the right end of the winding, and the magnetic field is
also returned through a ferrous metal housing
...
The principal disadvantage of this motor is also the inability of its
bonded armature to dissipate internal heat buildup rapidly because of its
low thermal conductivity
...
26
Chapter 1
Motor and Motion Control Systems
Figure 1-21 Exploded view of
a fractional horsepower brushtype DC servomotor
...
The construction of these motors, as shown in Figure 1-22, differs from that of a typical brush-type DC motor in that they are
“inside-out
...
Although this
geometry is required for brushless DC motors, some manufacturers have
adapted this design for brush-type DC motors
...
They are located within the stator windings and wired to solidstate transistor switching circuitry located either on circuit cards
mounted within the motor housings or in external packages
...
The cylindrical magnet rotors of brushless DC motors are magnetized
laterally to form opposing north and south poles across the rotor’s diameter
...
These materials permit motors offering
higher performance to be packaged in the same frame sizes as earlier
motor designs or those with the same ratings to be packaged in smaller
frames than the earlier designs
...
rotors can be made with smaller diameters than those earlier models with
alnico magnets, thus reducing their inertia
...
The HED is a Hall-effect sensor integrated with an ampli-
Figure 1-23 Simplified diagram
of Hall-effect device (HED) commutation of a brushless DC
motor
...
fier in a silicon chip
...
This is accomplished as follows:
1
...
This causes current to flow, energizing winding W2 to form a southseeking electromagnetic rotor pole
...
2
...
It then
switches on transistor T1, causing current to flow in winding W1,
thus forming a north-seeking stator pole that attracts the rotor’s
south pole, causing it to continue to rotate in the CCW direction
...
The
windings are energized in a pattern that rotates around the stator
...
They send the
signals to the motion controller that actually triggers the power transistors, which drive the armature windings at a specified motor current and
voltage level
...
The stator is formed as an ironless sleeve of copper coils
bonded together in polymer resin and fiberglass to form a rigid structure
similar to cup-type rotors
...
This method of construction permits a range of values for starting current and specific speed (rpm/V) depending on wire gauge and the number of turns
...
The Halleffect sensors and a small magnet disk that is magnetized widthwise are
mounted on a disk-shaped partition within the motor housing
...
The diagram in Figure 1-25 shows how three magnetic sensors can sense rotor position in a three-phase electronically commutated
brushless DC motor
...
This inexpensive version is adequate for
simple controls
...
The high-resolution signals from the resolver can
Figure 1-25 A magnetic sensor
as a rotor position indicator: stationary brushless motor winding
(1), permanent-magnet motor
rotor (2), three-phase electronically commutated field (3), three
magnetic sensors (4), and the
electronic circuit board (5)
...
be used to generate sinusoidal motor currents within the motor controller
...
Brushless Motor Advantages
Brushless DC motors have at least four distinct advantages over brushtype DC motors that are attributable to the replacement of mechanical
commutation by electronic commutation
...
• Without brushes to cause electrical arcing, brushless motors do not
present fire or explosion hazards in an environment where flammable
or explosive vapors, dust, or liquids are present
...
• Brushless motors can run faster and more efficiently with electronic
commutation
...
the
upper limit of about 5000 rpm for brush-type DC motors
...
• Brushless PM DC servomotors cannot be reversed by simply reversing the polarity of the power source
...
• Brushless DC servomotors cost more than comparably rated brushtype DC servomotors
...
• The motion controller and driver electronics needed to operate a
brushless DC servomotor are more complex and expensive than those
required for a conventional DC servomotor
...
Characteristics of Brushless Rotary Servomotors
It is difficult to generalize about the characteristics of DC rotary servomotors because of the wide range of products available commercially
...
62 lb-ft
(0
...
0 lb-ft (6
...
9 lb-ft (2
...
73 hp
(0
...
76 hp (2
...
Maximum speeds can vary from 1400
to 7500 rpm, and the weight of these motors can be from 5
...
3 kg)
to 23 lb (10 kg)
...
Linear Servomotors
A linear motor is essentially a rotary motor that has been opened out into
a flat plane, but it operates on the same principles
...
The same electromagnetic force that produces torque in a rotary motor
also produces torque in a linear motor
...
31
32
Chapter 1
Motor and Motion Control Systems
Figure 1-27 Operating principles of a linear servomotor
...
A linear motor consists of two mechanical assemblies: coil and magnet, as shown in Figure 1-27
...
The copper windings conduct current (I ), and
the assembly generates magnetic flux density (B)
...
Even a small motor will run efficiently, and large forces can be created
if a large number of turns are wound in the coil and the magnets are powerful rare-earth magnets
...
Only brushless linear motors for closed-loop servomotor applications
are discussed here
...
Each of these linear servomotors has characteristics and features that are optimal in different applications
The coils of steel-core motors are wound on silicon steel to maximize
the generated force available with a single-sided magnet assembly or
way
...
The steel in
these motors focuses the magnetic flux to produce very high force density
...
e
...
The steel in the cores is attracted to the permanent magnets in a direction that is perpendicular (normal) to the operating motor force
...
A constant magnetic force is present whether or not
the motor is energized
...
This flux rapidly diminishes to a few gauss as the measuring point is moved a few
centimeters away from the magnets
...
Because it can occur in steel-core
motors, manufacturers include features that minimize cogging
...
The features of epoxy-core or ironless-core motors differ from those
of the steel-core motors
...
Because the coil assemblies
do not contain steel cores, epoxy-core motors are lighter than steel-core
motors and less subject to cogging
...
This design maximizes the generated thrust force
and also provides a flux return path for the magnetic circuit
...
sequently, very little magnetic flux exists outside the motor, thus minimizing residual magnetic attraction
...
They also permit constant velocity to be
maintained, even at very low speeds
...
1 µm
...
Velocities are limited by the encoder data rate and the amplifier voltage
...
04 in
...
6 ft/s (2 m/s), but the
velocity of some models can exceed 26 ft/s (8 m/s)
...
By contrast, iron-core linear motors are available with
continuous force ratings of about 30 to 1100 lbf (130 to 4900 N) and
peak force ratings of about 60 to 1800 lbf (270 to 8000 N)
...
There are two ways to
commutate linear motors: sinusoidal and Hall-effect device (HED), or
trapezoidal
...
Chapter 1
Motor and Motion Control Systems
In sinusoidal commutation, the linear encoder that provides position
feedback in the servosystem is also used to commutate the motor
...
This produces extremely smooth motion
...
The HED sensors detect the polarity change in the magnet track and
switch the motor phases every 60º
...
As a result, the motors produce a constant force output when the
driving voltage on each phase matches the characteristic back EMF
waveform
...
These motors can be mounted
vertically, but if they are they typically require a counterbalance system
to prevent the load from dropping if power temporarily fails or is routinely shut off
...
If power is lost, servo control is interrupted
...
The stopping time
and distance depend on the stage’s initial velocity and system friction
...
However, positive stops and
travel limits can be built into the motion stage to prevent damage in situations where power or feedback might be lost or the controller or servo
driver fail
...
The host machine structure must include
bearings capable of supporting the mass of the motor parts while maintaining the specified air gap between the assemblies and also resisting
the normal force of any residual magnetic attraction
...
Feedback is typically supplied by such sensors as linear encoders, laser
interferometers, LVDTs, or linear Inductosyns
...
Rotary Servomotors
The advantages of linear servomotors over rotary servomotors include:
• High stiffness: The linear motor is connected directly to the moving
load, so there is no backlash and practically no compliance between
the motor and the load
...
• Mechanical simplicity: The coil assembly is the only moving part of
the motor, and its magnet assembly is rigidly mounted to a stationary
structure on the host machine
...
This
permits the user to form a track of any desired length by stacking the
modules end to end, allowing virtually unlimited travel
...
The only
alignments required are for the air gaps, which typically are from
0
...
(1 mm) to 0
...
(0
...
• High accelerations and velocities: Because there is no physical contact between the coil and magnet assemblies, high accelerations and
velocities are possible
...
• High velocities: Velocities are limited by feedback encoder data rate
and amplifier bus voltage
...
6 ft/s (2
m/s), although some models can reach 26 ft/s (8 m/s)
...
/s (0
...
7 m/s) because of resonances
and wear
...
• No backlash or wear: With no contact between moving parts, linear
motors do not wear out
...
• System size reduction: With the coil assembly attached to the load,
no additional space is required
...
• Clean room compatibility: Linear motors can be used in clean rooms
because they do not need lubrication and do not produce carbon
brush grit
...
Some rotary motors also have radiating fins on
their frames that serve as heatsinks to augment the heat dissipation capability of the frames
...
For example, an aluminum
attachment bar placed in close contact with the windings can aid in heat
dissipation
...
Stepper Motors
A stepper or stepping motor is an AC motor whose shaft is indexed
through part of a revolution or step angle for each DC pulse sent to it
...
The position
of the load can be determined with reasonable accuracy by counting the
pulses entered
...
Unlike PM DC servomotors with mechanical brush-type commutators, stepper motors depend on external
controllers to provide the switching pulses for commutation
...
Pulses from the external motor controller determine the amplitude and
direction of current flow in the stator’s field windings, and they can turn
the motor’s rotor either clockwise or counterclockwise, stop and start it
quickly, and hold it securely at desired positions
...
Because controllers can step
most motors at audio frequencies, their rotors can turn rapidly
...
These motors generate
very little heat while at rest, making them suitable for many different
instrument drive-motor applications in which power is limited
...
The same controller circuit can drive both
hybrid and PM stepping motors
...
These motors usually have two independent windings, with or without center taps
...
8º per
step as well as 7
...
Armature rotation occurs when the stator poles are alternately energized
and deenergized to create torque
...
Permanent-magnet steppers step at relatively low rates, but they can
produce high torques and they offer very good damping characteristics
...
At rest these magnets align
themselves in a natural detent position to provide larger holding torque
than can be obtained with a comparably rated PM stepper
...
The 30º angle is obtained with
a 4-tooth rotor and a 6-pole stator, and the 15º angle is achieved with an
8-tooth rotor and a 12-pole stator
...
To obtain continuous rotation, power must be applied to
the windings in a coordinated sequence of alternately deenergizing and
energizing the poles
...
At that
point, the rotor will turn, but it will still try to hold its new position at
each successive equilibrium point
...
A cutaway view of a typical industrial-grade hybrid stepper
Chapter 1
Motor and Motion Control Systems
39
Figure 1-30 Cutaway view of a
5-phase hybrid stepping motor
...
5°
...
The armature is built in two sections, with the teeth in the second section offset
from those in the first section
...
Hybrid stepper motors can
achieve high stepping rates, and they offer high detent torque and excellent dynamic and static torque
...
A cross-sectional view of a hybrid stepper motor illustrating the multitoothed poles with dual windings per pole and the multitoothed rotor is illustrated in Figure 1-31
...
The most popular hybrid steppers have 3- and 5-phase wiring, and
step angles of 1
...
6º per step
...
Some 5-phase motors have high resolutions of 0
...
With a compatible controller, most PM and
hybrid motors can be run in half-steps, and some controllers are designed
to provide smaller fractional steps, or microsteps
...
This range is achieved by scaling length and diameter dimensions
...
Hybrid stepper motors are available in NEMA size 17 to 42 frames, and
output power can be as high as 1000 W peak
...
For example, the ability of the stepper
motor to repeat the positioning of its multitoothed rotor depends on its
geometry
...
Stepper motors can perform precise positioning in
simple open-loop control systems if they operate at low acceleration
rates with static loads
...
Chapter 1
Motor and Motion Control Systems
41
DC and AC Motor Linear Actuators
Actuators for motion control systems are available in many different forms,
including both linear and rotary versions
...
It
consists of an AC or DC motor mounted parallel to either a ballscrew
or Acme screw assembly through a reduction gear assembly with a slip
clutch and integral brake assembly
...
One version designed for mobile applications can be powered by a 12, 24-, or 36-VDC permanent-magnet motor
...
Other linear actuators are designed for use in fixed locations where
either 120- or 220-VAC line power is available
...
Those with 120-VAC motors can be equipped with
optional electric brakes that virtually eliminate coasting, thus permitting
point-to-point travel along the stroke
...
Closed-loop feedback provides speed regulation down to one tenth of the maximum travel rate
...
Figure 1-32 This linear actuator
can be powered by either an AC
or DC motor
...
Courtesy of
Thomson Saginaw
...
With Hall-effect sensing, six
pulses are generated with each turn of the output shaft during which the
stroke travels approximately 1⁄32 in
...
033 in
...
84 mm)
...
The actuator can be stopped
at any 0
...
increment of travel along the stroke selected by programming
...
If a 10-turn, 10,000-ohm potentiometer is used as a sensor, it can be
driven by the output shaft through a spur gear
...
A separate control unit measures the resistance (or
voltage) across the potentiometer, which varies continuously and linearly with stroke travel
...
Stepper-Motor Based Linear Actuators
Linear actuators are available with axial integral threaded shafts and bolt
nuts that convert rotary motion to linear motion
...
Digital pulses fed to the actuator
cause the threaded shaft to rotate, advancing or retracting it so that a load
coupled to the shaft can be moved backward or forward
...
Chapter 1
Motor and Motion Control Systems
olution as fine as 0
...
per pulse
...
The maximum linear
force for the model shown is 75 oz
...
Common feedback sensors are encoders, resolvers, and linear
variable differential transformers (LVDTs) for motion and position feedback, and tachometers for velocity feedback
...
Generally speaking, the closer the feedback sensor
is to the variable being controlled, the more accurate it will be in assisting the system to correct velocity and position errors
...
Thus, direct position
measurement avoids drivetrain errors caused by backlash, hysteresis, and
leadscrew wear that can adversely affect indirect measurement
...
They provide rate and positioning information in servo feedback loops
...
The number is called points per revolution and is analogous to the steps per revolution of a stepper motor
...
Rotary encoders can measure
the motor-shaft or leadscrew angle to report position indirectly, but they
can also measure the response of rotating machines directly
...
There are also
direct contact or brush-type and magnetic rotary encoders, but they are
not as widely used in motion control systems
...
Standard rotary encoders are packaged in cylindrical cases with diameters from 1
...
5 in
...
A variation of the conventional configuration, the hollow-shaft encoder, eliminates problems associated with the installation and shaft runout of conventional models
...
04 to 1
...
(1 to 40 mm)
...
A glass or plastic code disk mounted on the encoder shaft
rotates between an internal light source, typically a light-emitting diode
(LED), on one side and a mask and matching photodetector assembly on
the other side
...
The electronic signals that are generated by the
encoder’s electronics board are fed into a motion controller that calculates position and velocity information for feedback purposes
...
Glass code disks containing finer graduations capable of 11- to more
than 16-bit resolution are used in high-resolution encoders, and plastic
(Mylar) disks capable of 8- to 10-bit resolution are used in the more
rugged encoders that are subject to shock and vibration
...
Chapter 1
The quadrature encoder is the most common
type of incremental encoder
...
The output signals
from the assembly are converted into two channels of square pulses (A and B) as shown in
Figure 1-36
...
If, for example, the pulses in channel
A lead those in channel B, the disk is rotating
in a clockwise direction, but if the pulses in
channel A lag those in channel B lead, the disk
is rotating counterclockwise
...
Many incremental quadrature encoders also
include a third output Z channel to obtain a
zero reference or index signal that occurs once
per revolution
...
The signal can also be used to align the encoder
shaft to a mechanical reference
...
Figure 1-36 Channels A and B
provide bidirectional position
sensing
...
Channel Z provides a zero reference for determining the number
of disk rotations
...
The code
disk provides a binary output that uniquely defines each shaft angle, thus
providing an absolute measurement
...
The arc lengths of the opaque and transparent sectors decrease with
respect to the radial distance from the shaft
...
Shaft
position accuracy is proportional to the number of annular rings or tracks
on the disk
...
The electronics board converts that output into a binary word
...
The principal reason for selecting an absolute encoder over an incremental encoder is that its code disk retains the last angular position of the
encoder shaft whenever it stops moving, whether the system is shut
down deliberately or as a result of power failure
...
Figure 1-37 Binary-code disk for
an absolute optical rotary
encoder
...
This four-bit binary-code
disk can count from 1 to 15
...
Figure 1-38 illustrates the basic parts of an optical linear
encoder
...
The scale, typically made as a strip of glass with opaque graduations, is bonded to a
supporting structure on the host machine
...
When the scanning unit moves, the scale modulates the light
beam so that the photocells generate sinusoidal signals
...
The encoder combines the phase-shifted signal to produce two symmetrical sinusoidal outputs that are phase shifted by 90º
...
A fine-scale pitch provides high resolution
...
The complete scanning unit is mounted on a carriage that moves on ball bearings
along the glass scale
...
48
Chapter 1
Motor and Motion Control Systems
slide by a coupling that compensates for any alignment errors between
the scale and the machine guideways
...
The practical maximum length
of linear encoder scales is about 10 ft (3 m), but commercial catalog
models are typically limited to about 6 ft (2 m)
...
Linear encoders can make direct measurements that overcome the
inaccuracies inherent in mechanical stages due to backlash, hysteresis,
and leadscrew error
...
Commercial linear encoders are available as standard catalog models,
or they can be custom made for specific applications or extreme environmental conditions
...
to 6 ft (50 mm to 1
...
Some
commercial models are available with resolutions down to 0
...
7 ft/s (5 m/s)
...
Figure 1-39
shows a magnet mounted on a motor shaft in close proximity to a twochannel HED array which detects changes in magnetic flux density as
the magnet rotates
...
The encoder output, either a square wave or a
Figure 1-39 Basic parts of a
magnetic encoder
...
The phase shift between channels A and B permits them to be
compared by the motion controller to determine the direction of motor
shaft rotation
...
Resolvers
resemble small AC motors, as shown in Figure 1-40, and generate an
electrical signal for each revolution of their shaft
...
The stator
is made by winding copper wire in a stack of iron laminations fastened to
the housing, and the rotor is made by winding copper wire in a stack of
laminations mounted on the resolver’s shaft
...
The coil
on the rotor couples speed data
inductively to the frame for
processing
...
Figure 1-41 is an electrical schematic for a brushless resolver showing
the single rotor winding and the two stator windings 90º apart
...
When a rotor winding is excited by an AC reference signal, it
produces an AC voltage output that varies in amplitude according to the
sine and cosine of shaft position
...
The absolute position
of the load being driven can be determined by the ratio of the sine output
amplitude to the cosine output amplitude as the resolver shaft turns
through one revolution
...
)
Connections to the rotor of some resolvers can be made by brushes
and slip rings, but resolvers for motion control applications are typically
brushless
...
Because brushless resolvers have no slip rings or
brushes, they are more rugged than encoders and have operating lives
that are up to ten times those of brush-type resolvers
...
The absence of brushes in these
resolvers makes them insensitive to vibration and contaminants
...
8 to 3
...
Rotor shafts are
typically threaded and splined
...
The magnitude of the voltage induced in any stator
winding is proportional to the cosine of the angle, q, between the rotor
coil axis and the stator coil axis
...
Accuracies of ±1 arc-minute can be achieved
...
Tachometers
A tachometer is a DC generator that can provide velocity feedback for a
servosystem
...
In a typical servosystem application, it is mechanically coupled to the DC motor and
feeds its output voltage back to the controller and amplifier to control
drive motor and load speed
...
Encoders or resolvers are part of separate loops that provide
position feedback
...
This emf is directly proportional to the rate at which
Figure 1-42 Section view of a
resolver and tachometer in the
same frame as the servomotor
...
Figure 1-44 This coil-type DC
motor obtains velocity feedback
from a tachometer whose rotor
coil is mounted on a common
shaft and position feedback from
a two-channel photoelectric
encoder whose code disk is also
mounted on the same shaft
...
The direction of the emf is
determined by Fleming’s generator rule
...
There are two basic types of DC tachometer: shunt wound and permanent magnet (PM), but PM tachometers are more widely used in servosystems today
...
The armature windings are
wound from fine copper wire and bonded with glass fibers and polyester
resins into a rigid cup, which is bonded to its coaxial shaft
...
As a result, the moving-coil tachometer is more responsive to speed changes and provides a
DC output with very low ripple amplitudes
...
They can be
rigidly mounted to the servomotor housings, and their shafts can be
mechanically coupled to the servomotor’s shafts
...
A brush-type DC motor with feedback furnished by a brush-type
tachometer is shown in Figure 1-43
...
This arrangement provides a high
resonance frequency
...
In applications where precise positioning is required in addition to
speed regulation, an incremental encoder can be added on the same
shaft, as shown in Figure 1-44
...
LVDTs are capable
of measuring position, acceleration, force, or pressure, depending on
how they are installed
...
54
Chapter 1
Motor and Motion Control Systems
Figure 1-46 Schematic for a linear variable differential transformer (LVDT) showing how the
movable core interacts with the
primary and secondary windings
...
The core is attached to a spring-loaded sensing shaft
...
Figure 1-46 is a schematic diagram of an LVDT
...
With a series-opposed connection,
as shown, the net voltage across the secondaries is zero because both
voltages cancel
...
However, if the core is moved to the left, secondary winding S1 is
more strongly coupled to primary winding P1 than secondary winding
S2, and an output sine wave in phase with the primary voltage is
induced
...
The amplitudes
of the output sine waves of the LVDT vary symmetrically with core displacement, either to the left or right of the null position
...
The amplitude of the resulting DC voltage output is proportional to the
magnitude of core displacement, either to the left or right of the null
position
...
An LVDT containing an integral oscillator/demodulator is a DC-to-DC LVDT, also known as a DCDT
...
005 in
...
127 mm)
...
Linearity is the
characteristic that largely determines the LVDT’s absolute accuracy
...
When the magnet is moved through the
coils, it induces a voltage within the coils in accordance with the Faraday
and Lenz laws
...
When the magnet is functioning as a transducer, both of its ends are
within the two adjacent coils, and when it is moved axially, its north pole
will induce a voltage in one coil and its south pole will induce a voltage
in the other coil
...
In both configurations the DC output voltage from the coils is proportional to magnet velocity
...
)
The characteristics of the LVT depend on how the two coils are connected
...
Also, noise generated in one coil will
be canceled by the noise generated in the other coil
...
Reduced sensitivity improves high-frequency response for
measuring high velocities, and the lower output impedance improves the
LVT’s compatibility with its signal-conditioning electronics
...
As shown in exploded
view Figure 1-47 it has a movable metal rotor sandwiched between a
single stator plate and segmented stator plates
...
The angular displacement of the rotor can then be determined accurately from the
demodulated AC signal
...
The base is the mounting platform for the transducer assembly
...
The base also supports the transmitting board, which contains a
metal surface that forms the lower plate of the differential capacitor
...
Positioned above the rotor is the receiving board
containing two separate semicircular metal sectors on its lower surface
...
An electronics circuit board mounted on top of the assembly contains
the oscillator, demodulator, and filtering circuitry
...
The cup-shaped housing encloses the entire assembly, and
the base forms a secure cap
...
The receiving plates
are at virtual ground, and the rotor is at true ground
...
A null point is obtained when the rotor is positioned under equal areas
of the receiving stator plates
...
However, as the rotor moves clockwise or counterclockwise, the capacitance between the transmitting plate
and one of the receiving plates will be greater than it is between the other
receiving plate
...
Inductosyns
The Inductosyn is a proprietary AC sensor that generates position feedback signals that are similar to those from a resolver
...
Much smaller than a resolver, a rotary
Inductosyn is an assembly of a scale and slider on insulating substrates
in a loop
...
An Inductosyn-to-digital (I/D) converter, similar to a resolver-todigital (R/D) converter, is needed to convert these signals into a digital
format
...
This corresponds to an angular rotation of less than 0
...
This angular information in a digital format is sent to the motion controller
...
They offer very high resolution (to 1
...
02
ppm
...
The laser
beam path can be precisely aligned to coincide with the load or a specific
point being measured, eliminating or greatly reducing Abbe error
...
It consists of a helium–neon laser, a polarizing
beam splitter with a stationary retroreflector, a moving retroreflector that
57
58
Chapter 1
Motor and Motion Control Systems
Figure 1-48 Diagram of a laser
interferometer for position feedback that combines high resolution with noncontact sensing,
high update rates, and accuracies
of 0
...
can be mounted on the object whose position is to be measured, and a
photodetector, typically a photodiode
...
Part of the laser beam goes
straight through the polarizing beam splitter, and part of the laser beam is
reflected
...
The part of the beam that is reflected by
the beam splitter reaches the stationary retroreflector, a fixed distance
away
...
As a result, the two reflected laser beams strike the photodetector,
which converts the combination of the two light beams into an electrical
signal
...
Because both light beams travel the same distance from the laser
to the beam splitter and from the beam splitter to the photodetector, these
distances are not involved in position measurement
...
If these two distances are exactly the same, the two light beams will
recombine in phase at the photodetector, which will produce a high electrical output
...
However, if the difference between the distances is as short
as one-quarter of the laser’s wavelength, the light beams will combine
out-of-phase, interfering with each other so that there will be no electrical output from the photodetector and no video output on the display, a
condition called a dark fringe
...
This will result in
electrical signals that can be counted and converted to a distance measurement to provide an accurate position of the load
...
For example, the
wavelength of the light beam emitted by a helium–neon (He–Ne) laser,
widely used in laser interferometers, is 0
...
000025 in
...
However, that accuracy can be degraded by changes in humidity and temperature as well as
airborne contaminants such as smoke or dust in the air between the beam
splitter and the moving retroreflector
...
Originally developed for use in analog computers, precision potentiometers can provide
absolute position data in analog form as a resistance value or voltage
...
If a potentiometer is used in a servosystem, the analog data
Figure 1-49 A precision potentiometer is a low-cost, reliable
feedback sensor for servosystems
...
Accuracies of 0
...
005º if the output signal is converted with a 16-bit ADC
...
Hybrid elements are wirewound elements coated with
resistive plastic to improve their resolution
...
During its service life wear on the resistive element caused by
the wiper can degrade the precision of the precision potentiometer
...
All solenoids include a coil for
conducting current and generating a magnetic field, an iron or steel shell
or case to complete the magnetic circuit, and a plunger or armature for
translating motion
...
Solenoids are built with conductive paths that transmit maximum
magnetic flux density with minimum electrical energy input
...
Linear solenoid plungers are either spring-loaded or use external methods to restrain axial movement caused by the magnetic flux when the
coil is energized and restore it to its initial position when the current is
switched off
...
When the coil is energized,
the plunger pulls in against the spring, and this motion can be translated
into either a “pull-in” or a “push-out” response
...
For example,
the plunger extension on the left end (end A) provides “push-out” motion
against the load, while a plunger extension on the right end terminated
by a clevis (end B) provides “pull-in” motion
...
Figure 1-51 is a cross-sectional
view of a typical pull-in commercial linear solenoid
...
End A of the plunger
pushes out when the solenoid is
energized while the clevis-end B
pulls in
...
One of these is the use of
internal lands or ball bearings and slots or races that convert a pull-in
stroke to rotary or twisting motion
...
When there are requirements for linear or rotary motion, solenoids
should be considered because of their relatively small size and low cost
when compared with alternatives such as motors or actuators
...
Figure 1-51 Cross-section view
of a commercial linear pull-type
solenoid with a clevis
...
The solenoid is
mounted with its threaded
bushing and nut
...
The solenoid must
have a magnetic return path capable of transmitting the maximum
amount of magnetic flux density with minimum energy input
...
A ferrous metal path is
more efficient than air, but the air gap is needed to permit plunger or
armature movement
...
By optimizing
the ferrous path area, the shape of the plunger or armature, and the magnetic circuit material, the output torque/force can be increased
...
In most applications the force can be a minimum at the start of the
plunger or armature stroke but must increase at a rapid rate to reach the
maximum value before the plunger or armature reaches the backstop
...
The pull force required by the load must
not be greater than the force developed by the solenoid during any portion of its required stroke, or the plunger or armature will not pull in
completely
...
Heat buildup in a solenoid is a function of power and the length of
time the power is applied
...
If constant voltage is applied, heat
buildup can degrade the efficiency of the coil by effectively reducing its
number of ampere turns
...
If the temperature of the coil is permitted to rise
above the temperature rating of its insulation, performance will suffer
and the solenoid could fail prematurely
...
Heat can be dissipated by cooling the solenoid with forced air from a
fan or blower, mounting the solenoid on a heat sink, or circulating a liquid coolant through a heat sink
...
The heating of the solenoid is affected by the duty cycle, which is
specified from 10 to 100%, and is directly proportional to solenoid on
time
...
Duty cycle is defined as the ratio of on time to
Chapter 1
Motor and Motion Control Systems
the sum of on time and off time
...
The amount of work performed by a solenoid is directly related to its
size
...
Open-Frame Solenoids
Open-frame solenoids are the simplest and least expensive models
...
Their simple design permits them to be made inexpensively in
high-volume production runs so that they can be sold at low cost
...
They are usually specified for applications where very
long life and precise positioning are not critical requirements
...
The frames are typically laminated steel formed in the
shape of the letter C to complete the magnetic circuit through the core,
but they leave the coil windings without a complete protective cover
...
However, the coils
are usually potted to resist airborne and liquid contaminants
...
They can be powered with either
AC or DC current
...
5 in
...
Box-Frame Solenoids
Box-frame solenoids have steel frames that enclose their coils on two
sides, improving their mechanical strength
...
The frames of some box-type solenoids are made from stacks of thin
insulated sheets of steel to control eddy currents as well as keep stray circulating currents confined in solenoids powered by AC
...
Standard catalog commercial box-frame solenoids can
be powered by AC or DC current, and can have strokes that exceed 0
...
(13 mm)
...
These DC
solenoids offer the highest volumetric efficiency of any commercial solenoids, and they are specified for industrial and military/aerospace equipment where the space permitted for their installation is restricted
...
Some commercial tubular linear solenoids in this class have strokes up to
1
...
(38 mm), and some can provide 30 lbf (14 kgf) from a unit less
than 2
...
Linear solenoids find applications in vending
machines, photocopy machines, door locks, pumps, coin-changing
mechanisms, and film processors
...
Rotary actuators
should be considered if controlled speed is a requirement in a rotary
stroke application
...
It includes an armature-plate assembly that rotates
when it is pulled into the housing by magnetic flux from the coil
...
The three ball bearings travel to the
lower ends of the races in which they are positioned
...
The
rotary solenoid armature is supported by three ball bearings that travel
around and down the three inclined ball races
...
When power is applied, a linear electromagnetic force pulls
in the armature and twists the armature plate, as shown in (b)
...
continues until the balls have traveled to the deep ends of the races, completing the conversion of linear to rotary motion
...
The steel housing provides the
high permeability path and low residual flux needed for the efficient conversion of electrical energy to mechanical motion
...
(115 kgf-cm) of
torque from a unit less than 2
...
(57 mm) long
...
When energized, the solenoid armature pulls
in, causing the three ball bearings
to roll into the deeper ends of the
lateral slots on the faceplate,
translating linear to rotary
motion
...
Rotary Actuators
The rotary actuator shown in Figure 1-54 operates on the principle of
attraction and repulsion of opposite and like magnetic poles as a motor
...
The patented Ultimag rotary actuator from the Ledex product group
of TRW, Vandalia, Ohio, was developed to meet the need for a bidirectional actuator with a limited working stroke of less than 360º but capable of offering higher speed and torque than a rotary solenoid
...
When the actuator is not energized, as shown in (a), the armature
poles each share half of a stator pole, causing the shaft to seek and hold
mid-stroke
...
The resulting flux interaction attracts half of the armature’s PM poles
while repelling the other half
...
Figure 1-54 This bidirectional
rotary actuator has a permanent
magnet disk mounted on its
armature that interacts with the
solenoid poles
...
If the
input voltage is reversed, armature rotation is reversed (c)
...
Consequently,
the opposite poles of the actuator armature are attracted and repelled,
causing the armature to reverse its direction of rotation
...
Typical actuators
offer a 45º stroke, but the design permits a maximum stroke of 160º
...
Gears, belts, and pulleys can amplify the stroke, but this results in reducing actuator torque
...
This is not always the
best approach
...
This is especially true
with mobile robots, whose interactions between sensors and actuators
must be carefully integrated, first one set at a time, then in the whole
robot
...
Debugging
Debugging effort, the process of testing, discovering problems, and
working out fixes, is directly related to the number of actuators
...
Frequently the actuators have an affect on each
other or act together and this in itself adds to the debugging task
...
Debugging a robot happens in many stages, and is often an iterative
process
...
The pieces are assembled into
larger blocks of the robot and tests and debugging are done on those subassemblies, which may be just breadboard electronics with some control
software, or perhaps electronics controlling some test motors
...
This is when the number of actuators has a large affect on debug complexity and time
...
The relationship between
the sensors and actuators is much more complicated than just one sensor
connected through software to one actuator
...
The control software must
look at the inputs from the all sensors, make intelligent decisions based
on that information, and then send commands to one, or many of the
actuators
...
Mechanical bugs, electronic bugs, software bugs, and bugs caused by
interactions between those engineering disciplines will appear and solutions must be found for them
...
Reliability
For much the same reasons, reliability is also affected by actuator
count
...
Every moving part has a limited lifetime, and every piece of the robot
has a chance of being made incorrectly, assembled incorrectly, becoming loose from vibration, being damaged by something in the environment, etc
...
Cost
Cost should also be figured in when working on the initial phases of
design, though for some applications cost is less important
...
The designer or
design team should seriously consider having a slightly less capable platform or manipulator and leave out one or two actuators, for a significant
increase in reliability, greatly reduced debug time, and reduced cost
...
Click here for Terms of Use
...
A
s mentioned in Chapter One, electric motors suffer from a problem
that must be solved if they are to be used in robots
...
Stepper motors are the least
prone to this problem, but even they loose some system efficiency at very
low speeds
...
The solution to the torque problem is to
attach the motor to some system that changes the high speed/low torque
on the motor output shaft into the low speed/high torque required for
most applications in mobile robots
...
Some attach directly to the motor and essentially make it a bigger and heavier but more effective motor
...
Power transfer mechanisms are normally divided into five general categories:
1
...
3
...
5
...
This ability
is not usually required on a mobile robot, indeed it can cause control
problems in certain cases because the computer does not have direct control over the actual speed of the output shaft
...
These devices could all be called synchronous because they
keep the input and output shafts in synch, but roller chain is usually left
out of this category because the rollers allow some relative motion
between the chain and the sprocket
...
For power transfer methods that require attaching one shaft to another,
like motor-mounted gearboxes driving a separate output shaft, a method
to deal with misalignment and vibration should be incorporated
...
In some cases where shock
loads might be high, a method of protecting against overloading and
breaking the power transfer mechanism should be included
...
Let’s take a look at each method
...
Each section has a short discussion on how well that
method applies to mobile robots
...
They can be used at power levels from fractional horsepower to
tens of horsepower
...
They are durable, in most cases quiet, and handle some misalignment
...
Their web sites contain an
enormous amount of information about belts of all types
...
com
fennerprecision
...
com
gates
...
com
• mectrol
...
com
Flat Belts
Flat belts are an old design that has only limited use today
...
In the late 18th and early 19th centuries, it was used
extensively in just about every facility that required moving rotating power
from one place to another
...
Leather
flat belts suffered from relatively short life and moderate efficiency
...
They
require good alignment between the driveR and driveN pulleys and the
pulleys themselves are not actually flat, but slightly convex
...
They are
found in some vacuum cleaners because they are resistant to dirt buildup
...
They too suffer from moderate efficiency, but their cost
is so low that they are used in toys and low power devices like VCRs etc
...
V-Belts
V-belts get their name from the shape of a cross section of the belt, which
is similar to a V with the bottom chopped flat
...
This
increases the friction force because of the steep angle of the V and therefore increases the transmittable torque under the same tension as is
required for flat or O-ring belts
...
They are a good choice for
power levels from fractional to tens of horsepower
...
This slip means the computer has no precise control of the orientation of the output shaft,
unless a feedback device is on the driveN pulley
...
Figure 2-1 shows the cross sectional
shape of each belt
...
Figure 2-2 (from
Mechanisms and Mechanical Devices Sourcebook, as are many of the
figures in this book) shows how variable speed drives work
...
Figure 2-2
Variable Belt
Chapter 2
Indirect Power Transfer Devices
SMOOTHER DRIVE WITHOUT GEARS
The transmission in the motor scooter in Figure 2-3 is torque-sensitive;
motor speed controls the continuously variable drive ratio
...
Variable-diameter V-belt pulleys connect the motor and chain drive
sprocket to give a wide range of speed reduction
...
At idle speed the belt rides on a ballbearing
between the retracted flanges of the pulley
...
Upon initial engagement, the overall drive ratio is approximately 18:1
...
The resulting variations in belt tension are absorbed by the spring-loaded flanges of
the rear pulley
...
When the clutch
engages, the floating half of the front pulley moves inward, increasing its
effective diameter and pulling the belt down between the flanges of the
rear pulley
...
A sudden engine acceleration
increases the effective diameter of the rear pulley, lowering the drive ratio
...
The belt now slips slightly on its
driver
...
Figure 2-3
Smoother Drive Without Gears
75
76
Chapter 2
Indirect Power Transfer Devices
Timing Belts
Timing belts solve the slip problems of flat, O ring, and V belts by using
a flexible tooth, molded to a belt that has tension members built in
...
Timing belts are part of a larger category of
power transmission devices called synchronous drives
...
Synchronous or positive drive also means these belts
can even be used in wet conditions, provided the pulleys are stainless
steel or plastic to resist corrosion
...
The most common timing belt has a trapezoidal shaped tooth
...
As each tooth comes in contact with the mating teeth on a pulley, the tooth tends to be deflected by the cantilever
force, deforming the belt’s teeth so that only the base of the tooth
remains in contact
...
The deformation also increases wear of the tooth material and causes the timing
belt drive to be somewhat noisy
...
A trade name for this shape
is HTD for High Torque Design
...
They are an
excellent method of power transfer, but for a slightly higher price than
chain or plastic-and-cable chain discussed later in this chapter
...
It is
actually the reverse of belt construction where the steel or synthetic cable
is molded into the rubber or plastic belt
...
The result appears almost like a roller chain
...
It is made in
three basic forms
...
Figure 2-7 shows a single cable form where the plastic teeth protrude out
of both sides of the cable, or even 4 sides of the cable
...
Figure 2-7 Plastic pins eliminate
the bead chain's tendency to cam
out of pulley recesses, and permit
greater precision in angular
transmission
...
shown in Figure 2-8
...
It is a
double cable form and is the kind that looks like a roller chain, except the
rollers are replaced with non-rolling plastic cross pieces
...
Another form of the cable-based drive wraps a spiral of plastic coated
steel cable around the base cable
...
This type can bend in any direction, allowing
it to be used to change drive planes
...
CHAIN
Chain comes in three basic types
...
Its
construction is extremely simple and inexpensive
...
See Figure
2-9
...
Roller Chain
Roller chain is an efficient power transfer method
...
Roller
chain is robust and can handle some misalignment between the driveR
and driveN gears, and in many applications does not require precise pretensioning of the pulleys
...
1
...
2
...
Roller chain can be used for single stage reductions of up to 6:1 with
careful attention to pulley spacing, making it a simple way to get an efficient, high reduction system
...
The most
common size chain, #40 (the distance from one roller to the next is
...
Even the smallest size, #25, can transmit more than 5 horsepower at
3000 rpm with adequate forced lubrication and sufficiently large pulleys
...
org
bostongear
...
com
ramseychain
...
com
As shown in Figure 2-10 (a–d), roller chain comes in many sizes and
styles, some of which are useful for things other than simply transferring
power from one pulley to another
...
Figure 2-10b Extended pitch
chain—for conveying
Figure 2-10c
adaptations
Standard pitch
82
Chapter 2
Figure 2-10d
adaptations
Indirect Power Transfer Devices
Extended pitch
Figure 2-11 Bent lug roller
chain used for rack and pinion
linear actuator
...
These lugs can be bolted directly to pads and
used for tracks on tracked vehicles, simplifying this sometimes complicated part of a high-mobility robot
...
This is why tracks
on excavators and military tanks are specially designed with the pivot
point as close to the ground as possible
...
Rack and Pinion Chain Drive
Bent lug roller chain can also be used as a low cost rack and pinion drive
to get linear motion from rotary motion
...
Figure 2-11 shows a basic layout for this concept
...
It is also more efficient than roller chain because the
clever shape of its inverted teeth provide smooth transfer of power from
Chapter 2
Indirect Power Transfer Devices
83
Figure 2-12 Silent chain tooth
profile
the chain to the pulley
...
It is a very good choice for transmitting high horsepower at thousands
of rpm from an electric motor or an internal combustion engine to the
transmission of large vehicles
...
It is not made in small sizes
because of the special shape of its teeth (Figure 2-12) and is designed
mainly for power ranges from tens to hundreds of horsepower
...
If high efficiency and high power are
required with operation in a clean environment, and the higher price can
be afforded, silent chain is the best choice of any power transfer device in
this book
...
This technique is usually
reserved for special cases, where its short life is acceptable
...
The usual layout
for a variable speed friction drive is a hardened steel wheel mounted on
the input shaft, which is pushed very hard against a steel disk mounted
on the output shaft
...
This drive has been used with some success in
walk-behind lawn mowers, but its life in that application is usually
only a couple seasons
...
CONE DRIVE NEEDS NO GEARS OR PULLEYS
A variable-speed-transmission cone drive operates without gears or
pulleys
...
As the drawing shows, two cones made of brake lining material are
mounted on a shaft directly connected to the engine
...
The outer disks
are mounted on pivoting frames that can be moved by a simple control
rod
...
By altering the position of the
frames relative to the driving cones, the direction of rotation and speed
can be varied
...
Davis of Indiana
...
Chapter 2
Indirect Power Transfer Devices
GEARS
Gears are the most common form of power transmission for several reasons
...
Properly mounted and lubricated, they
transmit power efficiently, smoothly, and quietly
...
For
all their pluses, there are a few important things to remember about
gears
...
They do not tolerate dirt and must be enclosed in a sealed case that
keeps the teeth clean and contains the required lubricating oil or grease
...
Gears come in many forms and standard sizes, both inch and metric
...
Any two gears with the same tooth size can be used
together, allowing very large ratios in a single stage
...
Figure 2-14 shows an example of a cluster gear
...
They
are ubiquitous in practically every gearbox with a gear ratio of more than
5:1, with the exception of planetary and worm gearboxes
...
Each type has its own pros and
cons, including differences in efficiency, allowable ratios, mating shaft
angles, noise, and cost
...
Gears are versatile mechanical components capable of performing
many different kinds of power transmission or motion control
...
Changing rotational direction
...
Multiplication or division of torque or magnitude of rotation
...
Offsetting or changing the location of rotating motion
...
Gear Terminology
addendum: The radial distance between the top land and the pitch circle
...
circular pitch: The distance along the pitch circle from a point on one
tooth to a corresponding point on an adjacent tooth
...
clearance: The radial distance between the bottom land and the clearance circle
...
dedendum circle: The theoretical circle through the bottom lands of a
gear
...
depth: A number standardized in terms of pitch
...
If the teeth have equal addenda (as in standard
interchangeable gears), the addendum is 1/P
...
Gears with a small number of teeth
might require undercutting to prevent one interfering with another during engagement
...
A measure of the coarseness of a gear, it is the index of tooth size
when U
...
units are used, expressed as teeth per inch
...
Coarse-pitch gears have teeth larger than a diametral pitch of 20 (typically 0
...
99)
...
The usual maximum fineness is
120 diametral pitch, but involute-tooth gears can be made with diametral
pitches as fine as 200, and cycloidal tooth gears can be made with diametral pitches to 350
...
87
88
Chapter 2
Indirect Power Transfer Devices
pitch diameter: The diameter of the pitch circle, the imaginary circle
that rolls without slipping with the pitch circle of the mating gear, measured in inches or millimeters
...
Standard angles are 20 and 25º
...
A high pressure angle decreases the contact ratio, but it permits the teeth to have
higher capacity and it allows gears to have fewer teeth without undercutting
...
It is the
shortest distance between the noncontacting surfaces of adjacent teeth
...
gear power: A gear’s load and speed capacity, determined by gear
dimensions and type
...
gear ratio: The number of teeth in the gear (larger of a pair) divided by
the number of teeth in the pinion (smaller of a pair)
...
In reduction gears, the ratio
of input to output speeds
...
It can be
increased by improving the accuracy of the gear teeth and the balance of
rotating parts
...
Gear Classification
External gears have teeth on the outside surface of a disk or wheel
...
Spur gears are cylindrical gears with teeth that are straight and parallel to
the axis of rotation
...
Rack gears have teeth on a flat rather than a curved surface that provide
straight-line rather than rotary motion
...
They are capable of smoother and quieter action than spur
gears
...
Herringbone and worm gears are based on helical gear geometry
...
This geometry neutralizes axial thrust from helical teeth
...
Pinions are the smaller of two mating gears; the larger one is called the
gear or wheel
...
They are used in applications where there are
right angles between input and output shafts
...
Straight bevel gears are the simplest bevel gears
...
These gears provide moderate torque transmission, but they are not as smooth running
or quiet as spiral bevel gears because the straight teeth engage with
full-line contact
...
Spiral bevel gears have curved oblique teeth
...
Consequently, teeth engage gradually and at least two teeth are in contact at the same time
...
They
permit high load capacity
...
Hypoid gears are spiral bevel gears with offset intersecting axes
...
They are designed to mate with instantaneous
point contact
...
Designing a properly sized gearbox is not a simple task and tables or
manufacturer’s recommendations are usually the best place to look for
help
...
All these variables must be taken into account to
come up with an effectively sized gearbox
...
In
most cases the gearbox is not designed at all, but easily selected from a
large assortment of off-the-shelf gearboxes made by one of many manufacturers
...
Worm Gears
Worm gear drives get their name from the unusual input gear which
looks vaguely like a worm wrapped around a shaft
...
Their main disadvantage is inefficiency caused by the worm gear’s sliding contact with the
worm wheel
...
The following section discusses an unusual double enveloping, internally-lubricated worm gear layout that is an attempt to increase efficiency and the
life of the gearbox
...
Lewis Research Center, Cleveland, Ohio
In a proposed worm-gear transmission, oil would be pumped at high
pressure through the meshes between the teeth of the gear and the worm
coil (Figure 2-16)
...
Each of the separating forces in the several meshes would contribute to the torque on the gear and to an axial force on the worm
...
This type of worm-gear transmission was conceived for use in the
drive train between the gas-turbine engine and the rotor of a helicopter
and might be useful in other applications in which weight is critical
...
Heretofore, the high sliding friction between the worm coils and the
gear teeth of worm-gear transmissions has reduced efficiency so much
92
Chapter 2
Indirect Power Transfer Devices
Figure 2-17 This test apparatus
simulates and measures some of
the loading conditions of the proposed worm gear with hydrostatic engagement
...
that such transmissions could not be used in helicopters
...
Preliminary calculations
show that the efficiency of the proposed transmission could be the same
as that of a conventional helicopter gear train
...
Two stationary disk sectors with oil pockets represent the
gear teeth and are installed in a caliper frame
...
Oil is pumped at high pressure through
the clearances between the rotating disk and the stationary disk sectors
...
The stationary disk sectors can be installed with various clearances
and at various angles to the rotating disk
...
A
flowmeter and pressure gauge will measure the pump power
...
The results of the tests are expected to show
the experimental dependences of the efficiency of transmission on these
factors
...
In addition, the new
hydrostatic meshes would offer longer service life and less noise
...
This work was done by Lev
...
Chalko of the U
...
Army Propulsion
Directorate (AVSCOM) for Lewis Research Center
...
Alternatively, the speed range can be increased at the expense of
the horsepower range
...
The features of the differential depend on the manufacturer
...
Both single and
double differentials are employed
...
Horsepower-increasing differential
...
An additional gear pair is
employed as shown in Figure 2-18
...
The output shaft
speed depends on the difference
in rpm between the two input
worms
...
Each
worm shaft carries a cone-shaped
pulley
...
Shifting the position of the drive belt on these
pulleys has a compound effect on
their output speed
...
This arrangement
achieves a wide range of speed with the low limit at zero or in the reverse
direction
...
One solution to this problem is to feed the power of two
motors of equal rating into a planetary gear drive
...
Each of the motors is selected to supply half the
required output power to the hoisting gear (see Figure 2-21)
...
The second motor drives the sun gear directly
...
If both
gears rotate at the same speed, the planetary cage, which is coupled to
96
Chapter 2
Indirect Power Transfer Devices
Figure 2-21 Power flow from
two motors combine in a planetary that drives the cable drum
...
It is as if the entire inner works of the planetary were fused
together
...
Then, if one motor fails, the
cage will revolve at half its original speed, and the other motor can still
lift with undiminished capacity
...
No need to shift gears
...
This makes is
unnecessary to shift gears to obtain either speed
...
HARMONIC-DRIVE SPEED REDUCERS
The harmonic-drive speed reducer was invented in the 1950s at the
Harmonic Drive Division of the United Shoe Machinery Corporation,
Beverly, Massachusetts
...
Although the Harmonic Drive
Division no longer exists, the manufacturing rights to the drive have been
sold to several Japanese manufacturers, so they are still made and sold
...
The history of speed-reducing drives dates back more than 2000
years
...
C
...
The flexspline
has a smaller outside diameter
than the inside diameter of the
circular spline, so the elliptical
wave generator distorts the flexspline so that its teeth, 180º apart,
mesh
...
Those gears offered about a 5 to 1 reduction
...
C
...
In 1556, the Saxon physician, Agricola, described geared, horsedrawn windlasses for hauling heavy loads out of mines in Bohemia
...
The harmonic drive is based on a principle called strain-wave gearing, a name derived from the operation of its primary torque-transmitting
element, the flexspline
...
The circular spline is a nonrotating, thick-walled, solid ring with
internal teeth
...
Smaller in external diameter than the inside
diameter of the circular spline, the flexspline must be deformed by the
wave generator if its external teeth are to engage the internal teeth of the
circular spline
...
Because the major axis of
the wave generator is nearly equal to the inside diameter of the circular
98
Chapter 2
Indirect Power Transfer Devices
Figure 2-23 Schematic of a typical harmonic drive showing the mechanical relationship between the two splines and the wave generator
...
Modern wave generators are enclosed in a ball-bearing
assembly that functions as the rotating input element
...
The shaft
attached to the flexspline is the rotating output element
...
The flexspline typically has two fewer
external teeth than the number of internal teeth on the circular
spline
...
The small circles around the shaft are the
ball bearings of the wave generator
...
In Figure 2-24A, the inside and outside arrows are aligned
...
Figure 2-24 Three positions of the wave generator: (A) the 12 o’clock or
zero degree position; (B) the 3 o’clock or 90° position; and (C) the 360°
position showing a two-tooth displacement
...
The teeth in line with
the minor axis are completely disengaged
...
Without full tooth disengagement at
the areas of the minor axis, this rotation would not be possible
...
The inside
arrow of the flexspline indicates a two-tooth per revolution displacement
counterclockwise
...
As might be
expected, any mechanical component that is flexed, such as the flexspline, is subject to stress and strain
...
Moreover,
there is no backlash in a harmonic drive reducer
...
Because the harmonic drive has a concentric shaft arrangement, the
input and output shafts have the same centerline
...
The ability of the drive to provide
high reduction ratios in a single pass with high torque capacity recommends it for many machine designs
...
One disadvantage of the harmonic drive reducer has been its wind-up or
torsional spring rate
...
This design condition is met only when there is no torsional
load
...
Paradoxically, what could be a disadvantage is turned into an advantage because more teeth share the load
...
However, this bending and flexing causes torsional wind-up, the major
contributor to positional error in harmonic-drive reducers
...
In a new design, one company replaced the original involute teeth on the flexspline and circular spline with noninvolute
teeth
...
The new tooth design is a composite of convex and concave arcs that
match the loci of engagement points
...
FLEXIBLE FACE-GEARS MAKE EFFICIENT
HIGH-REDUCTION DRIVES
A system of flexible face-gearing provides designers with a means for
obtaining high-ratio speed reductions in compact trains with concentric
input and output shafts
...
Patents on the flexible face-gear reducers were held
by Clarence Slaughter of Grand Rapids, Michigan
...
Single-stage gear reducers consist of three basic
parts: a flexible face-gear (Figure 2-25) made of plastic or thin metal; a
solid, non-flexing face-gear; and a wave former with one or more sliders
and rollers to force the flexible gear into mesh with the solid gear at
points where the teeth are in phase
...
Low-speed output can be derived from either the flexible or the solid
face gear; the gear not connected to the output is fixed to the housing
...
The two gears
have slightly different numbers of
teeth
...
Motion between the two gears depends on a
slight difference in their number of teeth (usually one or two teeth)
...
On each revolution of the wave former, there is a relative motion
between the two gears that equals the difference in their numbers of
teeth
...
Two-stage (Figure 2-26) and four-stage (Figure 2-27) gear reducers
are made by combining flexible and solid gears with multiple rows of
teeth and driving the flexible gears with a common wave former
...
Figure 2-26 A two-stage speed reducer is driven by a common-wave former operating against an integral flexible gear
for both stages
...
The train is both compact and simple
...
The gearheads can be coupled to the
smaller, higher-speed servomotors, resulting in simpler systems with
lower power consumption and operating costs
...
They can
convert high-speed, low-torque rotary motion to a low-speed, hightorque output
...
Gearheads have often been selected for driving long trains of mechanisms in machines that perform such tasks as feeding wire, wood, or
metal for further processing
...
One way to avoid this problem is
to choose a right-angle gearhead (Figure 2-28)
...
Horizontal mounting can save space because the gearheads and motors
can be positioned behind the machine, away from the operator
...
Conically shaped bevel gears with straight- or
spiral-cut teeth allow mating shafts to intersect at 90º angles
...
4, but the simultaneous mating of straight teeth along their entire lengths causes more vibration and noise than the mating of spiral-bevel gear teeth
...
0 to 3
...
The higher contact ratios
of spiral-bevel gears permit them to drive loads that are 20 to 30% greater
than those possible with straight bevel gears
...
As a result, operating efficiencies can exceed 90%
...
Inadvertent misalignment
between servomotors and gearboxes, which often occurs during installation, is a common source of vibration
...
It includes helical planetary output gears, a rigid sun gear, spiral bevel gears, and a
balanced input pinion
...
motors with gearboxes requires several precise connections
...
Unfortunately, each of these connections
can introduce slight alignment errors that accumulate to cause overall
motor/gearbox misalignment
...
Until recently it has been standard
practice to mount pinions in the field when the motors were connected to the
gearboxes
...
Engineers
realized that the integration of gearheads into the servomotor package
would solve this problem, but the drawback to the integrated unit is that failure of either component would require replacement of the whole unit
...
It is only necessary to insert the motor shaft into the collar that extends from the gearhead’s rear housing, tighten the clamp with a wrench, and bolt the motor
to the gearhead
...
This procedure permits them to spin at high speed without wobbling
...
However, the factory-installed pinion requires a floating bearing to
support the shaft with a pinion on one end
...
, Port Washington, New York, developed a selfaligning bearing for this purpose
...
A collar on the pinion shaft’s
other end mounts to the motor shaft
...
At that time a pair of bearings in the servomotor support the coupled shaft
...
The pinion and floating bearing help to seal the unit during its operation
...
This seal keeps out dirt while retaining the lubricants within the housing
...
Cost-Effective Addition
The installation of gearheads can smooth the operation of servosystems as
well as reduce system costs
...
Smaller servomotors inherently draw less current than larger ones, thus reducing operating costs, but
those power savings are greatest in applications calling for low speed and
high torque because direct-drive servomotors must be considerably larger
than servomotors coupled to gearheads to perform the same work
...
In those instances servo/gearhead combinations might not be
as cost-effective because power consumption will be comparable
...
The decision to purchase a precision gearhead should be evaluated on
a case-by-case basis
...
Then keep in mind that although in high-speed/low-torque
applications a direct-drive system might be satisfactory, low-speed/hightorque applications almost always require gearheads
...
The planetary gearbox is one of the most efficient and compact gearbox designs
...
Figure 2-29 and the following tables give the
formulas required to calculate the input/output ratios
...
Because of its even greater precision requirement
than spur gears, it is usually better to buy an off-the-shelf gearbox than to
design your own
...
Chapter 3 Direct Power
Transfer Devices
Copyright © 2003 by The McGraw-Hill Companies, Inc
...
This page intentionally left blank
...
Fortunately, there are many commercially
available couplers to pick from, each with its own strengths and weaknesses
...
Solid couplers must be strong enough to hold the shafts’ ends together as
if they were one shaft
...
The only other complication is that
the shafts may be different diameters, or have different end details like
splined, keyed, hex, square, or smooth
...
Solid couplers are very simple devices
...
The
shafts styles in each end of the coupler can be the same or different
...
For smooth shafts, the coupler must clamp to the shaft tight enough to
transmit the torque through friction with the shaft surface
...
As for online sources of couplers, and more detailed information
about torque carrying ability, check out these web sites:
•
•
•
•
•
powertransmission
...
com
flexibleshaftcouplings
...
com
mcmastercarr
...
Those including
chain belts, splines, bands, and rollers are shown here
...
Figure 3-14
Figure 3-15
Figure 3-16
Figure 3-17
Figure 3-18
Figure 3-17
113
114
Chapter 3
Direct Power Transfer Devices
TEN UNIVERSAL SHAFT COUPLINGS
Hooke’s Joints
The commonest form of a universal coupling is a Hooke’s joint
...
At slow speeds, on hand-operated mechanisms, the permissible angle can reach 45°
...
There are many
variations and a few of them are included here
...
Antifriction bearings are a refinement
often used
...
The result is a more compact joint
...
Torques on fastening
sleeves are bent over the sphere
on the assembly
...
Chapter 3
Direct Power Transfer Devices
115
Figure 3-23 A pinned-sleeve
shaft-coupling is fastened to one
saft that engages the forked,
spherical end on the other shaft
to provide a joint which also
allows for axial shaft movement
...
Also, the joint is only suitable for low torques
...
Its maximum velocity can be found by multiplying
driving-shaft speed by the secant of the shaft angle; for minimum speed,
multiply by the cosine
...
The minimum output is 100 × 0
...
9 rpm; the maximum output is
1
...
4 rpm
...
43 rpm
...
This is an objectionable feature in some mechanisms
...
This single constant-velocity coupling is based on the principle
(Figure 3-25) that the contact point of the two members must always lie
on the homokinetic plane
...
Such simple couplings are ideal for toys, instruments, and other
light-duty mechanisms
...
They must have
equal input and output angles to
work correctly
...
The shaft-alignment angle can be
double that for a single joint
...
It has two joints close-coupled with a sliding member
between them
...
There are other designs for heavy-duty universal couplings; one, known
as the Rzeppa, consists of a cage that keeps six balls in the homokinetic
plane at all times
...
Figure 3-25
Figure 3-26
Figure 3-27 This flexible shaft permits any shaft angle
...
Figure 3-28 This pump-type coupling has the reciprocating
action of sliding rods that can drive pistons in cylinders
...
The sliding swivel-rod must be
kept well lubricated at all times
...
Its major limitation
is the need for adequate center distance
...
This can be a plain pinion or
an internal gear
...
Figure 3-31 This coupling consists of two
universal joints and a short shaft
...
The velocity of the central shaft fluctuates during rotation, but high speed and wide
angles can cause vibration
...
Figure 3-32 This crossed-axis yoke coupling
is a variation of the mechanism shown in Fig
...
Each shaft has a yoke connected so that it
can slide along the arms of a rigid cross member
...
There is no axial freedom
...
Figure 3-33 This Oldham coupling provides
motion at a constant velocity as its central
member describes a circle
...
A small amount of axial freedom is possible
...
This can be
eliminated by enlarging its diameter and
milling the slots in the same transverse plane
...
They are used mainly for transmitting light loads, where accurate positioning is not critical
...
Figure 3-35 Serrations of small size are
used mostly for transmitting light loads
...
Originally
straight-sided and limited to small pitches,
45º serrations have been standardized (SAE)
with large pitches up to 10 in
...
For tight
fits, the serrations are tapered
...
Such splines are often used for sliding members
...
For different applications, tooth height
is altered, as shown in the table above
...
Internal parts can be ground
readily so that they will fit closely with the
lands of the external member
...
Tooth proportions are based on a 30º stub tooth form
...
(B) Use of the tooth width or side
positioning has the advantage of a full fillet radius at the roots
...
Contact stresses of 4,000 psi are used for accurate, hardened splines
...
Figure 3-39 Special Involute splines are made by using
gear tooth proportions
...
A compound pinion is shown made by
cropping the smaller pinion teeth and internally splining the
larger pinion
...
This method holds mating parts
securely
...
120
Chapter 3
Direct Power Transfer Devices
Face Splines
Figure 3-41 Milled Slots in hubs
or shafts make inexpensive connections
...
A pin and
sleeve method is used for light
torques and where accurate positioning is not required
...
(A) Tooth proportions decrease
radially
...
Figure 3-43 Curvic Coupling teeth are machined by a face-mill cutter
...
(A) This
process produces teeth with uniform depth
...
(B) Due to the cutting action, the shape of the teeth will
be concave (hour-glass) on one member and convex on the other—the member with
which it will be assembled
...
This is done by turning the drive motor into a generator, and
then placing a load across the motor’s terminals
...
To make the motor brake the robot, the
electrical power is fed through large load resistors, which absorb the
power, slowing down the motor
...
The energy required to stop the robot is given off in this
heat
...
In a case where the rotating shaft suddenly jams or becomes overloaded for some unexpected reason, the torque in the shaft could break
the shaft, the gearbox, or some other part of the rotating system
...
This mechanical device is
called a torque limiter
...
Magnets, rubber bands, friction
clutches, ball detents, and springs can all be used in one way or another,
and all have certain advantages and disadvantages
...
Figures 3-44 through 3-53
show several torque limiters, which are good examples of the wide variety of methods available
...
Control of the
drive in place is limited to removing magnets to reduce the drive’s
torque capacity
...
Springs keep the
roller in the slots, but excessive
torque forces them out
...
Increasing compression
on the spring by tightening the
nut increases the drive’s torque
capacity
...
The
outer pins are smaller than the
inner pins to ensure contact
...
Figure 3-49 The ring resists the
natural tendency of the rollers to
jump out of the grooves in the
reduced end of one shaft
...
Figure 3-50 Sliding wedges
clamp down on the flattened end
of the shaft
...
The strength of the springs in
tension that hold the wedges
together sets the torque limit
...
Square disks lock into the
square hole in the left shaft, and
round disks lock onto the square
rod on the right shaft
...
Adjustable spring
tension holds the two friction surfaces together to set the overload
limit
...
A
drawback to this design is that a
slipping clutch can destroy itself if
it goes undetected
...
A
spring holds a ball in a dimple in
the opposite face of this torque
limiter until an overload forces it
out
...
Thus,
this limiter is not recommended
for machines where overload is
common
...
In this case, a device called a
shear pin is used
...
With careful control of motor power,
both accelerating and braking, even torque limiters can be left out of
most designs
...
They don’t often
turn up in the drive system of mobile robots, because the slow moving
robot rarely generates an overload condition
...
If a torque limiter is used in the joint of a manipulator, the joint
must have a proprioceptive sensor that senses the angle or extension of
the joint so that the microprocessor has that information after the joint
has slipped
...
Figure 3-54 A shear pin is a
simple and reliable torque limiter
...
Be
sure that spare shear pins are
available in a convenient location
...
Chapter 4
Wheeled Vehicle
Suspensions
and Drivetrains
Copyright © 2003 by The McGraw-Hill Companies, Inc
...
This page intentionally left blank
...
The ability of the
these systems to effectively traverse what ever terrain is required is paramount to the success of the robot, but to my knowledge, there has never
been an apples to apples comparison of mobility systems
...
This means all motors, gearboxes,
suspension pieces, transmissions, wheels, tires, tracks, springs, legs, foot
pads, linkages, mechanisms for moving the center of gravity, mechanisms for changing the shape or geometry of the vehicle, mechanisms for
changing the shape or geometry of the drivetrain, mechanisms and linkages for steering, etc
...
The systems and mechanisms described in this book are divided into
four general categories: wheeled, tracked, walkers, and special cases
...
There are some that are described in the text that are not discussed in
Chapter Nine
...
Most of the systems discussed in Chapter
Eight fall into this category because they are designed to move through
very specific environments and are not general enough to be comparable
...
This chapter deals with
wheeled systems, everything from one-wheeled vehicles to eightwheeled vehicles
...
129
130
Chapter 4
Wheeled Vehicle Suspensions and Drivetrains
WHEELED MOBILITY SYSTEMS
By far the most common form of vehicle layout is the four-wheeled,
front-steer vehicle
...
The most important
changes (other than the internal combustion engine) were to the suspension and steering systems
...
Eventually the suspension was developed into
the nearly ubiquitous independently suspended wheels on all four corners of the vehicle
...
Most suspensions
are designed for high-speed control over mostly smooth surfaces, but
more importantly, they are designed to be controlled by a human
...
The exception is sprung bogies in some of the
tracked vehicle layouts and a sprung fourth wheel in a couple four-wheel
designs
...
Below that speed, they are actually a hindrance to mobility
because they change the force each wheel exerts on the ground as bumps
are negotiated
...
This reduces the traction of the lightly loaded wheels
...
This is precisely what happens in
rocker and rocker/bogie suspensions
...
Everything from
the largest military tank to the smallest motor cycle falls within that
range, though some specialized vehicles designed for travel on loose
powder snow have pressures of as low as five kilo-pascals
...
Vehicles with relatively low
ground pressure will perform better on softer materials like loose sand,
snow, and thick mud
...
The best example of this fact are vehicles designed to
travel on both hard roads and sand
...
Several military vehicles like the WWII amphibious DUKS were designed so tire pressure could be adjusted from inside
the cab, without stopping
...
This also points to the advantage of maintaining as even a ground
pressure as possible on all tires, even when some of them may be lifted
up onto a rock or fallen tree
...
Suspension systems that can change their ground pressure in response to
changes in ground materials, either by tire inflation pressure, variable
geometry tires, or a method of changing the number of tires in contact
with the ground, will also theoretically work well on a wider range of
ground materials
...
The
latter are shown because they are simple and easy to implement, allowing a basic mobile platform to be quickly built to ease the process of getting started building an autonomous robot
...
SHIFTING THE CENTER OF GRAVITY
A trick that can be applied to mobile robots that extends the robot’s
mobility, independent of the mobility system, is to move the center of
gravity (cg) of the robot, thereby changing which wheels, tracks, or legs
are carrying the most weight
...
Shifting the center of gravity can be accomplished by moving a dedicated weight, shifting the cargo, or reorienting the manipulator
...
If it is planned to move the
manipulator, then the manipulator must make up a significant fraction of
the total weight of the vehicle for the concept to work effectively
...
The figures show the basic concept and several variations of cg shifting that might be tried if no other mobility system can be designed to
negotiate a required obstacle, or if the concept is being applied as a retrofit to extend an existing robot’s mobility
...
When those parts reach the far side of the gap, the robot is
driven forward until it is almost across, then the cg is shifted forward,
lifting the rear ground contact points off the ground
...
For stair climbing or steep slopes, the cg is shifted forward so it
remains over the center of area of the mobility system
...
This reduces the tendency of the robot to slam down on the front
parts of the mobility system
...
The control
loop would be set to move the cg in relation to the fore and aft tilt of the
robot
...
Figures 4-1 and 4-2 show two
basic techniques for moving the cg
...
The location of the drive motor(s) is left to the
designer, but there are a few unusual techniques for connecting the drive
motor to the wheels that affect mobility that should be discussed
...
In many cases, the layouts that show the chassis
down low can be altered to have it up high, and vise-versa
...
The US Army’s High Mobility
Multipurpose Wheeled Vehicle (HMMWV, HumVee, or Hummer), uses
geared offset hubs (Figure 4-3) resulting in a ground clearance of 16"
with tires that are 37" in diameter
...
WHEEL SIZE
In general, the larger the wheel, the larger the obstacle a given vehicle
can get over
...
In a well-designed four-wheel drive off-road
truck, this can be increased a little, but the limit in most suspensions is
something less than half the diameter of the wheel
...
If a driven wheel is pushed against a wall that is
taller than the wheel diameter with sufficient forward force relative to the
vertical load on it, it will roll up the wall
...
Chapter 4
Wheeled Vehicle Suspensions and Drivetrains
Three wheels are the minimum required for static stability, and threewheeled robots are very common
...
Mobility and complexity are increased by adding
even more wheels
...
The most basic vehicle would have the least number of wheels
...
Its wheel is actually a ball with an internal movable counterweight that, when not over the point of contact of the ball and the
ground, causes the ball to roll
...
Its step-climbing ability is limited
and depends on what the actual tire is made of, and the weight ratio
between the tire and the counterweight
...
The common bicycle is perhaps one of the most recognized two-wheeled vehicles in the world
...
The side by side layout
is also not inherently stable, but is easier to control, at low speeds, than a
bike
...
It suffers from
Figure 4-4
Bicycle
135
136
Chapter 4
Figure 4-5
Wheeled Vehicle Suspensions and Drivetrains
Tail dragger
the same limitation the single wheeled ball suffers from and cannot get
over bumps much higher than one quarter a wheel height
...
This tail counteracts the torque produced by the wheels, makes
the vehicle statically stable, and increases, somewhat, the height of
obstacle the robot can get over
...
This serves to control
both velocity and steering
...
Too long
and it gets in the way when turning, too short and it doesn’t increase
mobility much at all
...
The tail end slides both fore and aft and side to side, requiring it to be of
a shape that does not hang up on things
...
THREE-WHEELED LAYOUTS
The tail dragger demonstrates the simplest statically stable wheeled
vehicle, but, unfortunately, it has limited mobility
...
Three wheels can be laid out in
several ways
...
The
most common and easiest to implement, but with, perhaps, the least
mobility of the five three-wheeled types, is represented by a child’s tricycle
...
Robots destined to be used indoors, in a test lab or other
controllable space, can use this simple layout with ease, but it has
extremely poor mobility
...
Powering only one
of the three wheels is the major cause of this problem
...
In order to improve the mobility and stability of motorcycles, the three
wheeled All Terrain Cycle (ATC) was developed
...
The
rear two wheels are powered through a differential, and the front steers
...
The ATC was eventually outlawed because of its major
flaw, very poor stability
...
This is also the most common
form of accident with a child’s tricycle
...
This layout works
fine for relatively low speeds, but the geometry is difficult to control
when turning at higher speeds as the forces on the rear steering wheel
tend to make the vehicle turn more sharply until eventually it is out of
control
...
A clever version of
this tail dragger-like layout gets around the problem of flipping over by
virtue of its ability to flip itself back upright simply by accelerating rapidly
...
Theoretically, this could be done with a tricycle
also
...
Steering with the front wheels on a reversed tricycle removes the
steering problem, but adds the complexity of steering and driving both
wheels
...
The layout is still dragging around a passive wheel, however, and mobility is further enhanced if this wheel is
powered
...
This layout is extremely
versatile, providing motion in any direction without the need to be moving; it can turn in place
...
Of the vehicles discussed so far, all, except the
front steer reversed tricycle, can be made holonomic if the third wheel
lies on the circumference of the circle whose center is midway between
the two opposing wheels, and the steering or passive wheel can swing
through 180 degrees
...
This enables it to turn at any time to find a path out
of its trap
...
Before we investigate four-wheeled vehicles, there is a mechanism
that must be, at least basically, understood—the differential
...
The most
basic differential uses a set of gears mounted inside a larger gear, but on
an axis that lies along a radius of the larger gear
...
When both wheels are rolling on relatively high fric-
140
Chapter 4
Wheeled Vehicle Suspensions and Drivetrains
Figure 4-9 The common and
unpredictable differential
tion surfaces, and the vehicle is going straight, the wheels rotate at the
same rpm
...
The differential facilitates this through the internal gears, which rotate
inside the large gear, allowing one axle to rotate relative to the other
...
It obviously works well
...
If one wheel is rolling on a
surface with significantly less friction, it can slip and spin much faster
than the other wheel
...
This is almost never noticed by a
human operator, but can cause mobility problems for vehicles that frequently drive on slippery surfaces like mud, ice, and snow
...
One is to add clutches between the
axles that slide on each other when one wheel rotates faster than the
other
...
The other solution is
the wonderfully complicated Torsen differential, manufactured by Zexel
...
These gears allow the required differentiation
between the two wheels when turning, but do not allow one wheel to spin
as it looses traction
...
The best
explanation of how it works can be found on Zexel’s web site:
www
...
com
...
It has two wheels on each side that are coupled together and is
steered just like differential steered tricycles
...
This sliding action gives this steering method its
name—Skid Steer
...
Skid steered vehicles are a robust, simple design with good mobility,
in spite of the inefficiency of the sliding wheels
...
There are many industrial off-road skid
steered vehicles in use, popularly called Bobcats
...
The problem with skid steered, non-suspended drivetrains is that as the
vehicle goes over bumps, one wheel necessarily comes off the ground
...
Though
not a requirement for good mobility, it is better to use some mechanism
that keeps all the wheels on the ground
...
Figure 4-10 All four fixed, skid
steered
142
Chapter 4
Wheeled Vehicle Suspensions and Drivetrains
Figure 4-11 Simple longitudinal
rocker
The longitudinal rocker design divides the entire vehicle right down
the middle and places a passive pivot joint in between the two halves
...
This layout allows the rocker arms to pivot
when any wheel tries to go higher or lower than the rest
...
Longitudinal rocker designs are skid steered, with
the wheels on each side usually mechanically tied together like a simple
skid steer, but sometimes, to increase mobility even further, the wheels
are independently powered
...
The well-known forklift industrial truck uses a sideways version of
the rocker system
...
These vehicles have four wheels without any suspension, and, therefore, require some method of keeping all the wheels on the ground
...
Figure 4-12 shows this layout
...
This works well for its application, and because so much of the weight of
the vehicle is over the front wheels
...
In a two-wheel drive vehicle, the
driven wheels must provide traction not only for whatever they are trying
to get over, but also must push or pull the non-driven wheels
...
Although this seems like a complicated solution from an
electrical and control standpoint, it is simpler mechanically
...
The transverse rocker layout can also be used with a front steered
layout (Figure 4-13) which makes it very much like an automobile
...
Figure 4-13 Rear transverse
rocker, front steer
144
Chapter 4
Wheeled Vehicle Suspensions and Drivetrains
ALL-TERRAIN VEHICLE WITH
SELF-RIGHTING AND POSE CONTROL
Wheels dr iven by gearmotors are mounted on pivoting struts
...
The vehicle is
designed for exploration of planets and asteroids, and could just as well
be used on Earth to carry scientific instruments to remote, hostile, or otherwise inaccessible locations on the ground
...
Another
maneuver enables the vehicle to overcome a common weakness of traditional all-terrain vehicles—a limitation on traction and drive force that
makes it difficult or impossible to push wheels over some obstacles: This
vehicle can simply lift a wheel onto the top of an obstacle
...
Each wheel is driven individually by
a dedicated gearmotor
...
The pivot assembly imposes a constant frictional torque T, so that it is possible to
(a) turn both wheels in unison while both struts remain locked, (b) pivot one strut, or (c)
pivot both struts in opposite directions by energizing the gearmotors to apply various
combinations of torques T/2 or T
...
Through pulleys or other mechanism
attached to their wheels, both gearmotors on each side of the vehicle
drive a single idler disk or pulley that turns about the pivot axis
...
The idler pulley and the pivot disks of the struts are made
of suitably chosen materials and spring-loaded together along the pivot
axis in such a way as to resist turning with a static frictional torque T; in
other words, it is necessary to apply a torque of T to rotate the idler pulley or either strut with respect to each other or the vehicle body
...
In this operational
mode, each gearmotor contributes a torque T/2 so that together, both gearmotors provide torque T to overcome the locking friction on the idler pulley
...
If it is desired to change the angle between one strut and the main
vehicle body, then the gearmotor on that strut only is energized
...
Since the gearmotor on the other strut is not energized and since it is coupled to the idler
pulley, a torque greater than T would be needed to turn the idler pulley
...
It is also possible to pivot both struts simultaneously in opposite directions to change the angle between them
...
If it is desired to pivot the
struts through unequal angles, then the gearmotor speeds are adjusted
accordingly
...
Current
and future work is focused on designing a simple hub mechanism, which
is not sensitive to dust or other contamination, and on active control
techniques to allow autonomous planetary rovers to take advantage of
the flexibility of the mechanism
...
Wilcox and Annette K
...
If a differential is installed between the halves of a longitudinal rocker
layout, with the axles of the differential attached to each longitudinal
rocker, and interesting effect happens to the differential input gear as the
145
146
Chapter 4
Wheeled Vehicle Suspensions and Drivetrains
Figure 4-15 Pitch averaging
mechanism
vehicle traverses bumpy terrain
...
This
pitch averaging effectively reduces the pitching motion of the chassis,
maintaining it at a more level pose as either side of the suspension system travels over bumps
...
This mechanism
also tends to distribute the weight more evenly on all four wheels,
increasing traction, and, therefore, mobility
...
Another mechanical linkage gives the same result as the differentialbased chassis pitch-averaging system
...
This design uses
a third rocker tied at each end to a point on the side rockers
...
The third rocker design can be more volumetrically efficient and perhaps lighter than the differential layout
...
The two sections are connected through
Chapter 4
Wheeled Vehicle Suspensions and Drivetrains
147
Figure 4-16 Chassis pitch averaging mechanism using
differential
an articulated (powered) vertical-axis joint
...
Even better would be to have each wheel driven with its
Figure 4-17 Chassis link-based
pitch averaging mechanism
148
Chapter 4
Wheeled Vehicle Suspensions and Drivetrains
own motor
...
Greater mobility is achieved if the center joint also allows a rolling
motion between the two sections
...
It also
improves traction while turning on bumps
...
Alternatively, the wheels could be powered through limited slip
differentials and the roll axis left passive for less mobility, but only three
motors
...
An unusual and unintuitive layout is the five-wheeled drivetrain
...
The front wheel is not
normally powered and is only for steering
...
Although
the front wheels must be pushed over obstacles, there is ample traction
from all that rubber on the four rear wheels
...
There are many layouts, suspensions, and drivetrains based on
six wheels
...
Six wheels put enough ground pressure, traction, steering mobility, and obstacle-negotiating ability on a vehicle
without, in most cases, very much complexity
...
The most basic six-wheeled vehicle, shown in Figure 4-21, is the skidsteered non-suspended design
...
The wheels
can be driven with chains, belts, or bevel gearboxes in a simple way,
making for a robust system
...
The lower
weight reduces the forces needed to skid them around when turning,
reducing turning power
...
Careful planning of the location of the center of gravity is
required to minimize this problem
...
Figure 4-21 Six wheels, all
fixed, skid steer
Chapter 4
Wheeled Vehicle Suspensions and Drivetrains
151
Figure 4-22 Six wheels, all
fixed, skid steer, offset center axle
An even trickier layout adds two pairs of four-bar mechanisms supporting the front and rear wheel pairs (Figure 4-23)
...
This semi-walking mechanism allows the vehicle
to negotiate obstacles that are taller than the wheels, and can aid in traversing other difficult terrain by actively controlling the weight on each
wheel
...
Skid steering can be improved by adding a steering mechanism to the
front pair of wheels, and grouping the rear pair more closely together
...
Incorporating the Ackerman steering layout removes the ability
of the robot to turn in place
...
Figure 4-24 shows the basic layout
...
The epitome of complexity in a once commercially available sixwheeled vehicle, not recommended to be copied for autonomous robot
use, is the Alvis Stalwart
...
It was a six-wheeled (all independently suspended on parallel links with torsion arms) vehicle whose front
four wheels steered
...
It had offset wheel hub reduction
gear boxes, a lockable central differential power transfer box with integral reversing gears, and twin water jet drives for amphibious propulsion
...
No sketch is included for obvious reasons, but a website with
good information and pictures of this fantastically complicated machine
is www
...
com/Mil/alvis/stalwart
...
The main problem with these simple layouts is that when one wheel is
up on a bump, the lack of suspension lifts the other wheels up, drastically
reducing traction and mobility
...
The
following suspension systems even out the load on each wheel—some
more than others
...
The center
section has longitudinal joints on its front and back that attach to the
cross pieces of the front and rear sections
...
This movement keeps all six wheels on the
ground
...
This layout has been experimented with
by researchers and has very high mobility
...
The rocker bogie suspension system shown in Figure 4-26 uses an
extension of the basic four-wheel rocker layout
...
Although this layout looks like it would produce asymmetrical loads on the wheels, if the length of the bogie is half
that of the rocker, and the rocker is attached to the chassis one third of its
length from the bogie end, the load on each wheel is actually identical
...
The rocker bogie’s big advantage is that it
154
Chapter 4
Wheeled Vehicle Suspensions and Drivetrains
Figure 4-26 Rocker bogie
can negotiate obstacles that are twice the wheel height
...
The part labeled “chassis” is
the backbone or main support piece for the main body, which is not
shown
...
Lockable pivots on the
bogie can extend the negotiable chasm width by making the center
wheels able to support the weight of the entire vehicle
...
This actuator can be
a simple band or disc brake
...
Since the wheels are at the end of arms that move relative to each other, the most common layout puts a motor in each wheel
...
This means that this layout uses 10 motors to
achieve its very high mobility
...
The steering geometry allows turning in place with no skidding at all
...
Mobility experts claim this layout has the highest mobility possi-
Chapter 4
Wheeled Vehicle Suspensions and Drivetrains
ble in a wheeled vehicle, but this high mobility comes at the cost of those
ten actuators and all their associated control electronics and debug time
...
These wheels are powered
with the three on each side and the vehicle is skid steered, but the front
set of wheels are only placed on the ground for extra traction and stair
climbing
...
The next logical progression, already commercially available from
Remotec in a slight variation, is to put the four center wheels on the
ground, and put both end pairs on flippers
...
The flippers
carry either wheels or short tracks
...
EIGHT-WHEELED LAYOUTS
If six wheels are good then eight wheels are better, right? For a certain
set of requirements, eight wheels can be better than six
...
If the robot
needs to be particularly low for its size, then eight wheels may be the
answer
...
Lowering
the center two pairs aids in skid steering just like on a six wheeled skid
steer, but the four wheels on the ground means there is less wobbling
when stopping and starting
...
With all the wheels fixed there are many times when several of the
wheels will be lifted off the ground, reducing traction greatly
...
A set of wheels may still leave the ground in some terrains, but
the other six wheels should remain mostly in contact with the ground to
give some traction
...
Since the bogie is a fairly simple arm connecting only a pair of wheels, a
single motor could potentially be mounted near the center of the bogie
and through a power transfer system, drive both wheels
...
No known instances of this layout, shown in Figure 4-28, have been built
for testing, though it seems like an effective layout
...
The two parts are then either connected through a passive joint and individually skid steered, or the joint
is articulated and steering is done by bending the vehicle in the middle
...
This can be a very effective layout for obstacle negotiation and
crevasse crossing, but cannot turn in place
...
Figure 4-30 adds a
roll joint to aid in keeping more wheels on the ground
...
It is skid steered, and is suited for bumpy terrain, but which has
few obstacles it must go around
...
This layout is similar to the double rocker
layout, with similar mobility and fewer moving parts
...
The ball joint allows pitch, roll, and yaw
between the two parts which facilitates keeping all eight wheels on the
ground most of the time
...
It has a limited range of motion around two of the axis, but the
third axis can rotate three hundred sixty degrees
...
This allows the vehicle to have a
tighter steering radius, but it cannot turn in place
...
The
ball joint is difficult to use with a four-wheeled vehicle because the
Chapter 4
Wheeled Vehicle Suspensions and Drivetrains
157
Figure 4-28 Eight wheels, double bogie
wheel torque would try to spin the section around the wheels
...
Figure 4-29 Two part, eight
wheeled, vertical center pivot
158
Chapter 4
Wheeled Vehicle Suspensions and Drivetrains
Figure 4-30 Two part, eight
wheeled, vertical and roll joints
For a truly complicated wheeled drive mechanism, the Tri-star LandMaster from the movie Damnation Alley is probably the most impressive
...
The Tri-star
wheels consist of three wheels, all driven together, arranged in a three-
Figure 4-31 Two part, eight
wheeled, vertical ball joint
Chapter 4
Wheeled Vehicle Suspensions and Drivetrains
pointed star on a shared hub that is also driven by the same shaft that
drives the wheels
...
The Tristar wheels are driven through differentials on the Land-Master, but powering each with its own motor would increase mobility even further
...
Chapter 5
Tracked Vehicle
Suspensions
and Drivetrains
Copyright © 2003 by The McGraw-Hill Companies, Inc
...
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...
While tracks can breeze through situations where
wheels would struggle, there are only a few obstacles and terrains which
would stop a six wheeled rocker bogie vehicle, but not stop a similar
sized tracked vehicle
...
Tracked vehicles first started to appear in the early 1900s and were
used extensively in WWI
...
This basic, simple layout is
robust and easy to control
...
The continuous surface in contact with the ground is what produces
the benefits of tracks
...
This lowers ground pressure,
allowing traveling on softer surfaces
...
The continuous surface eliminates a wheeled vehicle’s problem of
becoming high centered between the wheels on one side
...
The wheeled vehicle can get stuck in these situations,
where the track would simply roll over the obstacle
...
Clever suspension components can
be added to a six-wheeled or eight-wheeled vehicle to increase its nego163
164
Chapter 5
Tracked Vehicle Suspensions and Drivetrains
tiable crevasse width, but these add complexity to the wheeled vehicle’s
inherent simplicity
...
Add a mechanism for shifting the center of gravity, and a tracked vehicle can cross crevasses that are wider than half the
length of the vehicle
...
The greater number of moving parts also increase complexity, and one
of the major problems of track design is preventing the track from being
thrown off the suspension system
...
Track systems are made up of track, drive sprocket, idler/tension
wheel, suspension system, and, sometimes, support rollers
...
• The design of the track itself (steel links with hinges, continuous rubber, tread shapes)
• Method of keeping the tracks on the vehicle (pin-in-hole, guide
knives, V-groove)
• Suspension system that supports the track on the ground (sprung and
unsprung road wheels, fixed guides)
• Shape of the one end or both ends of the track system (round or
ramped)
• Relative size of the idler and/or drive sprocket
Variations of most of these system layouts have already been tried,
some with great success, others with apparently no improvements in
mobility
...
These various layouts have certain advantages and
disadvantages over each other
...
Robots are slowly coming into common use in the home and one
tough requirement in the otherwise benign indoor environment is climbing stairs
...
Tracks simplify the problem somewhat and
can climb stairs more smoothly than wheeled drivetrains, allowing
higher speeds, but they have difficulty staying aligned with the stairs
...
At the time of this writing there is
no known autonomous vehicle that can climb a full flight of stairs without human input
...
Tracks can be
used with good effectiveness on small vehicles, but problems can
develop due to the stiffness of the track material
...
These fully autonomous robots were about the size of a quarter
...
inuktun
...
The M1A2’s tracks are
...
75 meters long (longer than
most cars) and together, including the suspension components, make up
nearly a quarter of the total weight of the tank
...
A single link of the Crawler
Transporter’s tracks is nearly 2m long and weighs nearly eight thousand
newtons (about the same as a mid-sized car)
...
Although mobility of this behemoth is limited, it is
designed to climb the five-percent grade up to the launch site while holding the Space Shuttle exactly vertical on a controllable pitch platform
...
Most large vehicles like
these use metal link tracks because of the very large forces on the track
...
The smaller sizes can
use solid urethane belts with no steel at all
...
They also cause far less
damage to hard surface roads in larger sizes
...
They do not stretch, rust, or require any
maintenance like a metal-link track
...
Even the very
heavy M1A2 has a ground pressure of about eighty-two kilo pascals
(roughly the same pressure as a large person standing on one foot)
...
This low ground pressure
allows the Bv206 to drive over and through swamps, bogs, or soft snow
that even humans would have trouble getting through
...
That is reserved for vehicles
designed specifically for use on powdery snow
...
This is a little more than the pressure exerted on a table by a one-liter bottle of Coke
...
The sprockets, idlers,
and road wheels inside the track leave little volume for anything else
...
In
fact, the volume of a six wheeled rocker bogie suspension is about the
same as that of a track unit when the negotiable obstacle height is the
baseline parameter
...
In this situation, tracks are clearly better
...
A wheeled vehicle, even with eightwheels, would simply fall into the crevasse as the gap between the
wheels cannot support the middle of the vehicle at the crevasse’s edge
...
To simplify building a tracked robot, there are companies that manufacture the undercarriages of construction equipment
...
They are
Chapter 5
Tracked Vehicle Suspensions and Drivetrains
extremely robust and come in a large variety of styles and are made for
both steel and rubber tracks
...
They are not manufactured in sizes smaller than about 1m long,
but for larger robots, they should be given consideration in a design
because they are designed by companies that understand tracks and
undercarriages, they are robust, and they constitute a bolt-on solution to
one of the more complex systems of a tracked mobile robot
...
This is exactly the same as a
skid-steer wheeled vehicle
...
The
skidding power requirements on a tracked vehicle are about the same, or
perhaps a little higher, as on a four-wheel skid steer layout
...
Several novel layouts improve on this drive-and-brake steering system
...
A second
improvement to drive-and-brake steering uses a fantastically complicated second differential powered by its own motor
...
Varying the speed of the steering motor varies the relative speed of
the two tracks
...
Another method for steering tracked vehicles is to use some external
steerable device
...
This is a one-tracked separately steered layout
...
A steering method that can improve mobility is one called articulated
steering
...
This joint bends the vehicle in the middle, making it turn a corner
...
These
systems can aid mobility further if a second degree of freedom is added
which allows controlled or passive motion about a transverse pivot joint
at nearly the same location as the steering joint
...
e
...
This has the effect of raising the ends, reducing
the power required to skid them around when turning
...
VARIOUS TRACK CONSTRUCTION METHODS
Tracks are constructed in many different ways
...
Since the advent of Urethane and other very tough rubbers, tracks have
moved away from steel
...
On larger vehicles or vehicles
designed to carry high loads, steel linked tracks may be the best solution
...
•
•
•
•
•
All steel hinged links
Hinged steel links with removable urethane road pads
Solid urethane
Urethane with embedded steel tension members
Urethane with embedded steel tension members and external steel
shoes (sometimes called cleats)
• Urethane with embedded steel tension members and embedded steel
transverse drive rungs with integral guide teeth
All-steel hinged linked track (Figure 5-1) would seem to be the toughest design for something that gets beat on as much as tracks do, but there
are several drawbacks to this design
...
A solution to this problem is to mount the hinge point as far out on the track as possible
...
This is a subtle but important part of steel track design
...
Tracked vehicles, even autonomous robots, will drive on finished
roads at some point in their life, and all-steel tracks tear up macadam
...
These pads are designed to be easily replaceable
...
This allows them to be removed and replaced as they wear out
...
The way to completely remove the pinch point is to make the track all
one piece
...
There are no pinch points
at all; the track is a continuous loop with or without treads
...
It is very tough,
relatively high friction compared to steel, and inexpensive
...
Ironically, if higher traction is needed, steel
cleats can be bolted to the urethane
...
Urethane by itself is too stretchy for most track applications
...
The
steel is completely covered by the urethane so there is no corrosion prob-
170
Chapter 5
Tracked Vehicle Suspensions and Drivetrains
Figure 5-3 Urethane pads for
hard surface roads
Figure 5-4 Cross section of urethane molded track with
strengthening bars and internal
cables
Chapter 5
Tracked Vehicle Suspensions and Drivetrains
lem
...
For even greater strength, hardened steel crossbars are molded into the
track
...
This gives the urethane track much
greater tension strength, and extends its life
...
This is the most common layout for urethane tracks on industrial vehicles
...
TRACK SHAPES
The basic track formed by a drive sprocket, idler, and road wheels works
well in many applications, but there are simple things that can be done to
modify this oblong shape to increase its mobility and robustness
...
Robustness can be augmented by moving
vulnerable components, like the drive sprocket, away from possibly
harmful locations
...
The simplest way to increase negotiable obstacle height is to make the
front wheel of the system larger
...
This layout,
when combined with locating the drive sprocket on the front axle, also
raises up the drive system
...
Many early tanks of WWI used this
track shape
...
Adding ramps can increase the number of road wheels and therefore the
number of moving parts, but they can greatly increase mobility
...
As shown in Figure 5-5 (a–d), ramps are created by raising the drive and/or idler sprocket higher than the road wheels
...
More than one company has designed and built track systems that can
change shape
...
The road wheels are
171
172
Chapter 5
Tracked Vehicle Suspensions and Drivetrains
Figure 5-5a–d Various track
shapes to improve mobility and
robustness
Figure 5-5b
Figure 5-5c
Chapter 5
Tracked Vehicle Suspensions and Drivetrains
173
Figure 5-5d
usually mounted directly to the chassis through some common suspension system, but the idler wheel is mounted on an arm that can move
through an arc that changes the shape of the front ramp
...
This variability produces very good mobility when system height is
included in the equation because the stowed height is relatively small
compared to the negotiable obstacle height
...
With simple implementations of this concept, the
variable geometry track system is a good choice for a drive system for
mobile robots
...
Many others are possible
...
They can be located at either
the front or rear of the track, though they are usually in the rear to
keep them away from the inevitable bumps the front of an autonomous
vehicle takes
...
These modifications result in a common track shape, shown
in Figure 5-5c
...
The static
ramp extends in front and above the tracks and slides up obstacles that
are taller than the track
...
TRACK SUSPENSION SYSTEMS
The space between the drive sprocket and idler wheel needs to be uniformly supported on the ground to achieve the maximum benefit of
tracks
...
The main differences
between these methods is drive efficiency, complexity, and ride characteristics
...
The main types of ground support methods are
•
•
•
•
Guide blades
Fixed road wheels
Rocker road wheel pairs
Road wheels mounted on sprung axles
Guide blades are simple rails that are usually designed to ride in the V
shaped guide receivers on the track’s links
...
Unfortunately, they are also
quite inefficient since there is the long sliding surface that cannot be
practically lubricated
...
One step up from guide blades is fixed road wheels (Figure 5-7)
...
The wheels can be small relative to the track, since the thing they
roll on is always just the smooth inner surface of the track
...
Fixed rollers are a good choice for a robust track system on a robot
since ride comfort is not as important, at lower speeds, as on a vehicle
carrying a person
...
Reducing this
175
Fixed road wheels
176
Chapter 5
Figure 5-8
rockers
Tracked Vehicle Suspensions and Drivetrains
Road wheels on
motion is especially beneficial at higher speeds, and the rocker layout
used on wheeled vehicles is almost as effective on tracks
...
The rockers (Figure 5-8) allow the track to give a little when traversing bumpy terrain, which reduces vertical motion of the robot chassis
...
The most complex, efficient, and smooth ride is produced by mounting the road wheels on sprung axles
...
• Trailing arm on torsion spring
• Trailing arm with coil spring
• Leaf spring rocker
The trailing arm on a torsion spring is pictured in Figure 5-9
...
It gets its name because the arms that
support the wheel trail behind the point where they attach, through the
torsion springs, to the chassis
...
This system was quite popular in the 1940s and 1950s and
was used on the venerable Volkswagen beetle to support the front
wheels
...
You can also support the end of the trailing arm with a coil spring, or
even a coil over-shock suspension system that can probably produce the
smoothest ride of any track system (Figure 5-10)
...
The advantage of the coil
Chapter 5
Tracked Vehicle Suspensions and Drivetrains
Figure 5-9
177
Trailing arm
Figure 5-10 Trailing arm and
coil springs
spring over the torsion suspension is that the load is supported by the
spring very close to the load point, reducing forces and moments in the
trailing arm
...
178
Chapter 5
Tracked Vehicle Suspensions and Drivetrains
Figure 5-11 Leaf spring rockers
A simple variation of the rocker system is to replace the rockers with
leaf springs (Figure 5-11)
...
The springs are usually very stiff since the rocker
arm’s swinging motion still allows the wheels to make large motions
...
Having road wheels
on both sides of the spring reduces the twisting moment produced by
having wheels on only one side
...
TRACK SYSTEM LAYOUTS
One-Track Drivetrain
What would seem to be the simplest track layout is one that uses only
one track
...
The most common commercially available
form of a one-track vehicle is the snow mobile
...
The track on a snowmobile is quite wide to lower ground pressure as much as practicable, but
there is no reason why a narrower track can’t be used with the wheeled
layout
...
The first problem can be reduced by
powering the wheels
...
Figure 5-12 shows the typical ramped-front
track common on snowmobiles because they normally do not go backwards
...
It would be an interesting experiment to build a one-track, twowheel drive, Ackerman steered robot and test its mobility
...
In its basic form, it is
simple, easy to understand, and relatively easy to construct
...
Compact designs have the motor mounted substantially inside the track and attached directly to the drive sprocket
...
Figure 5-13 shows a
two-track layout, with drive motors, gearboxes, fixed track guide blades,
and non-ramped tracks
...
180
Chapter 5
Tracked Vehicle Suspensions and Drivetrains
Figure 5-13 Basic two-track
layout
Two-Tracked Drivetrains with Separate Steering Systems
A more complex, but less capable, layout is to have the two tracks driven
through a differential, and the robot steered by a conventional set of
wheels mounted in front of the tracks
...
These trucks (Figure 5-14) were called
half-tracks
...
An unusual variation of the two-track layout is to place the two tracks
inline, one in front of the other (Figure 5-15)
...
The tracks have to be supported from both sides, like on a snow mobile
...
This system also benefits from the trick of making the center of each
track a little lower than the ends
...
This
system has great mobility, but like the half-track, cannot turn in place
...
The two tracks could either each carry their own chassis, or a single chassis could be attached to the universal joint with the outer ends
of the track sections suspended to the chassis with a sprung or active
suspension
...
Adding more
tracks necessarily means more moving parts, but it also usually means
making the vehicle longer
...
This last criteria almost exclusively means a
reconfigurable layout, one where the length is longer when that is
needed, but can reconfigure into a shorter length when that is needed
...
Figure 5-16 shows the general layout of iRobot’s Urbie telerobotic
platform
...
They are
powered by the same motors that power the main tracks, and always turn
with them
...
The center of gravity of Urbie is located ahead of the center of the
vehicle so, with the flippers extended, Urbie can cross crevasses that are
wider than half the length of the basic vehicle
...
When the flippers are rotated around so they become very large
ramps, Urbie can climb over obstacles that are higher than the overall
height of the basic track
...
This makes the
robot much taller and allows a strategically placed camera to see over
short walls
...
With two actuators to power each of the
four tracks independently and a fifth actuator to power the pivot joint a
184
Chapter 5
Tracked Vehicle Suspensions and Drivetrains
very capable layout results
...
This trick raises the entire chassis, but it also offloads the weight of the
robot from the track guide blades, increasing rolling efficiency when
high traction is not needed
...
There are two basic layouts for four-tracked vehicles
...
The two modules must be able to move in several directions
relative to each other
...
The simplest connection that allows all three degrees of freedom is the
ball joint
...
This turns out to be tricky
...
A universal joint has a greater range of motion, and
is easier to use if the joint is to be powered
...
This steering method makes this layout very agile
...
It is even amphibious,
propelled through the water by the tracks
...
Nevertheless, it is a very capable layout
...
The
tracks are driven through limited slip differentials, allowing the inner and
outer tracks in each module to travel at different speeds just like in an
Ackerman steered wheeled vehicle
...
It is an extension of the
Urbie design, but was actually invented before Urbie’s layout
...
This layout allows the vehicle to stand up like the one
Chapter 5
Tracked Vehicle Suspensions and Drivetrains
Figure 5-18 Six-tracked, double flippers
shown in Figure 5-17
...
185
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...
Click here for Terms of Use
...
T
he Romans extensively used two wheeled carts, pulled by horses
...
The two wheels on the cart were mounted on the same axle, but
were attached in a way that each wheel could rotate at whatever speed
was needed depending on whether the cart was going straight or around
a corner
...
It became apparent (though it is unclear if it was the
Romans who figured this out) that this caused problems when trying to
turn
...
The simplest method for
fixing this problem was to mount the front set of wheels on each end of
an axle that could swivel in the middle (Figure 6-1)
...
Pulling on the tongue aligned the front
wheels with the turn
...
This method worked
well and, indeed, still does for four wheeled horse drawn buggies and
carriages
...
Vehicles were hard to control at speeds much faster
than a few meters per second
...
An attempt
around this problem was to make the axle long enough so that the front
wheels didn’t hit the cart’s sides when turning, but it was not very convenient having the front wheels wider than the rest of the vehicle
...
This
saved space and was easier to control and it appeared to work well
...
He
teamed with Rudolph Ackerman, whose name is now synonymous with
this type of steering geometry
...
It
turns out there are many other methods for turning corners, some intuitive, some very complex and unintuitive
...
Turning requires some change in this system
...
Turn the front wheel to a new heading and it
rolls in that direction
...
Straighten out the
front wheel, and the bicycle goes straight again
...
This important
detail, shown in Figure 6-3, occurs on all wheeled and tracked vehicles
...
If there are wheels on either side,
they must be able to rotate at different speeds
...
Driving straight in one direction requires at least one single direction
actuator
...
Driving straight in both directions requires at least one bidirectional actuator or two single-direction actuators
...
Add one more simple single-direction motor to the wind-up
toy, and it can turn to go in any new direction
...
In practice, this turns out to be quite limiting, at least partly because it
is tricky to turn in place with only two single direction actuators, but
mostly because there aren’t enough drive and steer options to pick from
to get out of a tight spot
...
The simplest statically stable vehicle has either three wheels or two
tracks, and the simplest power system to drive and steer uses only two
single-direction motors
...
Two single-direction motors powering a combined drive/steer wheel
or combined drive/steer track with some other passive wheels or
tracks
2
...
The common tricycle uses this exact layout, but so do some automatic guided
vehicles (AGVs) used in automated warehouses
...
This layout works well for the AGV application
because the warehouse’s floor is flat and clean and the aisles are
designed for this type of vehicle
...
There are many versions of AGVs—the most complicated types have
four drive/steer modules
...
Wheel modules
Chapter 6
Steering History
Figure 6-4
track
for AGVs are available independently, and come in several sizes ranging
from about 30 cm tall to nearly a meter tall
...
It can be used on tracked vehicles, but without being able to drive
the tracks backwards, the robot can not turn in place and must turn about
one track
...
This may be
acceptable for some applications, and the simplicity of single direction
electronic motor-driver may make up for the loss of mobility
...
The Next Step Up
The next most effective steering method is to have one of the actuators
bi-directional, and, better than that, to have both bi-directional
...
This steering geometry (Figure 6-5a, 6-5b) is called differential
steering
...
On some ultra-simple robots, like the Rug Warrior, the third
wheel does not even swivel, it simply rolls passively on a fixed axle and
skids when the robot makes a turn
...
As discussed in the chapter on wheeled vehicles, this is also the steering method used on some four-wheel loaders like the well-known
Bobcat
...
This steering method is so
effective and robust that it is used on a large percentage of four-, six-, and
even eight-wheeled robots, and nearly all modern tracked vehicles
whether autonomous or not
...
This is where the name “skid steer” comes
from
...
Placing the wheels close together or making the tracks
shorter reduces this skidding at the cost of fore/aft stability
...
Several all-terrain vehicle manufacturers have made six-wheeled vehicles with this very slight offset, and the concept can be applied to indoor
hard-surface robots also
...
The single wheel drive/steer module discussed earlier and shown on a
tricycle in Figure 6-6 can be applied to many layouts, and is, in general,
an effective mechanism
...
This is usually
accomplished by putting the drive motor, with a gearbox, inside the
wheel
...
These wires must go through the steering mechanism, which is easier
than passing power mechanically through this joint
...
This requires an electrical slip ring in the steering
joint
...
One type of mechanical solution to the problem of powering the
wheel in a drive/steer module has been done with great success on several sophisticated research robots and is commonly called a syncrodrive
...
All are driven and steered in unison, synchronously
...
As can be seen in the sketch, the drive
motor is directly above the wheel
...
This layout is probably the best to use if relying heavily on dead reckoning because it produces little rotational error
...
The four-wheeled
layout is not well suited for anything but flat terrain unless at least one
wheel module is made vertically compliant
...
Chapter 6
Steering History
197
Figure 6-8 Drive/steer module
with vertical compliance
All-terrain cycles (ATCs), when they were legal, ran power through a
differential to the two rear wheels, and steered with the front wheel in a
standard tricycle layout
...
Mobility was moderately good with a human driver, but
was not inherently so
...
Four wheels
make them much more stable, and many are produced with four wheel
drive, enhancing their mobility greatly although they cannot turn in
place
...
If a
mobility system in their size range is needed, they may be a good place
to start
...
Quads are manufactured by a number of companies
and are available in many size ranges offering many different mobility
capabilities
...
Most are based on variations of the types already mentioned,
but one is quite different
...
This layout is
common on large industrial front-end loaders and provides very good
steering ability even though it cannot turn in place
...
Power is transferred to the wheels from a single motor and differentials in the industrial version, but mobility would be increased if each
wheel had its own motor
...
Click here for Terms of Use
...
T
here are no multi-cell animals that use any form of continuously
rolling mechanism for propulsion
...
Walking must be the best way
to move then, right? Why aren’t there more walking robots? It turns out
that making a walking robot is far more difficult than making a wheeled
or tracked one
...
Stability is a major concern in walking robots, because they tend to be
tall and top heavy
...
They are statically stable
...
” They fall over if they stop at the wrong point in a step
...
An example of a dynamically-stable walker in nature is, in fact, any
two-legged animal
...
Two-legged dinosaurs,
humans, and birds are remarkably capable two legged walkers, but any
child that has played Red-light/Green-light or Freeze Tag has figured out
that it is quite difficult to stop mid-stride without falling over
...
Some animals with more than two legs are also dynamically stable
during certain gait types
...
The only time
they are statically stable is when they are standing absolutely still
...
When they want to
stop, they must plan where to put each foot to prevent falling over
...
Cats, on the other hand, can walk with
a gait that allows them to stop at any point without tipping over
...
This is called statically-stable
independent leg walking
...
They stand on three legs
while the forth leg is moved around until it finds, by feel, a suitable
place to set down
...
Animals have highly developed sensors, a highly evolved brain, and fantastically high power-density muscles, that allow this variety of motion
control
...
The design of dynamically-stable, walking mobile robots requires an
extensive knowledge of fairly complicated sensors, balance, high-level
math, fast-acting actuators, kinematics, and dynamics
...
The rest of this chapter will focus on the second
major category, statically-stable walkers
...
There are
three major techniques for moving legs on a mobile robot
...
Pneumatic
cylinders come in practically any imaginable size and have been used in
many walking robot research projects
...
Linear actuators have the advantage that they can be used directly as
the leg itself
...
This concept has been used to make robots that use
Cartesian and cylindrical coordinate walkers
...
Chapter 7
Direct-drive rotary actuators usually have to be custom designed to
get torque outputs high enough to rotate the walker’s joints
...
They are very easy to control accurately and facilitate a modular
design since the actuator can be thought of conceptually and physically
as the complete joint
...
Cable-driven joints have the advantage that the actuators can be
located in the body of the robot
...
In applications where the leg is very long or thin, this is critical
...
Cable management is a big job and can consume
many hours of debug time
...
There are so many varieties of layouts only the basic designs are
discussed
...
The simplest leg has a single joint at the hip that allows it to swing up
and down (Figure 7-1)
...
Since the joint is
already near the body, using a cable drive is unnecessary
...
This is necessary because the orientation of the foot is not controlled and the ball
gives the same contact surface no matter what orientation it is in
...
The following four figures show two-DOF legs with the different
actuation methods
...
Figure 7-2 shows that linear actuators make the
legs much wider in one dimension but are the strongest of the three
...
The actuator can be replaced with a passive link, making this a one-DOF leg whose second segment doesn’t
swing out as much as the leg shown in Figure 7-2
...
The cable driven layout (Figure 7-5) takes up the least volume and
has no exposed actuators
...
Their biggest drawback is that they need to be big to get
enough power to be useful
...
This robot, and several others like it, use simple straight
legs
...
To turn the two-DOF linear actuator layout into a three-DOF, a universal joint can be added at the hip joint
...
Figure 7-6 shows a simple
design for this universal hip joint
...
The three-DOF rotary actuator leg (Figure 7-7) adds a knee joint to
the Genghis layout for improved dexterity and mobility
...
It is quite difficult to drive a
two-DOF hip joint with cables, but it can be done
...
WALKING TECHNIQUES
Statically-stable walkers are easier to implement than dynamically-stable walkers
...
There are three useful sub groups: wave
walking, independent leg walking, and frame walking
...
Independent leg walking is used by just about every four, six, and eight-leg walker, although
some simplify things by moving their legs in groups for certain speeds or
motions
...
As we shall see, frame walking can be a very effective mobility method for a mobile robot
...
The robot lifts its rear-most set of legs and
swings them forward and sets them down, then the next set of legs is
moved similarly
...
The process can be
smoothed out some by averaging the position of the body as each set of
legs moves forward
...
Independent Leg Walking
Virtually all other legged animals in nature that don’t use wave walking
can control each leg independently
...
Figures 7-8 and 7-9 show four- and six-legged
walkers with three rotary-actuated joints in each leg
...
The four- and six-legged versions
Chapter 7
Walkers
209
Figure 7-8 Independent leg
walker, four legs, twelve DOF
Figure 7-9 Independent leg
walker, six legs, eighteen DOF
210
Chapter 7
Walkers
Figure 7-10 Extra wide feet
provide two-legged stability
theoretically have very high mobility
...
Although it would seem impossible to build a two-legged staticallystable robot, there is a trick that toys and some research robots use that
gives the robot the appearance of being dynamically stable when they are
actually statically stable
...
In effect, foot size reduces the required accuracy
of foot placement so that the foot can be placed anywhere it can reach
and the robot will not fall over
...
Two-legged walking, with oversized
and overlapping feet, is simply picking up the back foot, bringing it forward, and putting it down
...
Each leg must
have at least three DOF, and usually requires four
...
Notice that even with only two legs and no ability to turn, this
layout requires six actuators to control its six degrees of freedom
...
Although in the final implementation it may have eight DOF and its
Chapter 7
Walkers
211
knees bend backwards, it is familiar to the designer
...
Frame Walking
The third general technique for walking with a legged robot is frame
walking
...
Walking is
accomplished by raising the legs of one frame, traversing that frame forward relative to the frame whose legs are still on the ground, and then
setting the legs down
...
The coupling between the two frames usually has a second rotating
DOF to facilitate turning, rather than by adding a rotation in each leg
...
In nature, an inchworm uses a form of frame walking
...
The coupling is
the leg-less section in between
...
Unfortunately for
robot designers, the inchworm also has the ability to grasp with its claw-
Figure 7-11 Mechanism for
frame traversing and rotating
212
Chapter 7
Walkers
Figure 7-12 Traversing/rotating
frame eight-leg frame walker with
single-DOF legs
Figure 7-13 Eight-leg frame
walker with two-DOF legs
Chapter 7
Walkers
like feet, making it quasi-statically stable
...
This layout has 10 DOF
...
The actuator
count goes up to 17 with this layout
...
Still, 17 actuators is a lot to control and
maintain
...
This joint
would have a linear motion for traversing, a rotary motion for steering,
and a vertical motion to lift one frame and then the other
...
Perhaps the best is a six-leg tripodgait frame walker with one linear DOF in each leg and two in the coupling, bringing the total DOF to eight
...
Figure 7-14 Six-legged
tripod-frame walker with
single-DOF legs
213
214
Chapter 7
Walkers
ROLLER-WALKERS
A special category of walkers is actually a hybrid system that uses both
legs and wheels
...
There doesn’t seem to be any widely accepted term
for these hybrids, but perhaps roller walkers will suffice
...
The
machine is a logging machine that can stand level even on very steep
slopes
...
Because of its slow traverse
speed, it is transported to a job sight on the back of a special truck
...
Certain terrain types may be more easily traversed with this
unusual mobility system
...
If contemplating designing a roller walker, it
may be more effective to think of the mobility system as a wheeled vehicle with the wheels mounted on jointed appendages rather than a walking vehicle with wheels
...
This limitation is easily overcome by wheels
...
The ability to raise a wheel, or reconfigure the vehicle’s geometry to
allow a wheel to easily drive up a high object, reduces this limitation
...
There are no
figures included here, but the reader is urged to investigate these web
sites:
http://mozu
...
titech
...
jp/
http://www
...
go
...
html
FLEXIBLE LEGS
A trick taken from animals and being tested in mobility labs is the use of
flexible-leg elements
...
They are simple, extremely robust mobility systems that use independent
leg-walking techniques
...
The tires are replaced with several long
flexible arms, like whiskers, extending out from the wheel
...
They have very high mobility, able to
climb steps nearly as high as the legs are long
...
Figure 7-15 shows the basic concept
...
This
idea is taken from studying cockroaches whose legs act like paddles
when scrambling over bumpy terrain
...
• Using a statically-stable design requires far less expertise in several
fields of engineering and will therefore dramatically increase the
chances of success
...
• Studies have shown six legs are optimal for most applications
...
216
Chapter 7
Walkers
Walkers have inherently more degrees of freedom, which increases
complexity and debug time
...
Roller walkers offer the
advantages of both walking and rolling and in a well thought out design
may prove to be very effective
...
Some are variations on
what has been presented here
...
In general, with
the possible exception of the various roller walkers, they share two common problems, they are complicated and slow
...
Humans have figured out how to make the wheel and
its close cousin, the track
...
The fastest land vehicle has hit more than
seven times that speed
...
There
are no human-made locomotion devices that can even come close to a
goat’s or cockroach’s combined speed and agility
...
Her most intelligent product has not yet been able to produce anything
that can match the mobility of several of her most agile products
...
For the person just getting started in robotics, or for
someone planning to use a robot to do a practical task, it is suggested to
start with a wheeled or tracked vehicle because of their greater simplicity
...
Chapter 8
Pipe Crawlers
and Other
Special Cases
Copyright © 2003 by The McGraw-Hill Companies, Inc
...
This page intentionally left blank
...
One particularly interesting problem is inspecting and repairing pipelines
from the inside
...
The robot can be placed inside the pipe at a convenient location by simply separating the pipe at an existing joint or
valve
...
Pipe
crawlers already exist that inspect, clean, and/or repair pipes in nuclear
reactors, water mains under city streets, and even down five-mile long
oil wells
...
The vehicle might be required to go around very sharp bends, through
welded, sweated, or glued joints
...
Some
pipes transport slippery oil or very hot water
...
Some pipes change size
along their length or have sections with odd shapes
...
In fact, pipe
crawling robots are frequently completely autonomous because of the
distance they must travel, which can be so far that it is nearly impossible
to drag a tether or communicate by radio to the robot when it is inside the
pipe
...
All of these problems place unusual and
difficult demands on the crawler’s mechanical components and locomotion system
...
Sometimes mechanical tools are employed to scrape off surface rust or
other corrosion, plug holes in the pipe wall, or, in the case of oil wells,
blow holes in the walls
...
The pipe crawler mechanisms shown in the following figures give an
overview of the wide variety of methods of locomoting inside a pipe
...
In addition to those shown in this book, there are
many other techniques and layouts for robots designed to move about in
pipes or tanks
...
The crawler must still be able to steer to some degree because it must
negotiate corners in the pipes, but also because it must stay on the bottom of the pipe or it may swerve up the walls and tip over
...
The wheels of
wheeled pipe crawlers are specially shaped to conform to the round
shape of the pipe walls, on tracked crawlers the treads are tilted for the
same reason
...
Figures 8-1 and 8-2 show two examples
...
There are
two ways to do this, reaching across the pipe to push out against the
pipe’s walls, or putting magnets in the tires or track treads
...
Some pipes are too soft to
withstand the forces of tires or treads and must use a system that spreads
the load out over a large area of pipe
...
Going straight up a vertical pipe would at first glance seem
simple, but as the crawler travels through the pipe, it tends to corkscrew
because of slight misalignment of the locomotors or deformities on the
pipe’s surface
...
One solution to this problem is to attach the tether
to the chassis through a rotary joint, but this introduces another degree of
freedom that is both complex and expensive
...
222
Chapter 8
Pipe Crawlers and Other Special Cases
Traction Techniques for Vertical Pipe Crawlers
There are at least four tread treatments designed to deal with the traction
problem
...
The surface conditions of the pipe
walls and any active or residual material in the pipe should also be investigated and understood well to assure the treatment or material is not
chemically attacked
...
Galvanized pipe
would be scratched leading to corrosion, and some hard plastic pipe
material might stress crack along a scratch
...
Spiked wheels do find use in oil wells,
which can stand the abuse
...
The advantage of magnetic wheels is that the wheels pull themselves
against the pipe walls; the disadvantage is that the pipe must be made of
a ferrous metal
...
They
also have the advantage that the crawler can be smaller since it no longer
must reach across the whole of a large pipe
...
Tires made of abrasive impregnated rubber hold well to iron and plastic pipe, but these types loose effectiveness if the abrasive is loaded with
gunk or worn off
...
High-friction rubber treads work in many applications, but care must
be taken to use the right rubber compound
...
Some
compounds may also corrode rapidly in fluids that might be found in
pipes
...
Chapter 8
Pipe Crawlers and Other Special Cases
Figure 8-3
Wheeled Vertical Pipe Crawlers
Wheeled pipe crawlers, like their land-based
cousins, are the simplest type of vertical pipe
crawlers
...
Practical layouts range from three to
six or more wheels, usually all driven for maximum traction on frequently very slippery pipe
walls
...
Figure 8-3 shows the simplest layout required for moving up vertical pipe
...
The next best layout adds a fourth wheel
...
The center linear degree of freedom can be actuated to
keep the vehicle aligned in a pipe
...
They exert much less pressure on any given spot due to their
larger footprint
...
Spreading out the force of the mechanism that pushes the locomotor sections against the walls also means that the radial force itself can be
higher, greatly increasing the slip resistance of the vehicle
...
OTHER PIPE CRAWLERS
For pipes that cannot stand high internal forces, another method must be
used that further spreads the forces of the crawler over a larger area
...
One uses balloons, the other linear extending legs
...
The rubber bladders cover a very large
section of the pipe and only low pressure inside the bladder is required to
Chapter 8
Pipe Crawlers and Other Special Cases
Figure 8-6 Inchworm
multi-section roller walker
get high forces on the pipe walls, generating high-friction forces
...
This coupling is also the inchworm section, and forward motion of the
entire vehicle is done by retracting the front bladder, pushing it forward,
expanding it, retracting the rear section, pulling it towards the front section, expanding it, then repeating the whole process
...
A concept that uses this design was proposed for moving around in the flexible Kevlar pipes of the Space Shuttle
...
The large pipes inside
nuclear reactor steam pipes have sensors built into the pipes that extend in
from the inner walls nearly to the center of the pipe
...
The robot has to have a shape
that can get around these protrusions
...
Figure 8-6
shows a minimum layout of this concept
...
CMU’s asbestos removing external pipe walker, BOA, is just such a
vehicle
...
BOA is a frame walker
...
RedZone Robotics’ Tarzan, an in-tank vertical pipe walking arm, is an
example of a very unusual concept proposed to move around inside a
tank filled with pipes
...
Unlike the ISS arm, Tarzan must work against
the force of gravity
...
The arm is allhydraulic, using both rotary actuators and cylinders
...
Imagine the complexity of controlling 18 actuators and
managing a tether all on an arm that is walking completely out of view
inside a tank filled with a forest of pipes!
SNAKES
In nature, there is a whole class of animals that move around by squirming
...
Almost by definition, squirming requires many actuators, flexible members, and/or clever mechanisms to couple the segments
...
The disadvantage is that the number of actuators and high moving parts count
...
The
reader is encouraged to search the web to learn more of these varied and
sometimes strange solutions to the problem of moving around in uncommon environments like inside and outside pipes, inside underground
storage tanks, even, eventually, inside the human body
...
Click here for Terms of Use
...
WHAT IS MOBILITY?
N
ow that we have seen many methods, mechanisms, and mechanical
linkages for moving around in the environment, let’s discuss how to
compare them
...
There needs to
be some way to even the playing field so it is the effectiveness of the
mobility system that is being compared regardless of its size
...
Then, the many mobility challenges the outdoor environment presents will be investigated
...
THE MOBILITY SYSTEM
To level the playing field, the mobility systems being compared have to
be scaled to be effectively the same size
...
Since most robots are battery powered,
energy efficiency must also be included in the comparison because there
are advantages of shear power in overcoming some obstacles that battery
powered vehicles simply would not have
...
In some situations, simply going at an
obstacle fast can aid in getting over it
...
One last interesting criteria that bears mentioning is the vehicle’s
shape
...
However, for environments that are
crowded with obstacles that cannot be driven over, where getting around
things is the only way to proceed, a round or rounded shape is easier to
maneuver
...
This ability does not exist for vehicles
that are nonround
...
For most outdoor environments, simply rounding the corners somewhat is enough to
aid mobility
...
Size
Overall length and height of the mobility system directly affect a vehicle’s
ability to negotiate an obstacle, but width has little affect, so size is, at
least, mostly length and height
...
The third dimension, width, seems to be an important
characteristic of size because a narrower vehicle can potentially fit through
smaller openings or turn around in a narrower alley
...
For some obstacles, just being taller is enough to negotiate them
...
A simple way to compare these two
parameters together would be helpful
...
The length/height ratio gives an at-a-glance idea of how suited a system
is to negotiating an environment that is mostly bumps and steps or one
that is mostly tunnels and low passageways
...
It is mostly independent of the other size parameters, since the width can be expanded to increase the usable volume of
the robot without affecting the robot’s ability to get over or under obstacles
...
This is set by the expected minimum required turning width as determined by environmental constraints
...
A rule of thumb to use when figuring out the robot’s width is to
make it about 62 percent of the length of the robot
...
These pieces of the robot
are independent of the function of the robot, but take up volume
...
As will be
seen later, weight is critical, so the total mass of the mobility system’s
components needs to be included
...
Efficiency
Another good rule of thumb when designing anything mechanical is that
less weight in the structure and moving parts is always better
...
If there were no weight restriction and little
or no size restriction, then larger and therefore heavier wheels, tracks, or
legs would allow a vehicle to get over more obstacles
...
• The vehicle can be transported more easily
...
• Maintenance that requires lifting the vehicle is easier to perform and
less dangerous
...
For all these reasons, smaller and lighter suspension and drive train
components are usually the better choice for high mobility vehicles
...
The three axes of a
standard coordinate system are labeled X, Y, and Z, but for a mobile robot,
these are modified since most robot’s turn before moving sideways
...
A
robot can be doing any one, two, or all three at the same time, but the
power requirements of each is so different that they can easily be listed
independently by magnitude
...
This does not apply to all mobility systems but is a good general rule
...
The systems in this book
mostly focus on systems designed for the unpredictable and highly varied
outdoor environment, an environment that includes large variations in
temperature, ground cover, topography, and obstacles
...
Hot and cold may not seem related to mobility, but they are in that the
mobility system must be efficient so it doesn’t create too much heat and
damage itself or nearby components when operating in a desert
...
As for ground cover, the mobility system
might have to deal with loose dry sand, which can get everywhere and
rapidly wear out bearings, or operate in muddy water
...
The
mobility system will almost definitely have to travel over some or all of
those topographical challenges
...
This means that the mobility system’s effectiveness should be evaluated using the aforementioned parameters
...
The four categories of temperature, ground cover, topography, and
obstacles can be either defined clearly or broken up into smaller more
easily defined subcategories without ending up with an unmanageably
large list
...
Thermal
Temperature can be divided simply into the two extremes of hot and
cold
...
A more efficient machine will have fewer
problems in hot climates, but better efficiency, more importantly, means
battery powered robots will run longer
...
A useful
pair of temperature-related terms to think about in a comparison of
mobility systems would then be efficiency and pinch points
...
Sand is just sand no matter what size the vehicle is (except for tiny robots of course), and mud is still mud
...
Lower ground pressure
reduces the amount the driving element sinks, thereby reducing the
amount of power required to move that element
...
Robots are infrequently required to be tow trucks, but this may change
as the variety of tasks they are put to widens
...
The effect of ground pressure on hill climbing can be
overcome with careful tread design (independent of the mobility system), which combines the benefits of low ground pressure with high
traction
...
The theory that sand and mud are not scalable can’t be applied to
grass however, because tall field grass really is significantly larger than
short lawn grass
...
These problems can be roughly related to ground pressure since a lighter
pressure system would tend to ride higher on wet grass, reducing its tangling problems
...
Topography
Topography can be scaled to any size making it very simple to include
...
The problem with angle of slope,
though, is that it can be more a function of the friction of the material and
the tread shape of whatever is in ground contact, than a function of the
geometry of the mobility system
...
Negotiable slope angle is therefore important, but it
should be assumed that the material in ground contact is the same no
matter what type of mobility system is used
...
The effectiveness of the mobility system could be judged almost entirely by how
high, relative to its elevation area, an obstacle it can negotiate
...
• Mobility system overall height to negotiable obstacle height
• System length to negotiable obstacle height
• System elevation area to negotiable obstacle height
The comparison obstacle parameters can be defined to be the height of
a square step the system can climb onto and the height of a square topped
wall the system can climb over without high centering, or otherwise
becoming stuck
...
Negotiable chasm
width is mostly a function of the mobility system’s length, but some
clever designs can vary their length somewhat, or shift their center of
gravity, to facilitate crossing wider chasms
...
For those that are fixed, use the overall
length
...
This is important because a mobility system with a small turning radius is more likely
to be able to get out of or around confining situations
...
This is in contrast to ratings
given by some manufacturers that give turning radius as the radius of a
circle defined as the distance from the turning point to the center of the
vehicle width
...
A turning ability parameter must also show how tightly a vehicle can
turn around a post, giving some idea how well it could maneuver in a forest of closely spaced trees
...
Chapter 9
Comparing Locomotion Methods
COMPLEXITY
A more nebulous comparison criteria that must be included in an evaluation of any practical mechanical device is its inherent complexity
...
Ball or roller bearings are usually counted as one part
of a joint although there may be 10s of balls or rollers moving inside the
bearing
...
A second method is to count the number of actuators since their number relates to the number of moving parts and they are the usually the
source of greatest wear
...
The first method is probably a
better choice because robots are likely to be moving around in completely unpredictable environments and any moving part is equally susceptible to damage by things in the environment
...
They are velocity of the moving vehicle and cost of the locomotion system
...
These loads are difficult to calculate precisely because the terrain can be so unpredictable
...
Usually the simulation program’s predictions are proven
inaccurate to a significant degree
...
It is assumed that slowing is
an acceptable way to increase mobility, and that slowing can be done
with any suspension design
...
Cost can be related to size, weight, and complexity
...
The design time to get to the simplest, lightest design that meets the criteria may be longer, but the end
cost will usually be less
...
THE MOBILITY INDEX COMPARISON METHOD
Another, perhaps simpler, method is to create an index of the mobility
design’s capabilities listed as a set of ratios relating the mobility system’s
length, height, width, and possibly complexity, to a small set of terrain
parameters
...
Calculating the vehicle’s ground pressure would cover mobility in sand
or mud
...
No doubt, some mobility system designs will have very
high indexes in some categories, and low indexes in others
...
These six, however, should give a
fairly complete at-a-glance idea of how well a certain design will perform in many situations
...
A good place to start for the size ratios
is to make the width 62 percent of the length, and the height one quarter
of the length
...
The next step is to define the mobility requirements, allowing substantial leeway if the operating environment is not well known
...
•
•
•
•
•
•
Step or wall height
Minimum tunnel height
Crevasse width
Maximum terrain slope
Minimum spacing of immovable objects
Maximum soil density
All of these need to be studied carefully to aid in determining the most
effective mobility system layout to use
...
When this study is completed, selecting and designing the mobility
system is then a combination of scaling the system to the robot’s box
size, and meeting the mobility constraints
...
The more
information that can be obtained about the operating environment, the
more likely the robot will be successful
...
A generic rule of thumb for mobility system design can be extracted
from the investigations done in this chapter
...
If all these are maximized, they will make your robot a high
mobility robot
...
Chapter 10
Manipulator Geometries
Copyright © 2003 by The McGraw-Hill Companies, Inc
...
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...
A manipulator is
an assembly of segments and joints that can be conveniently
divided into three sections: the arm, consisting of one or more segments
and joints; the wrist, usually consisting of one to three segments and
joints; and a gripper or other means of attaching or grasping
...
Industrial robots are stationary manipulators whose base is permanently attached to the floor, a table, or a stand
...
There is a section covering them as a group because they demonstrate a
wide variety of sometimes complex manipulator geometries
...
A few
unusual manipulator designs are also included
...
The task of positioning, orienting,
and doing something useful based solely on input from frequently inadequate sensors is extremely difficult
...
Nevertheless, it is theoretically possible to make a truly
autonomous manipulator and their numbers are expected to increase dramatically over the next several years
...
There are layouts where
the wrist or arm are not distinguishable, but for simplicity, they are
treated as separate entities in this discussion
...
Each joint allows one degree of freedom of motion
...
In other words, there must be at
least three bending or extending motions to get position, and three twisting or rotating motions to get orientation
...
They almost always end up being divided into arm and wrist
...
Unfortunately, there is no easy labeling system for the arm itself
since there are many ways to achieve gross positioning using extended
segments and pivoted or twisted joints
...
A good example of a manipulator is the human arm, consisting of a
shoulder, upper arm, elbow, and wrist
...
It allows forward and backward motion, which is the second DOF, but it also allows
rotation, which is the third DOF
...
The wrist pitches up and down, yaws left and right, and rolls, giving
three DOFs in one joint
...
Theoretically the best wrist joint geometry is a ball joint,
but even in the biological world, there is only one example of a true full
motion ball joint (one that allows motion in two planes, and twists 360°)
because they are so difficult to power and control
...
On a mobile robot, the chassis can often substitute for one or two of
the degrees of freedom, usually fore/aft and sometimes to yaw the arm
left/right, reducing the complexity of the manipulator significantly
...
At the other extreme,
there are arms in the conceptual stage that have more than fifteen DOF
...
Wrists are shown separately
...
First, let’s look
at an unusual manipulator and a simple mechanism—perhaps the simplest mechanism for creating linear motion from rotary motion
...
It is based on
a flexible cable bundle carrier called E-Chain and has unique properties
...
This
allows it to cantilever out flat creating a long arm, but stored rolled up
like a tape measure
...
Figure 10-1 shows a
simplified line drawing of E-chain’s allowable motion
...
A connecting rod length to / crank radius ratio of four to one produces nearly linear motion of the slider over most of its stroke and is,
therefore, the most useful ratio
...
The motion of the slider is not linear in velocity over its full range of
motion
...
This effect can be put to good use as a
clamp
...
The slider crank
should be considered if linear motion is needed in a design
...
The equation for
calculating how far the slider travels as the crank arm rotates about the
motor/gearbox shaft is: x = L cos Ø+ r cos Ø
...
They are named for the shape of the volume that the manipulator can reach and orient the gripper into any position—the work envelope
...
Some use all sliding motions, some use only pivoting joints, some use both
...
Pivoting joints have the drawback of preventing the manipulator from
reaching every cubic centimeter in the work envelope because the elbow
cannot fold back completely on itself
...
On a
robot, it is frequently required for the manipulator to fold very compactly
...
180°
...
Many industrial robots and teleoperated vehicles use this or a
similar design for their manipulators
...
This means the
manipulator arm works from inside or from one
side of the work envelope
...
As shown in Figure
10-4, gantry manipulators are Cartesian or rectangular manipulators
...
In
fact, that is how it is controlled and how the
working end moves around in the work envelope
...
Mounted on the front of a robot, the first two
DOF of a cantilevered Cartesian manipulator can
move left/right and up/down; the Y-axis is not
necessarily needed on a mobile robot because the
robot can move back/forward
...
Though not
the best solution to the problem of working off
the front of a robot, it will work
...
CYLINDRICAL
The second type of manipulator work envelope is
cylindrical
...
While they are very
simple to picture and the work envelope is fairly
intuitive, they are hard to implement effectively
because they require two linear motion segments,
both of which have moment loads in them caused
by the load at the end of the upper arm
...
e
...
On a robot, the angle of the base can simply be the angle of the chassis of the robot itself,
leaving the height and extension of the second
segment
...
A second geometry that still has a cylindrical
work envelope is the SCARA design
...
This design has good stiffness in the vertical direction, but some compliance in the horizontal
...
A SCARA manipulator
replaces the second telescoping joint with two
vertical axis-pivoting joints
...
Figure 10-6 Three-DOF cylindrical manipulator
Figure 10-7 A SCARA manipulator
247
248
Chapter 10
Manipulator Geometries
POLAR OR SPHERICAL
The third, and most versatile, geometry is the
spherical type
...
In reality, though, it is difficult to reach everywhere
...
The most basic has a rotating base that carries an arm segment that can
pitch up and down, and extend in and out
(Figure 10-8)
...
Figures 10-10,
10-11, and 10-12 show variations of the spherical geometry manipulator
...
In
order to orient the gripper to the correct angle, in all three axes, a second
set of joints is usually required—the wrist
...
They must
pitch, roll, and yaw respectively
...
Most wrists consist of three separate joints
...
The order of the degrees of freedom in a wrist has a
large effect on the wrist’s functionality and should be chosen carefully,
especially for wrists with only one or two DOF
...
For this reason it is commonly called an
end-effector, but it is also called a gripper since that is a very common
task for it to perform when mounted on a robot
...
Closing too tightly on an object and crushing it is a major
problem with autonomous grippers
...
Even
for semi-autonomous robots where a human controls the manipulator,
using the gripper effectively is often difficult
...
Their mass, size, shape, and strength,
etc
...
Some objects require grippers that
have many jaws, but in most cases, grippers have only two jaws and
those will be shown here
...
The most basic
type has two simple jaws geared together so that turning the base of one
Figure 10-16 Simple direct
drive swinging jaw
Chapter 10
Manipulator Geometries
253
Figure 10-17 Simple direct
drive through right angle worm
drive gearmotor
turns the other
...
The jaws can be moved
through a linear actuator or can be directly mounted on a motor gearbox’s output shaft (Figure 10-16), or driven through a right angle drive
(Figure 10-17) which places the drive motor further out of the way of the
gripper
...
Figure 10-18
Rack and pinion drive gripper
Figure 10-19
Reciprocating lever gripper
254
Chapter 10
Manipulator Geometries
Figure 10-20 Linear actuator
direct drive gripper
A more effective jaw layout is the parallel jaw gripper
...
Another way to get parallel motion is to use a linear actuator to
move one or both jaws directly towards and away from each other
...
Figure 10-21 Parallel jaw on
linear slides
Chapter 10
Manipulator Geometries
255
Figure 10-22 Parallel jaw using
four-bar linkage
Figure 10-23 Parallel jaw using
four-bar linkage and linear
actuator
PASSIVE PARALLEL JAW USING CROSS TIE
Twin four-bar linkages are the key components in this long mechanism
that can grip with a constant weight-to-grip force ratio any object that fits
256
Chapter 10
Manipulator Geometries
Figure 10-24 Passive parallel
jaw using cross tie
within its grip range
...
The vertical links have extensions with grip pads mounted at their
ends, while the horizontal links are so proportioned that their pads move
in an inclined straight-line path
...
Some robots are designed to do one specific task, to carry one specific
object, or even to latch onto some specific thing
...
In many cases, a joint like this can be used independently of any manipulator
...
Marshall Space Flight Center, Alabama
A new joint, proposed for use on an attachable debris shield for the
International Space Station Service Module, has potential for commer-
Chapter 10
Manipulator Geometries
257
Figure 10-25 The threedegrees-of-freedom capability of
the passive capture joint provides
for quick connect and disconnect
operations
...
This joint can be useful in a variety of applications, including replacing the joints commonly used on trailer-hitch tongues and temporary
structures, such as crane booms and rigging
...
This new joint allows for quick connection between any two structural
elements where it is desirable to have rotation in all three axes
...
The joint is then
connected by inserting the ball into the bore of the base
...
Release of this
joint involves only a simple movement and rotation of one part
...
Most passive capture devices allow only axial rotation when fastened—if any movement is allowed at all
...
The design for this new joint is relatively simple
...
The socket contains all the moving parts and is
the important part of this invention
...
This work was done by Bruce Weddendorf and Richard A
...
258
Chapter 10
Manipulator Geometries
INDUSTRIAL ROBOTS
The programmability of the industrial industrial robot using computer
software makes it both flexible in the way it works and versatile in the
range of tasks it can accomplish
...
Industrial
robots can be floor-standing, benchtop, or mobile
...
There is no common agreement on or standardizations of
these designations in the literature or among industrial robot specialists
around the world
...
Four
classes are generally recognized: limited sequence and three forms of
unlimited sequence—point-to-point, continuous path, and controlled
path
...
Another classification related to control is nonservoed versus servoed
...
By contrast, servoed means that some form of closed-loop
feedback is used in the system, typically based on sensing velocity, position, or both
...
Industrial robots are powered by electric, hydraulic, or pneumatic
motors or actuators
...
Hydraulic-drive
industrial robots are generally assigned to heavy-duty lifting applications
...
The number of degrees of freedom is equal to the number of axes of
an industrial robot, and is an important indicator of its capability
...
Two or three of those
may be in the wrist or end effector
...
Others in the
same size range are powered by hydraulic motors
...
Chapter 10
Manipulator Geometries
Some industrial robot systems also include training pendants—handheld
pushbutton panels connected by cable to the console that permit direct
control of the industrial robot
...
At this time adjustments can be made to prevent any part of
the industrial robot from colliding with nearby objects
...
Some of these
are programmed with electromechanical relays, and others are programmed by setting mechanical stops on pneumatic motors
...
However, the full benefits of an industrial robot
can be realized only if it is properly integrated with the other machines
human operators, and processes
...
These might include high temperatures, high humidity, the presence of noxious or toxic fumes, and
proximity to molten metals, welding arcs, flames, or high-voltage sources
...
Other technical specialties that have contributed to industrial
robot development include servomechanisms, hydraulics, and machine
design
...
The largest number of industrial robots in the world are limitedsequence machines, but the trend has been toward the electric-motor
powered, servo-controlled industrial robots that typically are floorstanding machines
...
Trends in Industrial Robots
There is evidence that the worldwide demand for industrial robots has
yet to reach the numbers predicted by industrial experts and visionaries
259
260
Chapter 10
Manipulator Geometries
some twenty years ago
...
Moreover, the
software was frequently inadequate for the assigned tasks, and many
industrial robots were ill-suited to the tasks assigned them
...
By the late 1980s, the decline in orders for industrial robots drove
most American companies producing them to go out of business, leaving only a few small, generally unrecognized manufacturers
...
However, the Japanese electrical equipment manufacturer Fanuc Robotics North America and the Swedish-Swiss corporation Asea Brown Boveri (ABB) remain active in the U
...
robotics market today
...
Industrial
robots are now spot-welding car bodies, installing windshields, and
doing spray painting on automobile assembly lines
...
Benchtop industrial robots pick and place electronic components on circuit boards in
electronics plants, while mobile industrial robots on tracks store and
retrieve merchandise in warehouses
...
It turns out that the most costeffective industrial robots are those that have replaced human beings in
dangerous, monotonous, or strenuous tasks that humans do not want to
do
...
They might
also take place in areas with high relative humidity or temperatures that
are either excessively hot or cold
...
Management in factories where industrial robots were purchased and
installed for the first time gave many reasons why they did this despite
the disappointments of the past twenty years
...
This has been due, in large measure, to the declining costs of more pow-
Chapter 10
Manipulator Geometries
erful microprocessors, solid-state and disk memory, and applications
software
...
The shakeout of American industrial robot manufacturers has led to
the near domination of the world market for industrial robots by the
Japanese manufacturers who have been in the market for most of the past
twenty years
...
Nevertheless, industrial robots are still available in the same configurations that were available fifteen to twenty
years ago, and there have been few changes in the design of the end-use
tools that mount on the industrial robot’s “hand” for the performance of
specific tasks (e
...
, parts handling, welding, painting)
...
Some can now handle payloads of
as much as 200 pounds
...
High on the list of
other requirements are “stiffness”—the ability of the industrial robot to
perform the task without flexing or shifting; accuracy—the ability to
perform repetitive tasks without deviating from the programmed dimensional tolerances; and high rates of acceleration and deceleration
...
Movement is a key consideration in choosing an
industrial robot
...
Thus the industrial robot’s working
range or envelope is a critical factor in determining industrial robot size
...
Although most
tasks suitable for industrial robots today can be performed by industrial
robots with at least five axes, industrial robots with six axes (or degrees
of freedom) are quite common
...
Rotary wrist movement and
wrist bend are also widely available
...
Wrist
yaw is another available degree of freedom
...
To be most effective, all
axes should be servo-driven and controlled by the industrial robot’s computer system
...
Click here for Terms of Use
...
M
echanical limit switches are devices that sense objects by being
either directly or indirectly touched by the object
...
Two other types
that warrant their own categories are the magnetic reed switch and the
membrane switch, which is much like a long button actuated switch
...
The limit switch can be thought of as a device that has at least one
input and one output
...
The output is
almost always closing or opening an electric circuit
...
Other types are not strictly
mechanical and are more complex and beyond the scope of this book
...
The categories are proprioceptive and environmental
...
Environmental things are generally outside the robot
like nearby objects, ambient temperature, the slope of the surface the
robot is driving on, bumps, or drop-offs, etc
...
For instance, when the bumper bumps up against an
object, the object is in the environment (environmental sensing) but the
bumper’s motion and location, relative to the robot, is detected by a
limit switch mounted inside the robot’s body (proprioceptive sensing)
...
265
266
Chapter 11
Proprioceptive and Environmental Sensing Mechanisms and Devices
These two categories subject the switch to very different problems
...
The things around them and the things they sense are all contained
inside the robot, making their shape unchanging, moving generally in
the same direction, and with the same forces
...
Environmental sensing switches, especially the mechanical type,
are often very difficult to make effective and care must be taken in their
design and layout
...
This
chapter will focus on layouts and tripping mechanisms in addition to the
switches themselves
...
Others consist of several components which include one or more switches and
some device to trip them
...
The following figures show
several basic layouts
...
The simplest form of mechanical limit switch is the button switch
(Figure 11-1) It has a button protruding from one side that moves in and
out
...
The
button switch is slightly less robust than the other switch designs
because the button must be treated with care or else it might be pushed
too hard, breaking the internal components, or not quite inline with its
intended travel direction, breaking the button off
...
Some very precise button limit switches
can detect motions as small as 1mm
...
The lever comes in an almost
limitless variety of shapes and sizes
...
Figure
11-2 shows the basic layout
...
The whisker or wobble switch is shown separately in Figure 11-3
even though it is really just another form of lever switch
...
This makes it
Chapter 11
Figure 11-1 Button Switch
Figure 11-2 Lever Switch
Proprioceptive and Environmental Sensing Mechanisms and Devices
267
268
Chapter 11
Proprioceptive and Environmental Sensing Mechanisms and Devices
Figure 11-3 Whisker Switch
Figure 11-4 Slide Switch
Chapter 11
Proprioceptive and Environmental Sensing Mechanisms and Devices
more robust and easier to incorporate, but it is also much less precise
since the sensing arm is necessarily flexible
...
Since
it bends out of the way of the sensed object, neither the object nor the
switch is damaged by impact
...
Figure 11-3 shows a basic whisker
switch
...
This switch has
a different internal mechanism than the button switch and its variations,
and is considered less reliable
...
Figure 11-4 shows a slide switch
...
The most common design has a sensitive magnet attached to a hinged contact so that
when a piece of ferrous metal (iron) is nearby on the correct side of the
switch, the magnet is drawn towards a mating contact, closing the electric circuit
...
Just be sure that the thing being sensed is
ferrous metal and passes close enough to the switch to trip it
...
There are several ways to increase the area that is sensed by a mechanical limit switch
...
There is also a form of mechanical switch whose area is inherently large
...
These switches usually are in the shape of a long rectangle, since the internal components
lend themselves to a strip shape
...
For
some situations, they are very effective
...
Hopefully these pictures will spur the imagination to come up with even more clever ways mechanical limit switches
can be used in mobile robots
...
There are many ways to do this
...
In every sensor/actuator system, there is a time lag between when the
switch is tripped and when the actuator reacts
...
Object, in this case, can mean something in the environment, or something attached to the robot that is designed to detect things in the environment
...
This is done by using one of three methods
...
• The layout can allow the object to pass by the switch, tripping it but
not being physically stopped by anything
...
• The travel of the sensor’s lever or button, after the sensor has been
tripped, can be made long enough to allow sufficient time for the
robot to stop
...
Combination Trip (Sense) and Hard Stop
This is probably the simplest layout to implement
...
Alternatively, there is a separate hard stop that is in line with the
switch that absorbs the force of the impact after it has been tripped
(Figure 11-8)
...
278
Chapter 11
Proprioceptive and Environmental Sensing Mechanisms and Devices
Figure 11-9 By-pass linear
By-Pass Layouts
The by-pass layout shown in Figures 11-9 and 11-10 relieves the switch
of taking any force, but, more importantly, is less sensitive to slight variations in the positions of the switch and the sensed object, especially if a
switch with a long throw is used
...
With careful design, however, this layout is usually a better choice than
the previous layout because it requires less precision in the relationship
between the hard stop and the switch’s lever or button
...
This layout and its derivatives are the basis of virtually all mechanical
timers
...
They can be
stacked, as they are in appliances, to control many functions with a sin-
Chapter 11
Proprioceptive and Environmental Sensing Mechanisms and Devices
Figure11-10 Rotating cam
gle revolution of the timer
...
Reversed Bump
The reversed bump layout shown in Figure 11-11 is a sensitive and
robust layout
...
When
an object touches the bumper, it moves the sense arm away from the
switch, releasing and tripping it
...
For this reason, it is an effective layout
for sensing bumps
...
The robot must
have a sensor to detect collisions
...
It is a last line of defense against crashing
into things
...
To be perfectly safe, this sensor
must be able to detect contact with an object at any point on the outer
surface of the robot that might bump into something
...
Robots that travel in both directions must have sensors
around the entire outer surface
...
Some robot
designs attempt to get around this by using a measure of the current
going to the drive wheels to judge if an object has been hit, but this
method is not as reliable
...
It is another case in which the shape of
the robot is important as it directly affects the sensor’s design and location
...
Unfortunately, the larger the robot, the more
important it is to be able to detect contact with things in the environment,
since the large robot is more likely to cause damage to itself or the things
it collides with
...
Even large autonomous robots (robots around the size of
R2D2) are often built with no, or, at most, very small bumpers
...
Making the
shape simple, like a rectangle or, better yet, a circle, makes the bumper
simpler
...
Having the robot travel slowly, or slowing down when other sensors indicate many obstacles nearby means the bumper doesn’t have to
respond as fast or absorb as much energy when an object is hit
...
There are several basic bumper designs that can be used as starting
points in the design process
...
These smaller
pieces have the added benefit that the robot’s brain can get some idea of
where the body is hit, which can then be useful in determining the best
direction to take to get away from the object
...
A clever design that absolutely guarantees the bumper will completely
cover the entire outer surface of the robot is to float the entire shell of the
robot and make it the bumper, mounted using one of the techniques
described later
...
This concept works well for
small robots whose shells are light enough not to cause damage to themselves but may be difficult to implement on larger robots
...
This is due to the possibility that the robot might try to drive
under something that is not quite high enough, or try to drive up onto
something and get the bottom edge of the bumper stuck, before it trips
the sensor
...
This is where a bumper compliant and sensitive to bumps coming from any direction is very helpful
...
Let’s start by looking at the simplest case, the one-dimension sensing bumper
...
Although this may seem too
limiting, it can be made to work well if there are several smaller
bumpers, each with their own 1D sensor
...
There are also layouts that are basically 1D in design, but, by being compliant, can be made to sense bumps
from arbitrary directions
...
Bumps can be
detected around the sides of the robot without as much motion from the
bumper
...
There are many ways to attach bumpers that are basically
1D bumpers, but that can also function as 2D bumpers
...
Usually, though, a secondary device must
be incorporated into the layout to positively locate the nominal position
of the bumper
...
The
spring-centered plate layout is shown in Figure 11-14
...
The V-groove centering block shown in Figure 11-12, is a basic
method of realigning the bumper after encountering a bump, but there
are several others that work nearly as well
...
It is
therefore effective for bumpers designed to detect bumps from straight or
nearly straight on
...
It consists
of four links attached in the shape of a quadrilateral
...
A
3D version of this can be built by attaching two
planes (plates) together with three links so that
the plates are held parallel, but can move relative
to each other
...
A better name might be 3D four-bar, or perhaps
three link planar
...
If the base is attached to the chassis, and the
top plate is attached to the bumper or
bumper/shell, a robust layout results
...
Tension Spring Star
A simple to understand spring-centering layout uses three tension
springs in a star layout (Figure 11-14)
...
This layout is easy to
adjust and very robust
...
This layout requires a damper between the chassis and plate to reduce
wobbling
...
It is similar in complexity to the sideways leaf spring shown
in the next section, but is somewhat more difficult to understand because
it uses the less common property of twisting a rod to produce a spring
...
The center of the beam is attached to the chassis, and each end of the
trailing links supports the bumper
...
Horizontal Loose Footed Leaf Spring
Another suspension system, used since the days of horse drawn buggies,
that can be applied to robot bumper suspensions is a leaf spring turned on
it side
...
In a car, the leaf
spring performs the task of springs, but it also holds the axles in place,
with very few moving parts
...
The center of the
spring is attached to the axle, allowing it to move up and down but not in
any other direction
...
286
Chapter 11
Proprioceptive and Environmental Sensing Mechanisms and Devices
Figure 11-16 Horizontal
oose footed leaf spring
The leaf spring can also be used to suspend a robot’s bumper quite
effectively by turning the spring on its side and attaching the center to
the chassis and each end to points on the bumper
...
This layout can be used on larger robots also,
since the leaf spring is an efficient suspension element even in larger
sizes
...
If this
would produce a cumbersum or overly large spring, the sideways-leaf
spring layout can be enhanced by adding a second spring to further support the rear of a one-piece wrap around bumper
...
Sliding Front Pivot
Designing a bumper suspension system based on the fact that the bumper
needs primarily to absorb and detect bumps from the front produces a
system which moves easily and farthest in the fore-and-aft directions,
but pivots around some point in the front to allow the sides to move
some
...
Sliding joints are more difficult to engineer
than pivoting or rotating joints, but this concept does allow large motions
Chapter 11
Proprioceptive and Environmental Sensing Mechanisms and Devices
287
Figure 11-17 Sliding front pivot
in the most important direction
...
Suspension Devices to Detect Motions
in All Three Planes
The V-groove device can be applied to 3D layouts as well, simply by
making the V-block angled on top and bottom, like a sideways pyramid
...
For even more sensitivity, the V-block can be made of rollers or have small wheels on its mating
surfaces to reduce friction
...
These flexible members can be replaced with springs
and linkages, but the geometries required for 3D motion using mechanical linkages can be complex
...
A well-sprung bumper or bumper/shell
288
Chapter 11
Proprioceptive and Environmental Sensing Mechanisms and Devices
Figure 11-18 Vertical flexible
post bumper suspension
that uses one of these layouts can be used with no hard centering system
by using the “limit switch as hard stop” concept discussed previously
...
This system is simple and effective for smaller
robots and a very similar layout is used on the popular Rug Warrior
robot
...
A clever designer may even be
able to size a single-compression spring layout that would be simple
indeed
...
Chapter 11
Proprioceptive and Environmental Sensing Mechanisms and Devices
CONCLUSION
The information you’ve just read in this book is intended for those interested in the mehanical aspects of mobile robots
...
It is my sincere
hope that the information that is presented will provide a starting point
from which to design your unique mobile robot
...
They are
also complicated
...
289
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...
A
Aaroflex, Inc
...
See motor drivers
analog-to-digital converters (ADCs), 60
Andros (Remotec), 155
Angle, Colin, xiii
angular displacement transducers (ATDs), 55–57, 56f
arm geometries, 245–249
articulated steering, 167
Asea Brown Boveri (ABB), 260
automatic guided vehicles (AGVs), 192–193
autonomous, term defined, xiii
autonomous manipulators, 241
axis stages, in motion control systems, 3
B
backlash, 88
Ballistic Particle Manufacturing (BPM), xvi, xxvii–xxix,
xxviii(f)
ballscrew drive, 12f
ballscrew slide mechanism, 6–7f
Bayside Controls, Inc
...
S
...
Click here for Terms of Use
...
, xxiii
camming, electronic, 11
Carnegie Mellon University, xxx
cartesian arm geometry, 246f–247
center of gravity (cg) shifting, 131–134, 132f, 133f
cg
...
See crevasse negotiation
chassis elevation, 132, 134f
Cincinnati Milacron, 260
circular interpolation, 10
circular pitch, 87
clearance, 87
closed-loop motion control systems (servosystems), 5–9, 5f,
6f, 7f, 8f, 18
cluster gears, 86f
commutation, 26–28f, 27f, 30, 34–35
computer-aided design (CAD), xiv, xvi
computer-aided motion control emulation, 10–11
cone clutches, 122f
cone drives, 84f
constant-velocity couplings, 115f–116f
contact ratio, 87
contouring, 10
controlled differential drives, 93–95f, 94f
control structures, xiii
costs
and actuator count, 68
and gearhead installation, 104–105
couplers
bellows couplings, 14f–15
Bendix-Weiss joints, 116
constant-velocity couplings, 115f–116f
cylindrical splines, 116f–119f, 117f, 118f
face splines, 120f
flexible shaft couplings, 14f
helical couplings, 14f–15
Hooke’s joints, 114f
of parallel shafts, 115f
Crawler Transporter (NASA), 165
crevasse negotiation, 163–164, 166, 234
Cubital America Inc
...
See linear variable differential transformers
(LVDTs)
dead-reckoning error, 196
debugging, and actuator count, 67–68
dedendum circle, 87
degrees-of-freedom (DOF)
in manipulator arm geometry, 241–242, 245
degrees-of-freedom (DOF)
in manipulator wrist geometry, 250–251f
in walker mobility systems, 203–208, 204f, 205f, 206f,
207f
depth, in gears, 87
derivative control feedback, 9
design tools, xiv
diametrical pitch (P), 87
differential, 139–140f
Directed-Light Fabrication (DLF), xvi, xxix(f)–xxx
Direct-Metal Fusing, xxix
direct power transfer devices
couplers
Bendix-Weiss joints, 116
direct power transfer devices
couplers, 14f–15, 109–113f, 110f, 111f, 112f
bellows couplings, 14f–15
constant-velocity couplings, 115f–116f
cylindrical splines, 116f–119f, 117f, 118f
face splines, 120f
flexible shaft couplings, 14f
helical couplings, 14f–15
Hooke’s joints, 114f
of parallel shafts, 115f
torque limiters, 121–125f, 122f, 123f, 124f
Direct-Shell Production Casting (DSPC), xvi, xxvi(f)–xxvii
drive/steer modules, 195f–197f
drop on demand inkjet plotting, xx, xxviii(f)
DTM Corporation, xxi
dynamic stability, 201–202
E
E-chains, 243f
electric motors
...
)
stepper motors, 16, 18t, 37–40, 71
hybrid stepper motors, 38–40f, 39f
permanent-magnet (PM) stepper motors, 38
variable reluctance (VR) stepper motors, 38
electronic camming, 11
electronic commutation, 26–28f, 27f, 30
electronic gearing, 11
encoders
absolute encoders, 46f
incremental encoders, 44f–45f
linear encoders, 47f–48
magnetic encoders, 48f–49
rotary encoders, 6, 7f, 13, 19, 43–44
end-effectors
...
See also limit
switches, mechanical
EOS GmbH, xxi
epoxy-core linear motors, 33–34f
external gears, 88
external pipe vehicles, 226
F
face gears, 90
face splines, 120f
Fanuc Robotics North America, 260
feedback sensors
...
)
precision multiturn potentiometers, 59f–60
resolvers, 20, 30f, 49f–51
tachometers, 5, 20, 51f–53, 52f
flat belts, 73, 74f
flexible belt torque limiters, 122f
flexible face-gear reducers, 100–101f
flexible shaft couplings, 14f
foot size, walker, 210f
frame walking, 211f–213f, 212f
friction clutch torque limiters, 124f
friction disk torque limiters, 124f
friction drives, 83–84f
Fused-Deposition Modeling (FDM), xvi, xxiii–xxv, xxiv(f)
G
gait types, walker, 201–202
gantry manipulators, 246f
geared offset wheel hubs, 134f
gear efficiency, 88
gear power, 88
gear ratio, 88
gears, 85–105
bevel gears, 102, 103f
cluster gears, 86f
flexible face-gear reducers, 100–101f
gear classifications, 88–90
gear dynamics terminology, 88
gear terminology, 87–88
gear tooth terminology, 86f
harmonic-drive speed reducers, 96–100, 97f, 98f
helical planetary gears, 103f
high-speed gearheads, 102–105, 103f
planetary gear drives, 95–96f, 105f
worm gears, 90–93, 91f, 92f
gears, electronic, 11
gear speed, 88
General Electric, 260
General Motors, 260
Genghis (iRobot), 205
grass, 233
grippers (end-effectors)
direct drive jaws, 252–253f
parallel jaws, 254f–255f
passive capture joint with three DOF, 256–257f
passive parallel jaws, 255f–256f
rack and pinion jaws, 253f
reciprocating lever jaws, 253f
ground pressure
and mobility system comparisons, 233, 236, 237
and tracked mobility systems, 163, 165
294
Index
(ground pressure cont
...
, xxiii
herringbone gears, 89
high-speed gearheads, 102–105, 103f
High-torque (HTD) timing belts, 75, 76f
hill climbing, 233
holonomic motion, 139
Hooke’s joints, 114f
horizontal crawlers, 220f–221f
horsepower-increasing differential, 93–95f, 94f
hydraulics, xiv
hypoid gears, 89
I
inchworm multi-section bladders, 225f
inchworm multi-section roller walkers, 225f
inclinometers, 132
incremental encoders, 44f–45f
incremental motion control, 10
independent leg walking, 208–210, 209f
indirect power transfer devices
belts
about, 72–73
gears
gear classifications, 88–90
gear dynamics terminology, 88
gear terminology, 87–88
synchronous drives, 75
indirect power transfer devices
belts
flat belts, 73, 74f
O-ring belts, 73, 74f
timing belts, 75f–76f
V-belts, 73–74f, 76–77
chain
ladder chain, 80f
rack and pinion chain drive, 82f
roller chain, 80–82f, 81f
silent (timing) chain, 82–83f
cone drives, 84f
controlled differential drives, 93–95f, 94f
friction drives, 83–84f
gears
(indirect power transfer devices cont
...
, xiv
industrial robots
about, 241, 258–259
advantages, 259–261
characteristics, 261–262
integral control feedback, 8
internal gears, 89
International Business Machines, 260
Inuktun, 165
J
Jet Propulsion Laboratory, 144–145
K
Karmen, Dean, 135–136
L
ladder chain, 80f
Laminated-Object Manufacturing (LOM), xvi, xxii(f)–xxiii
Land-Master (Tri-star), 159
Lankensperger, George, 190
Laser Engineered Net Shaping (LENS), xxix
laser interferometers, 7f, 13, 20, 57–59, 58f
Laser Sintering, xxix
leadscrew drive, 11f
leg actuators, walker, 202–203
leg geometries, walker, 203–208, 204f, 205f, 206f, 207f
lever switches, 266, 267f
light fringe, 58
limit switches, mechanical
about, 265–266
bumper geometries
about, 280–282
3D motion detection, 287–288f
horizontal loose footed leaf spring, 285–286f
simple bumper suspension devices, 282, 283f
sliding front pivot, 286–287f
tension spring layout, 284f
Index
(limit switches, mechanical cont
...
)
about, 241, 258–259
advantages, 259–261
characteristics, 261–262
offset joints, 245f–246
pivoting joints, 245f
slider crank, 243–245, 244f
spherical arm geometry, 248f–249f
wrist geometry, 250f–251f
Massachusetts Institute of Technology, xxvi
mechanical arms
...
See limit switches, mechanical
membrane switches, 269
Michaelson interferometers, 57, 58f
microstepping, 18
miter gears, 89
mobility, term defined, xiii–xiv, 229
mobility systems
defined, 129
demands on, xii
pipe crawler mobility systems
about, 219–220
external pipe vehicles, 226
horizontal crawlers, 220f–221f
inchworm multi-section bladders, 225f
inchworm multi-section roller walkers, 225f
tracked crawlers, 224f
vertical crawlers, 221–223f, 222f
traction techniques, 222
wheeled crawlers, 223f
snake mobility systems, 226
tracked mobility systems
center of gravity (cg) shifting, 164
components, 164
crevasse negotiation, 163–164, 166
drive sprockets, 174
four-track drivetrains, 181–184, 182f, 183f
and ground pressure, 163, 165
ground support methods (suspension), 174–178
fixed road wheels, 175f
guide blades, 175
road wheels mounted on sprung axles, 176–178f,
177f
rocker road wheel pairs, 176f
half-track layout, 180f
ideal terrain for, 163–164, 166
obstacle negotiation height, 174
one-track drivetrains, 178–179f
pinch volume, 168–169
six-track drivetrains, 184–185f
296
Index
(mobility systems cont
...
)
Alvis Stalwart, 152
with DOF joints, 153
rocker bogie suspension system, 153–155, 154f,
166
skid steering, 150f–152f, 151f
spring suspension systems, 130–131
static stability minimums, 135, 136f
three-wheeled layouts, 136–140, 138f, 139f, 140f
steering, 190, 191f
two-wheeled layouts, 135f–136f
steering, 190, 191f
wheel size and spacing, 134, 152
mobility systems, comparing
complexity, 235
environmental considerations
and effectiveness, 232
ground cover, 233
obstacles, 234
temperature, 232–233
topography, 233–234
mobility index comparison method, 236
physical components
height-width, 230–231
shape, 230
size, 229–231
turning width, 234
weight, 231
practical comparison method, 236–237
speed and cost, 235–236
Mold Shape Deposition Manufacturing (MSDM),
xxxii–xxxiii(f)
motion controllers
developments in, 15–16
in motion control system, 3
position control loops, 6f
trapezoidal velocity profiles, 7–8f
motion control systems
about, 3–4
actuators for, 41–43, 66f–68
and base/host machine, 14–15
closed-loop systems (servosystems), 5–9, 5f, 6f, 7f, 8f,
18
computer-aided emulation, 10–11
electronic system components, 15–16
feedback sensors (See feedback sensors)
installation and operation, 20
kinds of, 9–10
mechanical components, 11f–12f
motor drivers, 18–19
motor selection, 16–18t
Index
(motion control systems cont
...
See also electric motors
mud, 233
N
Nasif, Annette K
...
See direct power transfer devices;
indirect power transfer devices
pressure angle, 88
programmable logic controller, 3
proportional control feedback, 8
proportional-integral-derivative (PID) control feedback, 9
proprioceptive sensors, 265, 266
...
, xxviii
Schroff Development Corporation, xxiii
SDM Laboratory, xxx, xxxi
Segway, 135–136
Selective Laser Sintering (SLS), xvi, xx–xxi(f)
sensors, feedback
...
See closed-loop motion control systems (servosystems)
Shape Deposition Manufacturing (SDM), xxx–xxxii, xxxi(f)
298
Index
shear pin torque limiters, 125f
silent (timing) chain, 82–83f
single-axis air-bearing stages, 7f, 13f
sinusoidal commutation, 34–35
skid steering (differential), 141, 150–152, 167, 193–195,
194f
slider cranks, 243–245, 244, 244f
slide switches, 268f, 269
snake mobility systems, 226
software, for motion controllers, 15
Sojourner, 155
solenoids
about, 60–63, 61f
box-frame, 63
C-frame, 63
open-frame, 63
rotary, 64–66, 65f
tubular, 64
solid free-form (SFF) fabrication, xxx
Solid-Ground Curing (SGC), xvi, xviii–xx, xix(f)
Soligen Technologies, xxvi, xxvii
speed control, 10
spherical arm geometry, 248f–249f
spiral bevel gears, 89
spring suspension systems, 130–131
spur gears, 89
stability
minimum requirements for static, 135, 136f, 192
and walker mobility systems, 201–202, 210f
stair climbing
and center of gravity, 132
tracked mobility systems and, 165
Stanford University, xxxii
static stability minimums, 135, 136f, 192
steel-core linear motors, 32–33f
steering
Ackerman steering layout, xii, 152, 179f, 190
all-terrain cycles (ATCs), 197
articulated steering, 167
drive/steer modules, 195f–197f
history, 189f–190
skid steering (differential), 141, 150–152, 167, 193–195,
194f
syncro-drives, 196–197f
three-wheeled layouts, 137–139f, 138f, 190, 191f, 195f
tracked mobility systems, 167–168
two-tracked drivetrains, 192–193f
two-wheeled layouts, 190, 191f
in walker mobility systems, 211f
step errors, 9
stepper motors, 16, 18t, 37–40, 71
(stepper motors cont
...
)
steering, 167–168
track construction methods, 166, 168–171, 169f, 170f
track shapes, 171–174, 172f, 173f
two-track drivetrains, 179–181f, 180f
two-tracked drivetrains
steering, 192–193f
variations in, 164–165
transmissions
...
See Hall-effect devices (HED)
trapezoidal velocity profiles, 7–8f
U
undercutting, 88
University of Texas at Austin, xxi
Urbie (iRobot), 182f
V
V-belts, 73–74f, 76–77
velocity control loops, 5–6, 6f
velocity profiles, trapezoidal, 7–8f
vertical crawlers, 221–223f, 222f
W
walker mobility systems
about, 201–202, 215–216
gait types, 201–202
leg actuators, 202–203
leg geometries, 203–208, 204f, 205f, 206f, 207f
slider cranks and, 244
walking techniques
flexible legs, 214–215f
foot size, 210f
frame walking, 211f–213f, 212f
independent leg walking, 208–210, 209f
roller walkers, 214
wave walking, 208
wave walking, 208
web sites
belts, 72–73
couplers, 109
roller walkers, 214
Torsen differential, 140
Westinghouse, 260
wheeled crawlers, 223f
wheeled mobility systems
about, 130
299
(wheeled mobility systems cont
...
, 145
worm-drive systems, 12f
worm gears, 89, 90–93, 91f, 92f
wrist, human, 242
wrist geometry, 250f–251f
Z
Z Corporation, xxvi
About the Author
Paul E
...
Previously, he
worked for RedZone Robotics, where he designed suspension components for large-scale toxic waste cleanup robots
...
He lives with his family in a
suburb of Boston, Massachusetts