Mechanical Design: Analysis and Synthesis

344 Pages·2001·63.851 MB·English

by  Arthur G. Erdman, George N. Sandor, Sridahr Kota

Volume 1
Mechanism Design
Analysis and Synth�1;;:;� 1
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ARTHUR G. ERDMAN
Morse Alumni Distinguished Teaching Professor
of Mechanical Engineering
University of Minnesota
GEORGE N. SANDOR
Research Professor Emeritus
of Mechanical Engineering
University of Florida
SR/DHAR KOTA
Professor of Mechanical Engineering
University of Michi�ga�n ������-
.
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Prentice Hall
Upper Saddle River, New Jersey 07458
Llbrarv 0JC011gress Cataloging·in-Publican·on Data
ERDMAN. ARTHL'R G.
Mechanism design: analysis a.nd synthesis I Anhur G. Erdman.
George N. Sandor. Sridhar K<'ta-
p. cm.
Includes bibliographical references .:ind index.
ISBN 0-13-0.0872-7(,·. I)
l. Machine-Design. L Sandor. George N. LL Kota, Sridhar Ill. Tille.
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Marketing Manager: HOLLY STARK An Erdman George Sandor Sridhar Kata and
Marketing Assisumt: K..\.REN '.\IOON
dedicates this work dedicates this work Art Erdman dedicate
o 2001 by Arthur G. Erdman. George N. Sandor. and Sridhar Kola to his wife Mary to his wife Magdi. this work to the.
� 1997, I 99 l. l 984 by Arthur G. Erdman and George '<. Sandor Jo, daughters memory of
• Published by Prentice-Hall, Inc. Kristy and Kari Professor
Upper Saddle River. New Jersey 07458 and son Aaron. Athmaram (Abe)
All rights reserved. No pan of this book may be reproduced. in any format or by any means. without permission in writing He thanks the Lord H. SoniJor his
from the publisher for blessing him lifelong contributions
and enabling him to the engineering
The author and publisher of this book have used their best efforts in preparing this book. These efforts include the develop to contribute to com1111111i1y.
ment, research. and testing of the theories and programs to determine their effectiveness. . The author and publisher make no
this book.
warranty of any kind. expressed or implied. with regard 10 these programs or the documemarion contained in this book.
The author and publisher ;h31J not be liable in any event for incidental or consequential damages in connection with. or
arising our of. the furnishing. performance, or use of these programs.
TRADEMARK 11'ff0Rlv1AT ION: ADAMS (Automatic Dynamic Analysis of Mechanical Systems) is 3 trademark of
Mechanical Dynamics Inc. DADS a trademark of CADS! Inc. Working Model software a trademark of Know ledge
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About the Cover Contents
Front Cover IN MEMORY
ix
The cover depicts the computer model of a three-fingered Universal Robotic Gripper that PREFACE xi
can grasp objects of any shape. The design was based on a single-input, three-output dif
ferential mechanism that allows all three fingers to exert same force regardless of their
position. Such single-input, plural-output differential mechanisms were invented by 1 INTRODUCTION TO KINEMATICS
S. Kota and S. Bidare (U.S. patents 5,423,726 and 5,435,790). The particular embodiment AND MECHANISMS
1
shown on the cover was developed by Dr. Mary Frecker. Penn State University, as a grad
uate student at the University of Michigan in 1994. The computer model was created by 1.1 Inrroduction l
Dr. Zhe Li, University of Michigan, using ADAMS software. 1.2 Motion I
1.3 The Four-Bar Linkage 2
Back Cover 1.4 Relative Motion 9
1.5 Kinematic Diagrams 9
Top right: A snapshot of cam synthesis program. called CAMSYN, developed in MAT 1.6 Six-Bar Chains 14
LAU by Dr. Zhe Li and S. Kota 1.7 Degrees of Freedom 21
1.8 Analysis versus Synthesis 39
Middle left: A page from Module I of the companion web site showing ADAMS simula
1.9 Mechanism Design Example: Variable Speed
tion of a sheet-metal feeding mechanism, its kinematic diagram and computation of de Transmission 30
grees of freedom.
Problems 40
Bottom right: A page from Module IO of the companion web-site showing computer sim
ulations of four (among numerous others) different types of mechanical grippers.
2 MECHANISM DESIGN PROCESS
96
2.1 Introduction 96
2.2 The Seven Stages of Computer-Aided Engineering
Design 96
2.3 How the Seven Stages Relate to This Text 101
2.4 A Need for Mechanisms I 02
I 2.5 Design Categories and Mechanism Parameters I 07
v
2.6 Troubleshooting Guide: Symptoms. Causes, 5.7 Discussion of the Superposition and Matrix
and Sources of Assistance 113 Approach to Kinetosratics 330
2.7 History of Computer-Aided Mechanism 5.8 Time Response to Mechanisms 330
Design I 16 5.9 Dynamic Simulation of Mechanisms 346
Appendix: Commercial Software Programs 354
Problems 358
3 DISPLACEMENT AND VELOCITY ANALYSIS 119
3.1 Displacement Analysis: Useful Indices for Position
6 CAM DESIGN 373
Analysis of Linkages 119
3.2 Displacement Analysis: Graphical Method 13 I 6.1 Introduction 373
3.3 Displacement Analysis: Analytical Method 135 6.2 Cam and Follower Types 374
3.4 Concept of Relative Motion l 37 6.3 Cam Synthesis 378
3.5 Velocity Analysis: Graphical Method 139 6.4 Displacement Diagrams: Graphical
3.6 Velocity Analysis. Analytical Method 149 Development 380
3.7 Instant Centers 152 6.5 Displacement Diagrams: Analytical
3.8 Velocity Analysis Using Instant Centers 160 Development 388
3.9 Mechanical Advantage 165 6.6 Advanced Cam Profile Techniques 394
3.JO Analytical Method for Velocity and Mechanical 6.7 Graphical Cam Profile Synthesis 408
Advantage Determination 176 6.8 Analytical Cam Profile Synthesis 410
3.11 Computer Program for the Kinematic: Analysis 6.9 Cam Synthesis for Remote Follower 425
of a Four-Bar Linkage 181 6.10 Cam-Modulated Linkages 4'.!6
Appendix: Review of Complex Numbers 183 Problems 435
Problems 192
Exercises 232
7 GEARS AND GEAR TRAINS 447
4 ACCELERATION ANALYSIS 233 7.1 lntroducrion 447
7.2 Gear Tooth Nomenclature 452
4.1 Introduction 233
7.3 Forming of Gear Teeth 456
4.2 Acceleration Difference 234
7.4 Gear Trains 458
4.3 Relative Acceleration 239
7.5 Planetary Gear Trains 465
4.4 Coriolis Acceleration 243
7.6 The Formula Method 473
4.5 Mechanisms with Curved Slots and l Iighcr-Pair
7.7 The Tabular Method 480
Connecrions 263
7.8 The Instant Center Method (or Tangential Velocity
Problems 268
Method) 484 ..
7.9 Tooth Loads and Power Flow in Branching
5 INTRODUCTION TO DYNAMICS Planetary Gear Systems 490
OF MECHANISMS 291 Problems 498
5.1 Introduction 291
S.2 Inertia Forces in Linkages 296 8 INTRODUCTION TO KINEMATIC SYNTHESIS:
5.3 Kinetostatic Analysis of Mechanisms 299 GRAPHICAL AND LINEAR ANALYTICAL METHODS 514
5.4 The Superposition Method (Graphical and
Analytical) 301 8.1 Introduction 514
5.5 Design Example: Analysis of a Variable-Speed 8.2 Tasks of Kinematic Synthesis 516
Drive 309 8.3 Type Synthesis 526
5.6 The Matrix Method 3 l 8 8.4 Tools of Dimensional Synthesis 539
vii
vi Contents Contents
8.5 Graphical Synthesis-Motion Generation: Two
Prescribed Positions 539
8.6 Graphical Synthesis-Motion Generation: Three
Prescribed Positions 542
In Memory
8.7 Graphical Synthesis for Path Generation: Three
Prescribed Positions 543
8.8 Path Generation with Prescribed Timing: Three
Prescribed Positions 544
8.9 Graphical Synthesis for Path Generation (without
Prescribed Timing): Four Positions 546
8.10 Function Generator: Three Precision Points 548
8.11 The Overlay Method 553
8.12 Analytical Synthesis Techniques 554
8.13 Introduction to Analytical Synthesis 555
8.14 The Standard Dyad Form 562
8.15 Number of Prescribed Positions versus Number
of Free Choices 566
8.16 Three Prescribed Positions for Motion, Path. and
Function Generation 568
8.17 Three-Precision-Point Synthesis Examples 574 We arc all saddened with the passing of Dr. George N. Sandor during the preparati0n of
8.18 Circle-Point and Center-Point Circles 580 the third edition of this book. George was a world renowned professor, engineer, a great
8.19 Ground-Pivot Specification 588 friend and major contributor to the kinematic community. At tbe age of 84 he was a re
8.20 Extension of Three-Precision-Point Synthesis tired Research Professor Emeritus and past Director of the Mechanical Engineering De
to Multiloop Mechanisms 591 sign Laboratory at the University of Florida, Gainesville. Dr. Sandor formerly taught at
8.21 Freudenstein's Equation for Three-Point Function Rensselaer Polytechnic Institute and at Yale and Columbia Universities. He was t�e
Generation 595 ALCOA Foundation Professor of Mechanisms Design from 1966 to 1975. He worked in
8.22 Loop-Closure-Equation Technique 598 U.S. industry for 21 years before starting his graduate work at Columbia. During th_at
8.23 Order Synthesis: Four-Bar Function time, he made numerous contributions including designing the first color press for life
Generation 60 I Magazine. . . . .
8.24 Three-Precision-Point Synthesis: Analytical versus Dr. Sandor received his Doctorate in Engineering Science at Columb1:.i University
Graphical 604 in 1959 and, in 1986, was honored with Doctor Honoris Causa in Mechanical Engineer
Appendix: Case Study-Type of Synthesis of ing at the Technological University, University of Budapest. Hungary. He had become the
Casement Window Mechanisms 604 first mechanical engineer in the previous 19 years to receive this honor. Dr. Sandor was
Problems 624 also elected Honorary Member of the Hungarian Academy of Sciences. .
Dr. Sandor wrote over 140 technical. scientific and educational papers. He invented
he
or co-invented six issued patents. In all, advised more than 50 master's and doctor's
ANSWERS TO SELECTED PROBLEMS 647 :ork
graduates. Dr. Sandor was a Life Fellow of ASME and a member of the New Ac�d
erny of Science. I le received numerous honors including the ASME Ma�hme Design
REFERENCES 650 Award and the OSU Applicc.l Mechanisms Award. He is one of the Outsrandmg Educators
in America and is listed in Who's Who in America and American Men and Women of
INDEX 661 Science.
Dr. Sandor held many engineering, administrative, executive and board positions in
machinery design, manufacture, and research and development. This book has .the benefit
of these experiences which include the Hungarian Rubber Co. (affiliated with Dunlop
Ltd.), Babcock Printing Press Corp., H.W. Facber Corp., and TTME Inc. Hew� a m�m
ber of the Board of Directors at Huck Co., from 1963-70 and held P.E. licenses in Flonda,
New York, North Carolina, and New Jersey.
ix
viii Contents
. Dr. Sandor w�s �n avid �ier, _sa!lor, musician, and family poet laureate who spoke
sev_en l�oguages. His interest in aV1a1100 spanned over 50 years. While a student at the
University �f Polytechnics in Budapest, Hungry, he helped design an open-cockpit, two
pas�enger biplane. for an engineering course project. Unlike many student projects. San Preface
dor s staggered-wing prototype flew perfectly the first try.
. George is well remembered by his kindness to all, his wisdom and unbound curios-
1t?' for the field of kinematics. His contributions 10 the science and application of rnecha
msm_s are many and are evident in this book. His enthusiasm for life and research is
poss1b!y unmatched. George is now with the Lord, continuing to uncover the secrets be
yond hfe.
The original two-volume work. consisting of Volume I. :-.rech:mism Design: Analysis and
Synthesis. and Volume 2. Advanced Mechanism Design: Analysis and Synthesis. was de
veloped over a 15-year period chiefly from the teaching. research, and consulting practice
or the authors, with contributions from their working associates and with adapraiions of
published papers. This work represented the culmination of research toward a general
method of kinematic. dynamic, and synthesis, starting with the dissertation of Dr. G.N.
Sandor under the direction of Dr. Freudenstein at Columbia University.
The authors acknowledge many colleagues who made contributions to the first edi
tion: John Gustafson. Lee Hunt. Tom Carlson. Ray Giese. Bill Dahlof. Sem Heng Wang.
Dr. Tom Chase, Dr. Sanjay G. Dhandi, Dr. Patrick Starr. Dr. William Carsen. Dr. Charles
F. Reinholtz. Dr. Manuel Hernandez, Manin 01 Girolamo, Xirong Zhuang, and others.
The second edition of Volume I was based on feedback that came from over a hun
dred institutions in the United States and abroad. including the authors· own universities.
Several chapters were reorganized and over 50 new problems and examples were added.
Also new to this edition was an 113M disk which supplemented chapters 3,4.6 and 8.
Readers were able to design four-bar linkages for three design positions and then analyze
the synthesized mechanism. Also a cam design module illustrated the concepts outlined in
Chapter 6.
The authors acknowledge many colleagues who made contributions to the second
edition: Dr. Sridhar Kora, Dr. Tom Chase, John Titus, Dr. Donald Riley, Dr. Alben C.
Esterline Dr. Suren Dwivdei, and Dr. Harold Johnson. Other contributors include Chris
Huber, Ralph Peterson. Mike Lucas, Jon Thoreson, Elizabeth Logan, Greg Vetter, and
Gary Bisrram, for photography.
The third edition of Volume I was a result of further improvement to the text. Over
60 new problems and examples were added - taken from industry, from patents or solu
tions to practical needs. Several chapters were modified with the objective of simplifying
the teaching of the materials. For example, in Chapter 2, a building block approach to
mechanism design was added based on input from Dr. Sridhar Kora. In Chapter 7, the
xi
x In Memory
planetary gear train section was improved with the help of Dr. Frank Kelso. A major Making easier to study
change to the third edition was the CD-ROM which included more than 90 animation's of Motion of the Linkage Body
real and computer-generated mechanisms. How they move in plane and Three Dee
The authors thank the following individuals for their contribution to this third edi Makes it clear and learning easy!
tion: Dr. Tom Chase, Dr. Jenny Holte, and Prof. Daryl Logan at the University of \Vis
consin, Planeville, as well as Dr. Raed Rizq, David Wulfman, Tim Berg, Jim Warren. That's the goal of this one writer
Dr. Boyang Hong, James Holroyd, Nick Gamble, Phil Schlanger, and Stephanie Clark. Other author even brighter!
We are very pleased to introduce the fourth edition which continues the tradition of So, we wish you happy reading
innovative approaches to teaching mechanism design. The CD-ROM has been replaced May your study earn high grading!
by a web-accessible set of over 200 mechanism simulations, many of which are full 3-D
models created in ADAMS™ (Automated Dynamic Analysis of Dynamic Systems). Dr.
Highland, North Carolina, May 9, 1994
Sridhar Kora, who has been a significant contributor to previous editions of this book, has
George N. Sandor
been brought on as a coauthor. He and Dr. Zhe Li at the University of Michigan have gen
erated all of the new Web-page material, available at hnp://www.prenhall.com/erdman.
A large number of the mechanisms in the book are now fully modeled and ani
mated. Thus, students may actually see kinematic and dynamic motions rather than at
tempt to envision movement. ln addition, ADAi\1S models of selected problems will be
available on the web. In some cases students can modify design parameters in order to test
systems response. There are many helpful tutorials and case studies on the Web page
which allows the instructor to teach a course in mechanism design almost entirely from
the web connection, including homework assignments.
Chapters 5 and 6 have been revised to reflect the web-enhanced fourth edition, A
compilation of student design projects will be regularly updated on the web site. Several
new design examples of type synthesis and applications of symmetrical coupler curves.
cognates, and paralJel motion mechanisms are included on the web ..A n extensive compi
lation of simulations of robotic grippers is also included. A new general purpose CAM
design module has been added and new material on type synthesis. path curvature. and ro
botic grippers are on die Web site. t
The authors wish to thank Dr. Ycsb Singh from UTSA and Dr. John Lenox of De f
sign Excellence, Inc. for their helpful input to this new addition. The authors thank Alyssa i
Burger for her help with the manuscript. As before, the authors acknow ledge numerous
i
students and colleagues from within and external to their universities for continued feed
back. encouragement, and influence that helped generate this book. f
j
I
Anhur G. Erdman
George N. Sandor
Sridhar Kota
i
l
This book deals with Kinematics 1
Synthetics and Analytics i
Written with love of the Science
Keeping in mind Srudent Clients!
\
t
xii Preface Sec. 1.1 Introduction xiii
1
Introduction to Kinematics
and Mechanisms
1. 1 INTRODUCTION
Engineering is based on the fundamental sciences of mathematics, physics, and chemistry:
In most cases. engineering involves the analysis of the conversion cf energy from some
source to one or more outputs, using one or more of the basic principles of these sciences.
Solid mechanics is one of the branches of physics which. among others. comains three
major subbranches: kinematics, which deals with the study of relative motion: statics.
which is the study of forces and moments. apart from motion: and kinetics. which deal�
with the action of forces on bodies. The combination of kinematics and kinetics is re
ferrcd 10 as dynamics. This text describes the appropriate mathematics, kinematics, ar.d
dynamics required to accomplish mechanism design.
A mechanism is a mechanical device that has t.i� purpose of transferring motitJon
and/or force from a source to an ourput. A lmku:;c consists of links tor bars) (see Tabk
l. l ), generally considered rigid, which arc connected by joints (Sec Table 1.2). such a.'£
pins (or rcvolutes), or prismatic joints, to form open or closed chains (or loops). Sud'.l
kinematic chains. with at least one link fixed. become (I) mechanisms if at least two oiher
links retain mobility. or (2) structures if no mobility remains. In other words, a mccha
nism permits relative motion between its "rigid" links; a structure does not. Since linkages
make simple mechanisms and can be designed to perform complex tasks, such as nonlirs
car motion and force transmission, thev will receive much attention in this book. Some 01f
the linkage design techniques presented here arc the result of a resurgence in the theory ovf
mechanisms based on the availability of the computer. Many of the design methods wer..e
discovered before the 1960s, but long, cumbersome calculation discouraged any further
development at that time.
MOTION
A large majority of mechanisms exhibit motion such that aJI the links move in paralleil
planes. This text emphasizes this type of motion, which is called two-dimensional, plane;
or planar motion. . Planar rigid-body motion consists of rotation about axes perpendiculan'
11
to the plane of motion and translation=-wuere all points in the body move along parallel p Path Tracer Point
str�1ght _o� plan": cun:itinear paths and all lines embedded in the body remain parallel to ---
their original orientation. Spatial mechanisms, introduced in Chap. 6 of Vol. 2, allow
movement in thr�e di_mensions. Co�binations of rotation around up to three nonparallel CCouurpvlee- r ,( / "
axe� an� translations 111 .u� to three different directions are possible depending on the con
stramts imposed by the Joints between links (spherical, helical, cylindrical, etc.: see Table
6.1, Vol. 2).
B
ln these discussions, all links are assumed lo be rigid bodies. In the second volume
(Chap. 5) of this text, this rigid-body assumption is relaxed. and it is assumed that the
links have elastic properties. But for now, lei us retain our rigid-body assumption for
mechanism links.
1.3 THE FOUR-BAR LINKAGE
Mech?nisms _are used in a great variety of machines and devices. The simplest closed
loop linkage is the four-bar, which has three moving links (plus one fixed link)" and four
"revolore," "pivoted." or "pin" joints (sec Fig. I. I a). The link that is connected to the Figure I.la Four-bar linkage notation.
power s�urce _or prime mover is called the i11p11t link (A01l). The follower link connects
the movmg pivot B 10 ground pivot 80. The coupler or floating link connects the two tracer point about Q m long. Since there is a hook at the path tracer point that holds a wire
moving pivots. A and B, thereby "coupling" the input link to the output link. Points on the rope (which will always hang vertically). the orientation of the coupler link is not impor
coupler li_nk (called path tracer points) generally trace out sixth-order algebraic coupler tant. Thus. this is clearly a path generation task.
c_urvcs. figure I. I b is taken from [89)t. in which very different coupler curves (dashed Figure 1.2b is a drive linkage for a lawn sprinkler. which is adjustable to obtain dif
lines) can be generated by using different path tracer points (the small solid circles). ferent ranges of oscillation of the sprinkler head. This adjustable linkage can be used to
The four-bar linkage is the most basic chain of pin-connected links that allows rcla vary the angle of rotation of the sprinkler head by using the clamping screw to change the
ti.ve motion be:wecn the links. (Three links pinned together is a structure.) Although a point of attachment of the coupler and follower links. The rcl�tive rotati?ns be_twcen the
simple mechan ism, the four-bar is very versatile and is used in thousands of applications. input and follower links of this mechanism accomplish the desired task ot function gener
The examples shown in Figs. I .2 through 1.6 illustrate a wide range of uses for the four ation.
bar. Even though these applications arc quite different, the linkages shown in the exam Fiuure l.2c shows a four-bar automobile hood linkage design. The linkage controls
ples (as well as all mechanisms) can be classified into three categories depending on the the relative orientation between the hood and the car frame. The hood must not interfere
t�sk that _th.e linkage �crforms: ji.111c1io11 generation. path generation, and motion genera with the frame of the car as it opens and must tit flush into the cavity in the car in the
tton (or rigid-body guidance). A.function generator (Figs. I .2b, I .4a, and 1.5) is a linkaue
in which the relative motion (or forces) between links connected to ground is of interest. .
pIn� tfhu ngcetnioenr agteionne r(aFtiiogns., t1h.2ea t aasnkd dtohees fnooutr -rbeqaru iproe rati opna tho ftr Faicge.r 1p.o3i)n, tw oen athree ccoonucpelernr elidn ko.n lIyn ,/ , ,,,,,. ... --, .. , \\ ,; , - ... '
w1th_ the p�th of a tracer point and not with the rotation of the coupler link. In morion gen ' '' I'I ',' I
era11011 (�1gs. 1.2c an� I .6). the entire motion of the coupler link is of concern: the path Il A / ::�------""'
tracer point x, y coordinates, and the angular orientation of the coupler link. These tasks I
',
are also discussed in Chaps. 2 and 8. \ __
-, ,..,,,..,,,.
Figure 1.2 shows a different four-bar that has been used to accomplish each task.
The level luffing crane of Fig. l .2a is a special type of four-bar that generates approximate Bo
straight-line morion of the path tracer point (point P). Cranes of this type can be rated at A0A = 1 AB = 2 B0B = 3 A0B0 = 3 AoA = 1 AB= 3 B0B = 2 Ao Bo= 3
50 tons capacity and typically have an approximate straight-line travel of the coupler
Figure l.lb Sample pages from the atlas of four-bar coupler curves by Hrones and Nel
son (89). Jn [89). lengths of dashes of the curves indicate I 0° increments of crank rota
• A linkage with one link fixed is a mechanism. tions. Here the lengths of dashes are not to scale. Solid circles are different path tracer
tNumbcrs in square brackets pertain to References at the end of this book. points.
2 Introduction to Kinematics and Mechanisms Chap. 1 Sec. 1.3 The Four-Bar Linkage 3
Input Link
(al
(b)
�
Sucker
Rod
(a) lb)
(c)
f'igure 1.2 Demonstration of four-bar tasks.
!cl ldl
closed position. The x. y locations of a path tracer point on the end of the hood as well as figure 1.3 (a and b) A scale model of the "Minnesota" oil pump. These fi�res sho,� the m��ha
the angle of the hood with respect to the car are critical. Thus this a case of motion gener ism near the limits of the straight-line portion of the path tracer point. (e) An imermediare posiuon
ation. :� the four-bar ponion produced by the Lineages� sofiware. (d) The ro.ur·bar along wit_h the driving
Figure 1.3 shows another example of a four-bar mechanism generating an approxi I1\0\, O th· eli1 n cko ucphlaeirn li"ndky a4d. "T (hleinske sa 5ll oawnd a d6j)u. sNtmoteicnet othfa tth eth setrreo kaer er asnevgeer. atlh cepreuboyn cs bf aonrg ci· onngn teh ce t iIn·cg n getht his o dfy tahde
mate straight-line path. In this case, the objective is to replace the standard "horse head" straight-line of the coupler curve.© University of Minnesota,
type of oil pumping mechanism shown in Fig. 1.4 with a design in which a cam (horse
ohbeajedc)t iivse nso btu rte aqruei rcelda.s sTifhieed f obuyr -dbifafre rmeenct htaasnkissm. Tsh seh ostwannd ainr dt hAemsee rtwicoa nf iPgeutrreosle huamv eI nssimtitiulater *�J It·.J'! " • �icon in margin indicates reference 10 CD·ROM m• back of book.
4 Introduction to Kinematics and Mechanisms Chap. 1 Sec. 1.3 The Four-Bar Linkage 5