Kinematics and Dynamics of Mechanical Systems, Second Edition: Implementation in MATLAB® and SimMechanics®

535 Pages·2018·32.447 MB·English

by  Russell, Kevin, Shen, Qiong, Sodhi, Rajpal S

Kinematics and Dynamics
of Mechanical Systems
Implementation in MATLAB®
and Simmechanics®

Kinematics and Dynamics
of Mechanical Systems
Implementation in MATLAB®
and Simmechanics®
Second Edition
Kevin Russell, Qiong Shen, Raj S. Sodhi
MATLAB® and Simulink® are trademarks of The MathWorks, Inc. and are used with permission. The MathWorks
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ticular pedagogical approach or particular use of the MATLAB® and Simulink® software.
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Library of Congress Cataloging-in-Publication Data
Names: Russell, Kevin (Mechanical engineer), author. | Shen, Qiong
(Mechanical engineer), author. | Sodhi, R. S. (Raj S.), author.
Title: Kinematics and dynamics of mechanical systems : implementation in
MATLAB and SimMechanics / Kevin Russell, Qiong Shen, Raj S. Sodhi.
Description: Boca Raton : CRC Press, Taylor & Francis, 2018. | Includes index.
Identifiers: LCCN 2018022923 | ISBN 9781138584044 (hardback)
Subjects: LCSH: Machinery, Kinematics of--Computer simulation. | Machinery,
Dynamics of—Computer simulation. | MATLAB. | SimMechanics.
Classification: LCC TJ175 .R87 2018 | DDC 621.01/5311—dc23
LC record available at https://lccn.loc.gov/2018022923
Visit the Taylor & Francis Web site at
http://www.taylorandfrancis.com
and the CRC Press Web site at
http://www.crcpress.com
Contents
Preface ...........................................................................................................................................xiii
Authors ........................................................................................................................................xvii
1. Introduction to Kinematics ..................................................................................................1
1.1 Kinematics ......................................................................................................................1
1.2 Kinematic Chains and Mechanisms ..........................................................................2
1.3 Mobility, Planar, and Spatial Mechanisms ................................................................3
1.4 Types of Mechanism Motion .......................................................................................5
1.5 Kinematic Synthesis .....................................................................................................7
1.6 Units and Conversions .................................................................................................8
1.7 Software Resources .......................................................................................................9
1.8 Summary ........................................................................................................................9
References ...............................................................................................................................10
Additional Reading ...............................................................................................................11
2. Mathematical Concepts in Kinematics ............................................................................13
2.1 Introduction .................................................................................................................13
2.2 Complex Numbers and Operations .........................................................................13
2.2.1 Complex Number Forms ..............................................................................13
2.2.2 Complex Number Addition ..........................................................................15
2.2.3 Complex Number Multiplication and Differentiation .............................17
2.3 Vector and Point Representation ..............................................................................20
2.4 Linear Simultaneous Equations, Matrices, and Matrix Operations ....................22
2.4.1 Linear Simultaneous Equation Systems and Matrices .............................22
2.4.2 Matrix Transpose, Addition, Subtraction, and Multiplication ................23
2.4.3 The Identity Matrix and Matrix Inversion .................................................26
2.5 Intermediate and Total Spatial Motion ....................................................................29
2.6 General Transformation Matrix ................................................................................33
2.7 Summary ......................................................................................................................36
References ...............................................................................................................................37
Additional Reading ...............................................................................................................37
Problems ..................................................................................................................................37
3. Fundamental Concepts in Kinematics .............................................................................41
3.1 Types of Planar and Spatial Mechanisms ...............................................................41
3.1.1 Planar Four-Bar Mechanism ........................................................................41
3.1.2 S lider-Crank Mechanism ..............................................................................41
3.1.3 Geared Five-Bar Mechanism ........................................................................42
3.1.4 Planar Multiloop Six-Bar Mechanisms .......................................................44
3.1.5 Spatial Four-Bar Mechanisms ......................................................................45
3.2 Links, Joints, and Mechanism Mobility ...................................................................46
3.3 Number Synthesis .......................................................................................................49
3.4 Grashof’s Criteria and Transmission Angle ............................................................50
3.5 Circuit Defect ...............................................................................................................53
v
vi Contents
3.6 Mechanism Inversion .................................................................................................54
3.7 Passive Degree of Freedom and Paradoxes .............................................................55
3.8 Summary ......................................................................................................................56
References ...............................................................................................................................57
Problems ..................................................................................................................................58
4. Kinematic Analysis of Planar Mechanisms ....................................................................63
4.1 Introduction .................................................................................................................63
4.2 Numerical Solution Method for Two Simultaneous Equations ...........................64
4.3 Link Velocity and Acceleration Components in Planar Space .............................64
4.4 Four-Bar Mechanism Analysis .................................................................................66
4.4.1 Displacement Equations ...............................................................................66
4.4.2 Velocity Equations .........................................................................................67
4.4.3 Acceleration Equations ..................................................................................68
4.4.4 Kinematics of Coupler Locations of Interest ..............................................70
4.4.5 Instant Center, Centrodes, and Centrode Generation ..............................76
4.5 Slider-Crank Mechanism Analysis ..........................................................................80
4.5.1 Displacement Equations ...............................................................................80
4.5.2 Velocity Equations .........................................................................................81
4.5.3 Acceleration Equations ..................................................................................83
4.5.4 Centrode Generation .....................................................................................89
4.6 Geared Five-Bar Mechanism Analysis ....................................................................91
4.6.1 D isplacement Equations ...............................................................................91
4.6.2 V elocity Equations .........................................................................................92
4.6.3 A cceleration Equations ..................................................................................93
4.6.4 K inematics of Intermediate Link Locations of Interest ............................95
4.7 Watt II Mechanism Analysis .....................................................................................97
4.8 Stephenson III Mechanism Analysis ......................................................................100
4.8.1 D isplacement Equations .............................................................................100
4.8.2 V elocity Equations .......................................................................................103
4.8.3 A cceleration Equations ................................................................................104
4.8.4 K inematics of Intermediate Link Locations of Interest ..........................105
4.9 Time and Driver Angular Velocity .........................................................................108
4.10 Mechanism Configurations .....................................................................................108
4.11 Constructing Cognates.............................................................................................109
4.12 Planar Mechanism Kinematic Analysis and Modeling in Simmechanics® ......112
4.13 Summary ....................................................................................................................117
References .............................................................................................................................118
Additional Reading .............................................................................................................118
Problems ................................................................................................................................118
5. Dimensional Synthesis......................................................................................................131
5.1 Introduction ...............................................................................................................131
5.2 Branch and Order Defects .......................................................................................133
5.3 Planar Four-Bar Motion Generation: Three Precision Positions ........................135
5.4 Order- and Branch-Defect Elimination .................................................................140
5.5 Path Generation versus Motion Generation ..........................................................144
5.6 Stephenson III Motion Generation: Three Precision Positions ...........................145
5.7 Planar Four-Bar Function Generation: Three Precision Points ..........................149
Contents vii
5.8 Planar Four-Bar Function Generation: FSPs and MSPs .......................................153
5.9 Mechanism Dimensions: From Dimensional Synthesis to
Kinematic Analysis ...................................................................................................158
5.10 Summary ....................................................................................................................163
References .............................................................................................................................164
Additional Reading .............................................................................................................165
Problems ................................................................................................................................165
6. Static Force Analysis of Planar Mechanisms ................................................................175
6.1 Introduction ...............................................................................................................175
6.2 Static Loading in Planar Space ................................................................................176
6.3 Four-Bar Mechanism Analysis ...............................................................................177
6.4 Slider-Crank Mechanism Analysis ........................................................................182
6.5 Geared Five-Bar Mechanism Analysis ..................................................................185
6.6 Watt II Mechanism Analysis ...................................................................................190
6.7 Stephenson III Mechanism Analysis ......................................................................196
6.8 P lanar Mechanism Static Force Analysis and Modeling in SimMechanics® ....201
6.9 Summary ....................................................................................................................204
References .............................................................................................................................205
Additional Reading .............................................................................................................206
Problems ................................................................................................................................206
7. Dynamic Force Analysis of Planar Mechanisms .........................................................223
7.1 Introduction ...............................................................................................................223
7.2 Dynamic Loading in Planar Space .........................................................................224
7.3 Four-Bar Mechanism Analysis ...............................................................................224
7.4 Slider-Crank Mechanism Analysis ........................................................................230
7.5 Geared Five-Bar Mechanism Analysis ..................................................................233
7.6 Watt II Mechanism Analysis ...................................................................................238
7.7 Stephenson III Mechanism Analysis ......................................................................243
7.8 Mass Moment of Inertia and Computer-Aided Design Software ......................248
7.9 Planar Mechanism Dynamic Force Analysis and Modeling in
Simmechanics® ..........................................................................................................250
7.10 Summary ....................................................................................................................256
References .............................................................................................................................256
Additional Reading .............................................................................................................256
Problems ................................................................................................................................256
8. Design and Kinematic Analysis of Gears .....................................................................271
8.1 Introduction ...............................................................................................................271
8.2 Gear Types .................................................................................................................272
8.3 SPUR-Gear Nomenclature and Relationships of Mating Gears ........................274
8.3.1 Spur-Gear Nomenclature ...........................................................................274
8.3.2 Pressure Angle and Involute Tooth Profile ..............................................277
8.3.3 Gear Center Distance and Contact Ratio ..................................................280
8.3.4 Gear-Tooth Interference and Undercutting..............................................282
8.3.5 Backlash .........................................................................................................283
8.4 Helical-Gear Nomenclature ....................................................................................284
8.5 Gear Kinematics ........................................................................................................287
viii Contents
8.5.1 Spur Gears and Gear Trains .......................................................................287
8.5.2 Planetary Gear Trains .................................................................................291
8.5.3 Rack and Pinion Gears ................................................................................295
8.5.4 Helical Gears ................................................................................................296
8.5.5 Bevel Gears ...................................................................................................298
8.5.6 Worm Gears ..................................................................................................301
8.6 Summary ....................................................................................................................305
References .............................................................................................................................305
Additional Reading .............................................................................................................306
Problems ................................................................................................................................306
9. Design and Kinematic Analysis of Disk Cams ............................................................311
9.1 Introduction ...............................................................................................................311
9.2 Follower Types ...........................................................................................................312
9.3 Follower Motion ........................................................................................................313
9.3.1 Rise, Fall, and Dwell ....................................................................................313
9.3.2 Displacement, Velocity, Acceleration, and Jerk ........................................315
9.3.3 Constant Velocity Motion ...........................................................................315
9.3.4 Constant Acceleration Motion ...................................................................317
9.3.5 Simple Harmonic Motion ...........................................................................320
9.3.6 Cycloidal Motion ..........................................................................................322
9.3.7 Polynomial Motion ......................................................................................325
9.4 Disk Cam Design and Pressure Angle ..................................................................331
9.5 Summary ....................................................................................................................336
References .............................................................................................................................337
Additional Reading .............................................................................................................337
Problems ................................................................................................................................338
10. Kinematic Analysis of Spatial Mechanisms .................................................................343
10.1 Introduction ...............................................................................................................343
10.2 RRSS Mechanism Analysis .....................................................................................344
10.2.1 Displacement Equations .............................................................................344
10.2.2 Velocity Equations .......................................................................................346
10.2.3 Acceleration Equations ................................................................................347
10.3 RSSR Mechanism Analysis ......................................................................................350
10.3.1 Displacement Equations .............................................................................350
10.3.2 Velocity Equations .......................................................................................351
10.3.3 Acceleration Equations ................................................................................352
10.4 Four-Revolute Spherical Mechanism Analysis .....................................................355
10.5 Planar Four-Bar Kinematic Analysis Using RRSS and RSSR Kinematic
Equations ....................................................................................................................359
10.6 Spatial Mechanism Kinematic Analysis and Modeling in Simmechanics® ......362
10.7 Summary ....................................................................................................................364
References .............................................................................................................................365
Problems ................................................................................................................................365
11. Introduction to Robotic Manipulators ...........................................................................373
11.1 Introduction ...............................................................................................................373
11.2 Terminology and Nomenclature ............................................................................374
Contents ix
11.3 Robotic Manipulator Mobility and Types .............................................................375
11.4 The General Transformation Matrix ......................................................................377
11.5 Forward Kinematics .................................................................................................381
11.5.1 Definition and Application .........................................................................381
11.5.2 P-P-P ...............................................................................................................381
11.5.3 R-P-P ...............................................................................................................383
11.5.4 R-R-P ..............................................................................................................385
11.5.5 R-R-R ..............................................................................................................387
11.5.6 R -R-C ..............................................................................................................389
11.6 Inverse Kinematics ....................................................................................................392
11.6.1 D efinition and Application .........................................................................392
11.6.2 P -P-P ...............................................................................................................392
11.6.3 R -P-P ...............................................................................................................394
11.6.4 R -R-P ..............................................................................................................396
11.6.5 R -R-R ..............................................................................................................397
11.6.6 R-R-C ..............................................................................................................399
11.7 Robotic Manipulator Kinematic Analysis and Modeling in
Simmechanics® ...................................................................................................401
11.8 Summary ....................................................................................................................402
References .............................................................................................................................402
Additional Reading .............................................................................................................403
Problems ................................................................................................................................403
Appendix A: User Information and Instructions for MATLAB® ....................................409
A.1 Required MATLAB Toolkits ....................................................................................409
A.2 Description of MATLAB Operators and Functions .............................................409
A.3 Preparing and Running Files in MATLAB and Operations in
SimMechanics .......................................................................................................409
A.4 Rerunning MATLAB and SimMechanics Files with Existing *.csv Files ........413
A.5 Minimum Precision Requirement for Appendix File User Input ......................413
Appendix B: User Instructions for Chapter 4 MATLAB® Files ........................................415
B.1 Planar Four-Bar Mechanism ...................................................................................415
B.2 Planar Four-Bar Fixed and Moving Centrode Generation .................................415
B.3 Slider-Crank Mechanism .........................................................................................417
B.4 Geared Five-Bar Mechanism (Two Gears) .............................................................419
B.5 Geared Five-Bar Mechanism (Three Gears) ..........................................................419
B.6 Watt II Mechanism ....................................................................................................420
B.7 Stephenson III Mechanism ......................................................................................422
Appendix C: User Instructions for Chapter 6 MATLAB® Files .......................................425
C.1 Planar Four-Bar Mechanism ...................................................................................425
C.2 Slider-Crank Mechanism .........................................................................................425
C.3 Geared Five-Bar Mechanism (Two Gears) .............................................................428
C.4 Geared Five-Bar Mechanism (Three Gears) ..........................................................429
C.5 Watt II Mechanism ....................................................................................................430
C.6 Stephenson III Mechanism ......................................................................................431
Appendix D: User Instructions for Chapter 7 MATLAB® Files .......................................435
D.1 P lanar Four-Bar Mechanism ...................................................................................435
D.2 Slider-Crank Mechanism .........................................................................................435