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JOHN J. UlCKER, JR. GORDON R. PENNOCK

JOSEPH E. SHIGLEY• I '■»’v.. ‘ ■

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This version of rtie text has been odapted and customized. Not for sale in tfie U.S.A. or Canada.

* Theory of Machines and MechanismsInternational Fourth Edition

John J. Dicker, Jr.P r o fe s s o r E m e r itu s o f M e c h a n ic a l E n g in eer in g U n iv e rs ity o f W isc o n s in -M a d iso n

Gordon R. PennockA s s o c ia te P r o fe s s o r o f M e c h a n ic a l E n g in eer in g P u rd u e U n iv e rs ity

Joseph E.ShigleyL a te P r o fe s s o r E m e r itu s o f M ech a n ica l E n g in e e r in g T he U n iv e rs ity o f M ic h ig a n

N ew Y ork O xfo rd OXFORD UNIVERSITY PRESS 2011

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Library o f Congress Cataloging-in-Publication Data Uicker, John Joseph.

Theory o f machines and mechanisms/John J. Uicker. Jr., Gordon R. Pennock,Joseph E. Shigley. - International 4th ed.

p. cm.Shigley's name appears first on the earlier edition.Includes bibliographical references and Index ISBN 978-0-19-977781-5I. Mechanical engineering. I. Pennock. G. R. II. Shigley. Joseph Edward. III. Title.

TJ145.S54 201162l.8-ilc22 2010035735

ISBN 978-0-19-977781-5

Oxford International edition: For sale in Europe, Middle East, and Asia only and not for export therefrom. Nor for sale in the USA. Canada, and the UK.

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Printed in the United States o f America on acid-free paper

This tex tbook is dedicated to the memory o f m y late father, John J. U icker, Em eritus D ean o f Engineering, U niversity o f Detroit, to my late m other; E lizabeth F. U icker, and to my six children, T heresa A. Zenchenko, John J. Uicker, III, Joseph M. Uicker, Dorothy J. Winger, B arbara A. Peterson, and Joan E. Home.

- John J. Uicker, Jr.

This w ork is a lso dedicated first and foremost to m y wife, M ollie B., and m y son, C allum R. Pennock. T he w ork is also dedicated to my friend and m entor, the late Dr. An (A ndy) Tzu Yang, and to m y colleagues in the School o f M echanical Engineering, Purdue University, W est Lafayette, Indiana.

— G ordon R. Pennock

Finally, this tex t is dedicated to the memory o f the third author, the late Joseph E. Shigley, P rofessor Em eritus, M echanical Engineering D epartm ent, U niversity o f M ichigan, Ann Arbor, on w hose previous w ritings much o f this text is based.

Contents

PREFACE xviiABOUT THE AUTHORS xxv

PARTI KINEMATICS AND MECHANISMS 3

1 The World of Mechanisms 5

1.1 Introduction 5

1.2 A nalysis and Synthesis 61.3 The Science o f M echanics 6

1.4 Term inology, D efinitions, and A ssum ptions 7

1.5 Planar, Spherical, and Spatial M echanism s 121.6 M obility 141.7 C lassification o f M echanism s 19

1.8 K inem atic Inversion 34

1.9 G rasho f’s L a w 351.10 M echanical A dvantage 38

1.11 References 40 P roblem s 40

2 Position and Displacement 44

2.1 Locus o f a M oving Point 442.2 Position o f a Point 47

2.3 Position D ifference Between Two Points 492.4 A pparent Position o f a Point 50

2.5 A bsolute Position o f a Point 512.6 T he L oop-C losure Equation 522.7 G raphic Position A nalysis 572.8 A lgebraic Position A nalysis 64

2.9 C om plex-A Igebra Solutions o f Planar V ector Equations 672.10 C om plex Polar A lgebra 692.11 T he Chace Solutions to Planar Vector Equations 72

2.12 Position A nalysis Techniques 772.13 C oupler-C urve G eneration 81

vii

vlli CONTENTS

2.14 D isplacem ent o f a M oving Poin t 832.15 D isplacem ent D ifference betw een Two Points 842.16 R otation and T ranslation 852.17 A pparent D isplacem ent 872.18 A bsolu te D isplacem ent 88

2.19 A pparent A ngular D isp lacem ent 882.20 R eferences 93

Problem s 93

Velocity 983.1 D efin ition o f V elocity 983.2 R otation o f a R igid Body 99

3.3 V elocity D ifference betw een Points o f a R igid Body 1023.4 G raphic M ethods; V elocity Polygons 1043.5 A pparent V elocity o f a Point in a M oving C oordinate System 1113.6 A pparent A ngular V elocity 1183.7 D irect C ontact and R olling C ontact 118

3.8 System atic S trategy fo r V elocity A nalysis 1203.9 A nalytic M ethods 1213.10 C om plex-A Igebra M ethods 1223.11 The V ector M ethod 1263.12 The M ethod o f K inem atic C oefficients 1283.13 Instantaneous C en ter o f Velocity 1373.14 The A ronho ld -K ennedy T heorem o f Three C enters 1403.15 L ocating Instant C enters o f V elocity 141

3.16 V elocity A nalysis U sing Instant C enters 1443.17 T he A ngular V elocity Ratio T heorem 148

3.18 R elationships betw een F irst-O rder K inem atic C oefficients and Instant C en ters 148

3.19 F reudenste in ’s T heorem 1523.20 Indices o f M erit; M echanical A dvantage 1533.21 C entrodes 155

3.22 R eferences 157 P roblem s 158

Acceleration 166

4.1 D efinition o f A cceleration 1664.2 A ngular A cceleration 169

4.3 A cceleration D ifference betw een Points o f a R igid Body 1694.4 A cceleration Polygons 177

CONTENTS Ix

4.5 A pparen t A cceleration o f a Point in a M oving C oordinate System 180

4.6 A pparent A ngular A cceleration 1914.7 D irect C ontact and Rolling Contact 191

4 .8 System atic S trategy for A cceleration A nalysis 1944.9 A nalytic M ethods 196

4.10 C om plex-A Igebra M ethods 1974.11 T he C hace Solutions 199

4.12 T he M ethod o f K inem atic C oefficients 2004.13 T he E u ler-S avary Equation 2094.14 T he B obillie r Constructions 214

4.15 Instantaneous Center o f A cceleration 217

4 .16 T he B resse C ircle (or de La Hire C irc le) 2194.17 R adius o f Curvature o f a Point T ra jectory U sing K inem atic

C oefficients 2234.18 T he C ubic o f S tationary Curvature 225

4.19 R eferences 233

P roblem s 233

5 Multi-Degree-of-Freedom Planar Linkages 238

5.1 Introduction 2385.2 Position A nalysis; A lgebraic Solution 242

5.3 G raphical M ethods; Velocity Polygons 2435.4 Instan t C enters o f Velocity 244

5.5 F irst-O rder K inem atic Coefficients 248

5.6 T he M ethod o f Superposition 2535.7 G raphical M ethod; A cceleration Polygons 2565.8 Second-O rder K inem atic Coefficients 2585.9 Path C urvature o f a C oupler Point 262

5.10 T he Finite D ifference M ethod 2675.11 R eferences 269

P roblem s 270

PART 2 DESIGN OF M ECHANISMS 273

6 Cam Design 2756.1 In troduction 275

6.2 C lassification o f Cam s and Follow ers 2766.3 D isplacem ent D iagram s 278

6.4 G raphical L ayou t o f C am Profiles 281

CONTENTS

6.5 K inem atic C oefficien ts o f the F o llow er M otion 2856.6 H igh-Speed C am s 289

6.7 Standard C am M otions 2916.8 M atching D erivatives o f D isplacem ent D iagram s 300

6.9 Plate Cam w ith R eciprocating F lat-Face F o llow er 3046.10 Plate Cam w ith R eciprocating R oller F ollow er 308

6 .11 References 326 Problem s 327

Spur Gears 330

7.1 Term inology and D efin itions 3307.2 Fundam ental Law o f Toothed G earing 3337.3 Involute P roperties 334

7.4 Interchangeable G ears; A G M A Standards 3367.5 Fundam entals o f G ear-T oo th A ction 337

7.6 The M anufacture o f G ear Teeth 3 4 17.7 Interference and U ndercutting 344

7.8 C ontact Ratio 3467.9 Varying the C en ter D istance 3487.10 Involutom etry 350

7.11 N onstandard G ear Teeth 3537.12 References 362 P roblem s 362

Helical Gears, Bevel Gears, Worms, and Worm Gears 365

8.1 Parallel-A xis H elical G ears 3658.2 H elical G ear Tooth R elations 3668.3 H elical G ear Tooth Proportions 3688.4 C ontact o f H elical G ear Teeth 369

8.5 Replacing S pur G ears w ith H elical G ears 370

8.6 H erringbone G ears 3718.7 C rossed-A xis H elical G ears 3728.8 S traight-Tooth Bevel G ears 374

8.9 Tooth P roportions fo r Bevel G ears 3778.10 C row n and F ace G ears 378

8 .11 Spiral Bevel G ears 380

8.12 H ypoid G ears 3818.13 W orms and W orm G ears 3828.14 N otes 385

Problem s 386