THEORY OF MACHINES AND MECHANISMS Third Edition PDF

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THEORY OF MACHINES AND MECHANISMS Third Edition John J. Dicker, Jr. Professor of Mechanical Engineering University of Wisconsin-Madison Gordon R. Pennock Associate Professor of Mechanical Engineering Purdue University Joseph E. Shigley Late Professor Emeritus of Mechanical Engineering The University...

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T heory Of Machine solut ion manual-Oxford Universit y Press (2014) Saif Ali

THEORY AND

O F M A C H IN E S

M E C H A N IS M S

T h ir d E d itio n

J o h n J . D ic k e r , J r . P rofessor of M echanical E ngineering U niversity of W isconsin-M adison

G ordon R . P ennock A ssociate P rofessor of M echanical E ngineering P urdue U niversity

J o s e p h E . S h ig le y L ate P rofessor E m eritus of M echanical E ngineering T he U niversity of M ichigan

New York

Oxford

OXFORD UNIVERSITY PRESS 2003

Oxford University Press Oxford New York Auckland Bangkok Buenos Aires Cape Town Chennai Dar es Salaam Delhi Hong Kong Istanbul Karachi Kolkata Kuala Lumpur Madrid Melbourne Mexico City Mumbai Nairobi Sao Paulo Shanghai Taipei Tokyo Toronto

Copyright © 2003 by Oxford University Press, Inc. Published by Oxford University Press, Inc. 198 Madison Avenue, New York, New York, 10016 http://www.oup-usa.org Oxford is a registered trademark of Oxford University Press All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior permission of Oxford University Press.

IS B N

0-1 9-5 I 5598-X

Printing number:

9 8 7 6 5 4 3 2 I

Printed in the United States of America on acid-free paper

This textbook is dedicated to the memory of the third author, the late J o s e p h E . S h i g l e y , Professor Emeritus, Mechanical Engineering Department, University of Michigan, Ann Arbor, on whose previous writings much of this edition is based.

This work is also dedicated to the memory of my father, John J. Uicker, Emeritus Dean of Engineering, University of Detroit; to my mother, Elizabeth F. Uicker; and to my six children, Theresa A. Uicker, John J. Uicker Ill, Joseph M. Uicker, Dorothy J. Winger, Barbara A. Peterson, and Joan E. Uicker. -J o h n

J . V ic k e r , J r .

This work is also dedicated first and foremost to my wife, Mollie B., and my son, Callum R. Pennock. The work is also dedicated to my friend and mentor Dr. An (Andy) Tzu Yang and my colleagues in the School of Mechanical Engineering, Purdue University, West Lafayette, Indiana. -G o r d o n

R . P ennock

C o n te n ts

PREFACE ABOUT

P a rt 1

X III

THE AUTHORS

X V II

K IN E M A T IC S A N D M E C H A N IS M S 1 T h e W o rld o f M e c h a n is m s 1.1

Introduction

1.2

Analysis and Synthesis

1 3

3 4

1.3

The Science of Mechanics

1.4

Terminology, Definitions, and Assumptions

5

1.5

Planar, Spherical, and Spatial Mechanisms

10

1.6

Mobility

1.7

Classification of Mechanisms

1.8

Kinematic Inversion

1.9

Grashof's Law

II 14

26

27

1.10 Mechanical Advantage Problems

4

29

31

2 P o s itio n a n d D is p la c e m e n t

33

2.1

Locus of a Moving Point

33

2.2

Position of a Point

2.3

Position Difference Between Two Points

2.4

Apparent Position of a Point

38

2.5

Absolute Position of a Point

39

2.6

The Loop-Closure

2.7

Graphic Position Analysis

2.8

Algebraic Position Analysis

2.9

Complex-Algebra

36

Equation

37

41 45 51

Solutions of Planar Vector Equations

2.10 Complex Polar Algebra

57

2.11 Position Analysis Techniques

60

2.12 The Chace Solutions to Planar Vector Equations 2.13 Coupler-Curve

Generation

64

68

2.14 Displacement of a Moving Point

70

2.15 Displacement Difference Between Two Points

71

55

vi

CONTENTS

2.16 Rotation and Translation

72

2.17 Apparent Displacement

74

2.18 Absolute Displacement

75

Problems 3 V e lo c ity

76 79

3.1

Definition of Velocity

3.2

Rotation of a Rigid Body

3.3

Velocity Difference Between Points of a Rigid Body

3.4

Graphic Methods; Velocity Polygons

3.5

Apparent Velocity of a Point in a Moving Coordinate System

3.6

Apparent Angular Velocity

3.7

Direct Contact and Rolling Contact

3.8

Systematic Strategy for Velocity Analysis

3.9

Analytic Methods

3.10 Complex-Algebra

79 80

92

97 98 99

100 Methods

101

3.11 The Method of Kinematic Coefficients 3.12 The Vector Method 3.13 Instantaneous

82

85

105

116

Center of Velocity

3.14 The Aronhold-Kennedy

117

Theorem of Three Centers

3.15 Locating Instant Centers of Velocity

120

3.16 Velocity Analysis Using Instant Centers 3.17 The Angular-Velocity-Ratio

119

Theorem

123 126

3.18 Relationships Between First-Order Kinematic Coefficients and Instant Centers 3.19 Freudenstein' s Theorem

129

3.20 Indices of Merit; Mechanical Advantage 3.21 Centrodes Problems

130

133

135

4 A c c e le ra tio n

141

4.1

Definition of Acceleration

4.2

Angular Acceleration

4.3

Acceleration Difference Between Points of a Rigid Body

4.4

Acceleration Polygons

4.5

Apparent Acceleration of a Point in a Moving Coordinate System

4.6

Apparent Angular Acceleration

4.7

Direct Contact and Rolling Contact

4.8

Systematic Strategy for Acceleration Analysis

4.9

Analytic Methods

4.10 Complex-Algebra

141

144 144

151 163

168 Methods

169

164 167

155

127

CONTENTS 4.11 The Method of Kinematic Coefficients 4.12 The Chace Solutions

175

4.13 The Instant Center of Acceleration 4.14 The Euler-Savary

171

Equation

178

4.15 The Bobillier Constructions

183

177

4.16 Radius of Curvature of a Point Trajectory Using Kinematic Coefficients 4.17 The Cubic of Stationary Curvature Problems

P a rt 2

188

190

D E S IG N O F M E C H A N IS M S

5 C a rn D e s ig n

195

197

5.1

Introduction

197

5.2

Classification of Cams and Followers

5.3

Displacement Diagrams

5.4

Graphical Layout of Cam Profiles

5.5

Kinematic Coefficients of the Follower Motion

5.6

High-Speed Cams

5.7

Standard Cam Motions

5.8

Matching Derivatives of the Displacement Diagrams

5.9

Plate Cam with Reciprocating Flat-Face Follower

203

212

Roller Follower

250

6 S p u r G e a rs

252

6.1

Terminology and Definitions

6.2

Fundamental Law of Toothed Gearing

6.3

Involute Properties

252

Interchangeable

6.5

Fundamentals

6.6

The Manufacture of Gear Teeth

6.7

Interference and Undercutting

6.8

Contact Ratio

6.9

Varying the Center Distance

Gears; AGMA Standards of Gear-Tooth Action 262 265

268 270

271

6.11 Nonstandard Gear Teeth Problems

274

282

7 H e lic a l G e a rs

255

256

6.4

6.10 Involutometry

207

211

5.10 Plate Cam with Reciprocating Problems

198

200

286

7.1

Parallel-Axis Helical Gears

7.2

Helical Gear Tooth Relations

286 287

259

257

222 225

230

187

vii

viii

CONTENTS

7.3

Helical Gear Tooth Proportions

7.4

Contact of Helical Gear Teeth

7.5

Replacing Spur Gears with Helical Gears

7.6

Herringbone Gears

7.7

Crossed-Axis Helical Gears

Problems

289 290

292 292

295

8 B e v e l G e a rs

297

8.1

Straight-Tooth Bevel Gears

8.2

Tooth Proportions for Bevel Gears

8.3

Crown and Face Gears

8.4

Spiral Bevel Gears

8.5

Hypoid Gears

Problems

Basics

Problems

297 301

302

303

304

305

9 W o rm s a n d W o rm G e a rs 9.1

291

306

306 310

1 0 M e c h a n is m T ra in s

311

10.1 Parallel-Axis Gear Trains

311

10.2 Examples of Gear Trains

313

10.3 Determining Tooth Numbers 10.4 Epicyclic Gear Trains

314

315

10.5 Bevel Gear Epicyclic Trains

317

10.6 Analysis of Planetary Gear Trains by Formula 10.7 Tabular Analysis of Planetary Gear Trains 10.8 Adders and Differentials

319

323

10.9 All Wheel Drive Train Problems

317

327

329

1 1 S y n th e s iso f L in k a g e s

332

11.1 Type, Number, and Dimensional Synthesis

332

11.2 Function Generation, Path Generation, and Body Guidance 11.3 Two-Position Synthesis of Slider-Crank Mechanisms 11.4 Two-Position Synthesis of Crank-and-Rocker

333

333

Mechanisms

334

11.5 Crank-Rocker Mechanisms with Optimum Transmission Angle 11.6 Three-Position

Synthesis

338

11.7 Four-Position Synthesis; Point-Precision

Reduction

339

. 11.8 Precision Positions; Structural Error; Chebychev Spacing 11.9 The Overlay Method

343

341

335

CONTENTS 11.10 Coupler-Curve

Synthesis

344

11.11 Cognate Linkages; The Roberts-Chebychev 11.l2 Bloch's Method of Synthesis 11.I3 Freudenstein's

Equation

350

11.15 Synthesis of Dwell Mechanisms II.I 6 Intermittent Rotary Motion

361

368

12.1

Introduction

12.2

Exceptions in the Mobility of Mechanisms

12.3

The Position-Analysis

12.4

Velocity and Acceleration Analyses

12.5

The Eulerian Angles

12.6

The Denavit-Hartenberg

12.7

Transformation-Matrix

12.8

Matrix Velocity and Acceleration Analyses

12.9

Generalized Mechanism Analysis Computer Programs

1 3 R o b o tic s

368 Problem

369

373 378

384 Parameters

387

Position Analysis

389 392

400

403

13.1

Introduction

13.2

Topological Arrangements of Robotic Arms

13.3

Forward Kinematics

13.4

Inverse Position Analysis

13.5

Inverse Velocity and Acceleration Analyses

13.6

Robot Actuator Force Analyses

Problems

P a rt 3

356

360

366

1 2 S p a tia l M e c h a n is m s

Problems

348

352

11.I4 Analytic Synthesis Using Complex Algebra

Problems

Theorem

403

411 418

421

D Y N A M IC S O F M A C H IN E S

423

1 4 S ta tic ;:F o rc e A n a ly s is 14.1

Introduction

14.2

Newton's Laws

404

407

425

425 427

14.3

Systems of Units

14.4

Applied and Constraint Forces

428

14.5

Free-Body Diagrams

14.6

Conditions for Equilibrium

14.7

Two- and Three-Force Members

14.8

Four-Force Members

429

432

443

433 435

414

397

x

CONTENTS

14.9

Friction-Force

Models

445

14.10 Static Force Analysis with Friction

448

14.11 Spur- and Helical-Gear Force Analysis

451

14.12 Straight- Bevel-Gear Force Analysis 14.13 The Method of Virtual Work Problems

457

461

464

1 5 D y n a m ic F o rc e A n a ly s is (P la n a r)

470

15.1

Introduction

15.2

Centroid and Center of Mass

470

15.3

Mass Moments and Products of Inertia

15.4

Inertia Forces and D' Alembert's Principle

15.5

The Principle of Superposition

15.6

Planar Rotation About a Fixed Center

15.7

Shaking Forces and Moments

15.8

Complex Algebra Approach

15.9

Equation of Motion

Problems

470 475

485 489

492 492

502

511

1 6 D y n a m ic F o rc e A n a ly s is (S p a tia l)

515

16.1

Introduction

16.2

Measuring Mass Moment of Inertia

16.3

Transformation

515 of Inertia Axes

515

519

16.4

Euler's Equations of Motion

16.5

Impulse and Momentum

16.6

Angular Impulse and Angular Momentum

Problems

478

523

527 528

538

1 7 V ib ra tio n A n a ly s is

542

17.1

Differential Equations of Motion

17.2

A Vertical Model

17.3

Solution of the Differential Equation

17.4

Step Input Forcing

17.5

Phase-Plane Representation

17.6

Phase-Plane Analysis

17.7

Transient Disturbances

17.8

Free Vibration with Viscous Damping

17.9

Damping Obtained by Experiment

547

551 553

555 559

17.10 Phase-Plane Representation 574

563 565

of Damped Vibration

17.11 Response to Periodic Forcing 17.12 Harmonic Forcing

542

546

571

567

CONTENTS 17.13 Forcing Caused by Unbalance 17.14 Relative Motion 17.15 Isolation

579

580

580

17.16 Rayleigh's Method

583

17.17 First and Second Critical Speeds of a Shaft 17.18 Torsional Systems Problems

586

592

594

1 8 D y n a m ic s o f R e c ip ro c a tin g E n g in e s 18.1

Engine Types

18.2

Indicator Diagrams

598 603

18.3

Dynamic Analysis-General

18.4

Gas Forces

18.5

Equivalent Masses

18.6

Inertia Forces

18.7

Bearing Loads in a Single-Cylinder

18.8

Crankshaft Torque

18.9

Engine Shaking Forces

1 9 B a la n c in g

606

606 609

610 Engine

613

616

18.10 Computation Hints Problems

598

616

617

620

621

19.1

Static Unbalance

621

19.2

Equations of Motion

19.3

Static Balancing Machines

622 624

19.4

Dynamic Unbalance

19.5

Analysis of Unbalance

626

19.6

Dynamic Balancing

635

19.7

Balancing Machines

638

19.8

Field Balancing with a Programmable

Calculator

19.9

Balancing a Single-Cylinder

643

627

Engine

19.10 Balancing Multicylinder Engines

640

647

19.11 Analytical Technique for Balancing Multicylinder Reciprocating 19.12 Balancing Linkages

656

19.13 Balancing of Machines Problems

661

663

2 0 C a m D y n a m ic s

665

20.1

Rigid- and Elastic-Body Cam Systems

20.2

Analysis of an Eccentric Cam

20.3

Effect of Sliding Friction

670

666

665

Engines

651

xi

x ii

CONTENTS 20.4

Analysis of Disk Cam with Reciprocating Roller Follower

20.5

Analysis of Elastic Cam Systems

20.6

Unbalance, Spring Surge, and Windup

Problems

673

2 1 F ly w h e e ls

678

21.1

Dynamic Theory

21.2

Integration Technique

21.3

Multicylinder Engine Torque Summation

Problems

678 680 682