Mechanism and Machine Theory

787 Pages·2007·29.49 MB·English

by  Ashok G. Ambekar

an
Machine Theory |
Rs, 525.00

MECHANISM AND MACHINE THEORY
Ashok G. Ambekar

© 2007 by Prentice-Hall of India Private Limited, New Delhi. All rights reserved. No part of this book
may be reproduced in any form, by mimeograph or any other means, without permission in writing fram
the publisher.

ISBN-978-81-203-3134-1
The export rights of this book are vested solely with the publisher.
Published by Asoke K. Ghosh, Prentice-Hall of India Private Limited, M-97, Connaught Circus,

New Delhi-110001 and Printed by Rajkamal Electric Press, B-35/9, G.T. Karnal Road Industrial Area,
Delhi-1 10033.
FIREMEN aS RETIRE PET gn oe sera maremeencom mane SME aS

CONTENTS

MME ET EADS, So eR ARE naire acer,

Preface xv

1. Introduction to Kinematics and Mechanisms ===————1-18

1 en
___The Four-bar Mechanism ___

1. eMac of a Particle _2

1.4 __ Motion of a Rigid Body 3

1.5___Motion of Translation _3

1.6 Motion of Rotation 4

1.7___Planar Motion and Euler’s Theorem __4

1.8 Degrees of Freedom 4

1.9___Vectors and Their Treatment___5

1.10 Methods of Expressing Vectors 8

1. Position Vectors 40

1.13 Rigid Body Displacement 17
1.14 Relative Displacement _12
Review Qu 18

Planar Mechanisms and Geometry of Motion 19-60

2.1__Introduction _19
2.2 Definitions and Basic Concepts 19
_2.3___Classification of Links __22
2.4 Classification of Pairs __23
2.4.1 Classification of Pairs Based on Type of Relative Motion 23
2.4.2 Classification of Pairs Based on Type of Contact 25
2.4.3 Classification of Pairs Based on Degrees of Freedom 26
2.4.4 Classification of Pairs Based on Type of Closure Pid
ii
2.5 Mechanism and Machine 27

2.6___Inversions. 28

2.7 Quadric Cycle Chain and Its Inversions 28

2.8 Inversion of Slider Crank Chain __33

2.9 The Double Slider Crank Chain and Its Inversion __35
2.10 Transmission of Torque and Force in Mechanisms 36

2.11 Constrained Motion and Degrees of Freedom of a Mechanism 38
2.12 Expression for D.O.F. of Chains and Mechanisms 38
2.13 Interpretation of Mobility Equation 40
2.14 Inconsistencies of Grubler’s Equation 43
2.15 Degrees of Freedom Permitted by Joints other than

Turning and Sliding 45
2.16 Equivalent Linkages 48
2.17 Number Synthesis 49

2.17.1 _ Effect of Even/Odd Number of Links on Degrees

of Freedom ___50
2.17.2 Minimum Number of Binary Links in a Mechanism 51

2.17.3 Maximum Possible Number of Turning Pairs on any
of the m Links ina Mechanism 52
2.18 Enumeration of Kinematic Chains __ 53
2.19 Spatial Mechanisms __57
2.20 Manipulators 58 .
Review Questions 58

Velocity and Acceleration Analysis (Graphical Approaches) 61-126

3.1___Introduction _67

__Linear and Angular Velocity _6/
Velocity of a Point on Rotating Rigid Body _ 63
3.4 Graphical Differentiation _ 64

Relative Velocity 67
ity between Two Points on the Same Link 68
e 68

3.9 Velocity of Rubbing 75

3.10 Mechanical Advantage and Power Transmission 77
3.11__ Instantaneous Centres of Rotation __78

3.12 Properties of Instantaneous Centre 79.
3.13 Location of Velocity Pole (1.C.) 80
3.14__Instant Centres of 4-bar Mechanism __81

3.15 Aronhold-Kennedy’s Theorem of Three Centres 82
3.16 Locating ICs. in Mechanisms _ 83

3.17 Acceleration in Mechanisms 87

3.18 Motion of a Particle along Curved Path 88
Contents_v

3.19
3.20
3.21
3.22
3.23
3.24
3.25
3.26
aaF

3.28

Acceleration of a Rigid Link 88

Acceleration Image of a Link 90

General Acceleration Equation for a Link 91

Necessary Conditions for A to Exist 94

Acceleration Polygon 94

Combined Four-Bar Chain and Slider-Crank Mechanism 07
Acceleration Polygon Involving Coriolis Component of Acceleration
Klein’s Construction 109

Approximate Analytical Expression for Displacement, Velocity and
Acceleration of Piston of Reciprocating Engine Mechanism 1/5
Kinematic Analysis of Complex Mechanisms 1/8

Review Questions 121

Velocity and Acceleration Analysis (Analytical Approach)

4.6

47
48
49

Introduction 127
Vector Method 127

Types of Analysis Problems 128

The Loop Closure Equation /3/

Algebraic Position Analysis 131

4.5.1 Case of Slider-Crank Mechanism 132

4.5.2. Case of Four-Bar Mechanism 133

Velocity and Acceleration Analysis Using Complex Algebra
(Raven’s Approach) 135

Application to Slider-Crank Mechanism 136
Application to Four-Bar Mechanism 137

Application to Quick-Return Mechanism 139

Review Questions — 153

Mechanisms with Lower Pairs

$1
5.2
53
54
55

5.6

Introduction 158

Offset Slider-Crank Mechanism as a Quick Return Mechanism 158
The Pantograph 160

Straight Line Motion Mechanisms 162

Exact Straight Line Motion Mechanisms 163

5.5.1 Condition for Generating Exact Straight Line Motion 163
5.5.2 Peaucellier Mechanism 164

5.5.3 The Hart Mechanism 165

5.5.4 The Scott-Russel Mechanism 166

The Approximate Straight Line Motion 167

5.6.1 The Watt Mechanism 167

5.6.2 The Grasshopper Mechanism 168

5.6.3. The Tchebicheff Straight Line Motion Mechanism 169
5.6.4 The Roberts Straight Line Motion Mechanism 171

103

127-157

158-202
vi__Contents

5.7 Engine Indicators 171
5.7.1 Simplex Indicator 171
5.7.2 Crosby Indicator 172
5.7.3 Thompson Indicator 173
5.74 Dobbie-McInnes Indicator 175
5.8 Motor Car Steering Gear 177
5.8.1 Condition of Correct Steering 177
5.8.2 Davis Steering Gear 178
5.8.3 Ackerman Steering Gear /8/
5.9 Hooke’s (Cardan) Joint or Universal Coupling 185
5.9.1 Transmission Characteristics 186
5.9.2 Double Hooke’s Joint 192
5.10 Toggle Mechanism 197
5.11 Scotch Yoke Mechanism 199
Review Questions 199

6. Elements of Kinematic Synthesis of Mechanisms
(Graphical and Algebraic Methods) 203-240

6.1 Kinematic Synthesis 203
6.2 Approximate and Exact Synthesis 205
63 Chebyshev’s Spacing of Accuracy Points 205
6.4 Graphical Methods of Dimensional Synthesis 208
Motion Generation
6.5 Poles and Relative Poles 208
6.6 Motion Generation: Three Prescribed Positions 2/0
6.7 Relative Poles (Roto-Centres) of the 4-Bar Mechanism 2/2
6.8 Relative Poles of Slider-Crank Mechanism 2/4
6.9 Function Generation (Three Precision Points) 2/7
6.10 Algebraic Method of Function Generation 219
6.11 Comments on Design Parameters and Special Nature of Results 226
6.12 Coupler Curves 228
6.13 Synthesis for Path Generation 230
6.14 Graphical Synthesis for Path Generation
(Three Specified Positions) 237
6.15 Roberts-Chebyshev Theorem (Cognate Linkages) 232
6.16 Coupler Curves from 5-Bar Mechanisms 235
Review Questions 238

7._Cams 241-299

7.1__Introduction _241
7.2__Comparison between Cams and Lower Paired Mechanisms 241
7.3__Classification of Cams and Followers 242
73.1__Classification of Cams __242
73.2 Classification of Followers 244
Contents _ vii

74
75

76
17

Terminology for Radial Cam 247
Types of Follower Motion 248
7.5.1 Uniform Motion or Constant Velocity Follower Motion 249
7.5.2. Modified Uniform Motion 249
7.5.3 Simple Harmonic Motion 250
7.5.4 Uniformly Accelerated and Retarded (Parabolic)
Follower Motion 254
7.5.5 Cycloidal Follower Motion 258
Pressure Angle (y) 260
Parameters Affecting Pressure Angle 261

7.8 Effect of Offset Follower Motion __263

19

Main Consideration Influencing Choice of Cam 266
).1___ Smaller Lateral Pressure on Guides __266
7.9.2 Smaller Force Required to Accelerated Follower 267
7.9.3 __ Smooth Jerkless Motion _268
7.9.4 Smaller Base-Circle 268
jius of Curvature and Undercutting 269

7.11_Construction of Cam Profiles 269

1. 14 Cam with Oscillating Roller Follower 284

7.12__Cam Layout: General Type of Problems 272

7.15 Cams with Specified Contours 287

7.15.1 Circular Arc Cam with Tangent Follower 287
7.15.2 Tangent Cam with Roller Follower 292

Review Questions 296

Gears 300-365
8.1 Introduction 300
8.2 Rolling Contact and Positive Drive 300
8.3 Classification of Gears 301
8.3.1 Gears Mounted on Parallel Axes 30/
8.3.2 Gears Mounted on Intersecting Shaft Axes 303
8.3.3. Gears Mounted on Skew Shaft Axes 304
8.4 Nomenclature for Straight Spur Gears 305
8.5 Fundamental Law of Toothed Gearing 3/0
8.6 Conjugate Teeth 312
8.7___ Tooth Profiles 313
8.7.1 Cycloidal Tooth Profile 3/4
8.7.2___Involute Tooth Profile __315
88 Length of Path of Contact 3/8
8.9 Length of Arc of Contact 320

8.10 Contact Ratio 327
viii_Contents

10.

8.11 Interference and Undercutting 324

8.12 Standard Proportions of Interchangeable Gears 327

8.13 Minimum Number of Teeth to Avoid Interference 328

8.14 Minimum Number of Teeth on Pinion to Avoid
Interference with Rack 336

8.15 Comparison between Involute and Cycloidal Tooth Profiles 342

8.16 Methods of Reducing or Eliminating Interference 343

8.17 Helical Gears 344

8.18 Spiral Gears (Skew or Screw Gears) 347

8.19 The Efficiency of Spiral and Helical Gears 350

8.20 Worm and Worm Gear 355

8.21 Bevel Gears 360

8.22 Special Bevel Gears 362

Review Questions 363

Gear Trains 366-403

9.1 Introduction _366

9.2 Classification _ 366

9.3 Epicyclic Gear Trains with Bevel Gears 372

9.4 Algebraic Method of Analysing Epicyclic Gear Trains __373
5 Tabulation Method for Analysing Epicyclic Gear Train 379
9.6 Torques and Tooth Loads in Epicyclic Gear Trains 384
9.7 Bevel Gear Differential 397

Review Questions 398

Gyroscopic Effects 404-442

10.1 Introduction 404
10.2 Angular Motion and Conventional Vector Representation 405
10.3 Precessional Motion and Angular Acceleration 406
10.4 Gyroscopic Couple 4/0
10.5 Gyro-couple and Gyro-reaction Couple 41
10.6 Analogy with Motion of a Particle in Circular Path 411
10.7 Gyroscopic Effects on an Aeroplane 414
10.8 Stability Analysis of 4-Wheeler Vehicle 4/5
10.9 Stability Analysis of a Two-wheel Vehicle 423
10.10 Gyroscopic Effects on Naval Ships 427
10.11 Gyroscopic Ship Stabilization 432
10.12 Gyroscopic Analysis of a Disc Fixed Rigidly to a
Rotating Shaft at Certain Angle 435
10.13 Gyroscopic Analysis of Grinding Mill 437
Review Questions 440
Contents ix

11. Friction Gears 443-512

12.

11
11.2
11.3
114
11.5
11.6
ba We
11.8
11.9
11.10

1.11
11.12
11.13
11.14
11.15
11.16
11.17
11.18
11.19
11.20
11.21
11.22
11.23
11.24
11.25
11.26

Introduction 443
Types of Friction 443

Dry Friction 444

Angle of Repose and Angle of Friction 446

Motion along Inclined Plane 446

Friction of Nut and Screw 450

Wedge 457

Rolling Friction 461

Pivot and Collar Friction 463

Axial Force and Friction Moment in Pivots and Collars 464
11.10.1 Assumption of Uniform Pressure Intensity 466
11.10.2. Assumption of Uniform Rate of Wear 467

Design Considerations in the Choice of Assumption 469
Thrust Bearing 470

Friction Clutches 474

Cone Clutch 475

Single Plate Clutch 479

Multi-Disc Clutch 481

Effect of Number of Pairs of Active Surfaces 482
Centrifugal Clutch 492

Friction Circle and Friction Axis 495

Lubricated Surfaces 500

Friction between Lubricated Surfaces 501

Film Lubrication in Rotating Shafs 504

Michel Thrust Bearing 505

Hydrostatic Lubrication 506

Rolling Contact Bearings 506

Advantages and Disadvantages of Rolling Contact Bearings 508

Review Questions 509

Belt, Rope and Chain Drives 513-558

12.9
12.10
12.11

Belt Length 517

Limiting Ratio of Belt-Tensions 519

Maximum Effective Tension and HP. Transmitted 522
Centrifugal Tension and Stresses in Belts or Rope 525
Maximum Tension in Bel/Rope 526

Initial Tension and its Role in Power Transmission 526
Condition for Maximum Power Transmission 535
Power Transmitted by Belt: Further Comments 537
Idler and Jockey Pulleys 540
X_Contents

13.

14

12.12 Timing Belt 547

12.13 Rope Drive 54/

12.14 Materials of Belt and Rope 552

12.15 Chains 553

12.16 Inverted Tooth Chain (Silent Chain) 555
Review Questions 556

Brakes and Dynamometers

13.1 Introduction 559

13.2 Classification of Brakes 559

13.3 The Simple Block or Shoe Brake 560
13.4 Short-Shoe Brakes (Condition of Self Energization) 561
13.5 Double Block Brakes 563

13.6 Long Shoe Brakes 566

13.7 Long Shoe Brakes (Shorter Method) 570
13.8 Internally Expanding Shoes 573

13.9 Band Brakes 583

13.10 Band and Block Brake 587

13.11 The Braking of a Vehicle 596

13.12 Types of Dynamometers 604
Absorption Dynamometers

13.13 Prony Brake Dynamometer 605

13.14 Rope Brake Dynamometer 606
Transmission Dynamometers

13.15 Epicyclic Train Dynamometers 608
13.16 Belt Transmission Dynamometer 609
13.17 Torsion Dynamometers 6/1

Review Questions 614

Dynamics of Machines, Turning Moment, Flywheel

14.1 Role of Force Analysis in Design Calculations 617

14.2 Laws of Motion and D’Alembert’s Principle 6/8

143. Static Force Analysis 620

14.4 Static Force Analysis for Mechanisms 62/

14.5 Mass Moment of Inertia and Inertia Torques 622

14.6 Simple Harmonic Motion 625

14.7 Dynamically Equivalent Two Mass System 634

14.8 Centre of Percussion 636

14.9 Significance of Kinetic Equivalence 639

14.10 Equivalent Dynamic System: Graphical Determination 639

14.11 Correction Couple Required for Arbitrary Choice of Both
the Mass Locations 640

559-616

617-704