Mechanism and Machine Theory

Mechanism and Machine Theory
Ashok G. Ambekar
الجزء المتاح فقط هو الجزء المعروض على جوجل كتب
CONTENTS
Preface xy

1. Introduction to Kinematics and Mechanisms
   ].1 Introduction J
   ].2 The Four-bar Mechanism 2
   1J Motion of a Particle. 2
   1.4 Motion of a Rigid Body 3
   13 Motion of Translation i
   ].6 Motion of Rotation 4
   1.7 Planar Motion and Euler’s Theorem
   1.8 Degrees of Freedom 4
   1.9 Vectors and Their Treatment J
   1.10 Methods of Expressing Vectors 8
   1.11 Position Vectors 10
   1.12 Displacement of a Particle 11
   1.13 Rigid Body Displacement //
   IJ4 Relative Displacement 12
   Review Questions 18
   1-18
   2* Planar Mechanisms and Geometry of Motion 19-60
   2J Introduction 19
   22 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 27 mjy Contents 2.5 Mechanism and Machine 27 26 Inversions 28 2.7 Quadric Cycle Chain and Its Inversions 28 2.8 Inversion of Slider Crank Chain 33 29 The Double Slider Crank Chain and Its Inversion 35
   210 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.OF* of Chains and Mechanisms 38
   2 13 Interpretation of Mobility Equation 40 2.14 Inconsistencies of Gmbler’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 A 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 Pairt on any
   of the n Links in a Mechanism 52
   2.18 Enumeration of Kinematic Chains 53
   219 Spatial Mechanisms 57
   2.20 Manipulators 55
   Review Questions 58
2. Velocity and Acceleration Analysis (Graphical Approaches) 61-126
   3.1 Introduction 61
   3.2 Linear and Angular Velocity 61
   3.3 Velocity of a Point on Rotating Rigid Body 53
   3.4 Graphical Differentiation 64
   3.5 RelatiyeJ/elocity 67
   3.6 Relative Velocity between Two Points on the Same Link 68
   3.7 Velocity Image 68
   3.8 Velocity Polygon 70
   39 Velocity of Rubbing 75 3.10 Mechanical Advantage and Power Transmission 77 3.11 Instantaneous Centres of Rotation 75 3.12 Properties of Instantaneous Centre 79 3.13 Location of Velocity Pole (I.C.) 50 3.14 Instant Centres of 4-bar Mechanism 5i 3.15 Aronhold-Kennedy’s Theorem of Three Centres 52 3.16 Locating I,Cs. in Mechanisms S3 317 Acceleration in Mechanisms 57
   3,18 Motion of a Particle along Curved Path 55Contents V
   3J9 Acceleration of a Rigid Link 88
   3.20 Acceleration Image of a Link 90
   3.21 General Acceleration Equation for a Link 91
   3.22 Necessary Conditions for Acor to Exist 94
   3.23 Acceleration Polygon 94
   3.24 Combined Four-Bar Chain and Slider-Crank Mechanism 101
   3.25 Acceleration Polygon Involving Coriolis Component of Acceleration 103
   3.26 Klein’s Construction 109
   3.27 Approximate Analytical Expression for Displacement, Velocity and
   Acceleration of Piston of Reciprocating Engine Mechanism 115
   3.28 Kinematic Analysis of Complex Mechanisms 118
   Review Questions 121
   4, Velocity and Acceleration Analysts (Analytical Approach) 127-157
   4.1 Introduction J27
   4.2 Vector Method /27
   4.3 Types of Analysis Problems 128
   4.4 The Loop Closure Equation 131
   4.5 Algebraic Position Analysis 131
   4.5.1 Case of Slider-Crank Mechanism 132
   4.5.2 Case of Four-Bar Mechanism 133
   4.6 Velocity and Acceleration Analysis Using Complex Algebra
   (Raven’s Approach) 135
   4.7 Application to Slider-Crank Mechanism 136
   4.B Application to Four-Bar Mechanism 137
   4.9 Application to Quick-Retum Mechanism 139
   Review Questions- 153
   S. Mechanisms with Lower Pairs 158-202
   5.1 Introduction
   Offset Slider-Crank Mechanism as a Quick Return Mechanism
   The Pantograph 160
   Straight Line Motion Mechanisms 162
   Exact Straight Line Motion Mechanisms 163
   5.5.3 The Han Mechanism 165
   5.5.4 The Scott-Russel Mechanism 166
   The Approximate Straight Line Moiion 167
   5.6.1 The Watt Mechanism 167
   Condition for Generating Exact Straight Line Motion
   PeaucdMer Mechanism 164
   lire Grasshopper Mechanism 168
   The Tchebieheff Straight Line Motion Mechanism 169
   The Roberts Straight Line Motion Mechanism 171yj Contents
   5,7 Engine Indicators Ill
   Simplex Indicator 111
   Crosby Indicator 772
   Thompson Indicator 113
   5.7.4 Dobbie-Mdnnes Indicator 7 75
   5.8 Motor Car Steering Gear 777
   5.8.1 Condition of Correct Steering Ill
   5.8.2 Davis Steering Gear 118
   5.8.3 Ackerman Steering Gear 181
   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 191
   5.11 Scotch Yoke Mechanism 199
   Review Questions 199
3. Elements of Kinematic Synthesis of Mechanisms
   (Graphical and Algebraic Methods)
   6.1 Kinematic Synthesis 203
   6.2 Approximate and Exact Synthesis 205
   6.3 Chebyshev’s Spacing of Accuracy Points 205
   6.4 Graphical Methods of Dimensional Synthesis
   Motion Generation
   6.5 Poles and Relative Poles 208
   6.6 Motion Generation: Three Prescribed Positions 210
   6-7 Relative Poles (Roto-Ccntres) of the 4-Bar Mechanism 212
   6.8 Relative Poles of Slider-Crank Mechanism 214
   6.9 Function Generation (Three Precision Points) 27 7
   6.10 Algebraic Method of Function Generation 219
   6.11 Comments on Design Parameters and Special Nature of Results
   6.12 Coupler Curves 228
   6.13 Synthesis for Path Generation 230
   6.14 Graphical Synthesis for Path Generation
   (Three Specified Positions) 2J7
   6.15 Roberts-Chebyshev Theorem (Cognate Linkages) 232
   6.16 Coupler Curves from 5-Bar Mechanisms 235
   Review Questions
   7 Cams
   7J Introduction 24.1
   7.2 Comparison between Cams and Lower Paired Mechanisms 247
   73 Classification:of Cams and Followers 242
   13A Classification of Cams 242
   13.2 Classification of Followers 244
   241-299Contents yjj
   74 Terminology for Radial Cam 247 75 Types of Follower Motion 248
   7.5.3 Simple Harmonic Motion 250
   75,4 Uniformly Accelerated and Retarded (Parabolic) Follower Motion 254 7.5.5 Cycloidal Follower Motion 258 7.6 7.7 Pressure Parameters Angle Affecting (^) Pressure 260 Angle 261 7.8 Effect of Offset Follower Motion 263 7.9 Main Consideration Influencing Choice of Cam 266 7.9.1 Smaller Lateral Pressure on Guides 266 7.9.2 Smaller Force Required to Accelerated Follower 2tf 7 7.9J Smooth Jerkkss Motion 268 7.9.4 Smaller Base-Circle 268 7.10 Radius jrfCuryature and Undercutting 269 7.11 Construction of Cam Profiles 269 1A2 Cam Layout: General Type of Problems 272 7J3 Translating Flat_ Face Follower: Analytical Desjgn_ 7.14 Cam with Oscillating Roller Follower 284 7.15 Cams with Specified Contours 287 7.15.1 Circular Arc Cam with Tangent Follower 287 715*2 Tangent Cam with Roller Follower 292
   Review Questions 296
   Uniform Motion or Constant Velocity Follower Motion 249
   Modified Uniform Motion 249
4. Gears
   8.1 Introduction 300
   8.2 Rolling Contact and Positive Drive 300
   8.3 Classification of Gears 301
   8.4 Nomenclature for Straight Spur Gears 305
   8.5 Fundamental Law of Toothed Gearing 310
   86 Conjugate Teeth 312 87 Tooth Profiles 313
   8.7.1 Cycloidal Tooth Profile 314
   8.7.2 Involute Tooth Profile 115
   8.8 Length of Path of Contact 318
   8.9 Length of Arc of Contact 320
   S10 Contact Ratio 321 300-365 Gears Mounted on Parallel Axes Gears Mounted on Intersecting Shaft Axes Gears Mounted on Skew Shaft Axes 304Vfii Contents SHII 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, 1b Methods of Reducing or Eliminating Interference 343 8 H17 Helical Gears 344 8.18 Spiral Gears (Skew or Screw Gears) 347 8.19 The Efficiency of Spiral and Helical Gears 350 82Q Worm and Worm Gear 355
   8.21 Bevel Gears 360
   8.22 Special Bevel Gears 362
   Review Questions 363
5. Gear Trains
   9A Introduction .366
   9.2 Classification .3.66
   9.3 Epicyclic Gear Trains with Bevel Gears 372
   9A Algebraic Method of Analysing Epicyclic Gear Trains 373
   9.5 Tabulation Method for Analysing Epicyclic Gw Train 379
   9.6 Torques and Tooth Loads in Epicyclic Gear Trains
   9.7 Bevel Gear Differentia] 397
   Review Questions 398
   366^403
   384
6. Gyroscopic Effects
   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 JO
   10.5 Gyro-couple and Gyro-reaction Couple 411
   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 415
   10.9 Stability Analysis of a Two-wheel Vehicle 423
   10.10 Gyroscopic Effects on Naval Ships 427
   10, It 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 4J 7
   Review Questions 440
   404-442Contents ix
7. Friction Gears
   ] ]. I Introduction 443
   11.2 Types of Friction 443
   11.3 Dry Friction 444
   11.4 Angle of Repose and Angle of Friction 446
   11.5 Motion along Inclined Plane 446
   11.6 Friction of Nut and Screw 450
   11.7 Wedge 457
   11.8 Rolling Friction 461
   11.9 Pivot and Collar Friction 463
   11.10 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
   11.11 Design Considerations in the Choice of Assumption 469
   11.12 Thrust Bearing 470
   11.13 Friction Clutches 474
   11 14 Cone Clutch 475 11.15 Single Plate Clutch 479 11.16 Multi-Disc Clutch 481 11.17 Effect of Number of Pairs of Active Surfaces 482 11.18 Centrifugal Clutch 492 11.19 Friction Circle and Friction Axis 495 11.20 Lubricated Surfaces 500 11.21 Friction between Lubricated Surfaces 501 I L22 Film Lubrication in Rotating Shafs 504 11.23 Michel Thrust Bearing 505 11.24 Hydrostatic Lubrication 506 11.25 Rolling Contact Bearing 506
   11.26 Advantages and Disadvantages of Rolling Contact Bearings 508
   Review Questions 509
   443-512
8. Belt, Rope and Chain Drives 513-558
   12.1 Introduction 5.13
   12.2 Velocity Ratio 513
   12J Belt Length 517
   [ 2.4 Limiting Ratio of Belt-Tensions 519
   12.5 Maximum Effective Tension and H.P. Transmitted 522
   12.6 Centrifugal Tension and Stresses in Belts or Rope 525
   12.7 Maximum Tension in Belt/Rope 526
   12.8 Initial Tension and its Role in Power Transmission 526
   12.9 Condition for Maximum Power Transmission 535
   12.10 Power Transmitted by Belt: Further Comments 537
   12.11 Idler and Jockey Pulleys 540X Contents
   12.12 Timing Bell 541
   12.13 Rope Drive 541
   12.14 Materials of Belt and Rope 552
   12.15 Chains 553
   12.16 Inverted Tooth Chain (Silent Chain) 555
   Review Questions 556
9. Brakes and Dynamometers
10. ) 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 ) 56J
    13.5 Double Block Brakes 563
    13.6 Long Shoe Brakes 5<5<5
    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 Epicydic Train Dynamometers 608
    13.16 Belt Transmission Dynamometer 609
    13.17 Torsion Dynamometers 611
    Review Questions 614
    559-616
11. Dynamics of Machines, Turning Moment, Flywheel
    14.1 Role of Force Analysis in Design Calculations
    14.2 Laws of Motion and D’Alembert’s Principle
    14.3 Static Force Analysis
    14.4 Static Force Analysis for Mechanisms
    14.5 Mass Moment of Inertia and Inertia Torques
    14.6 Simple Harmonic Motion
    14.7 Dynamically Equivalent Two Mass System
    14.8 Centre of Percussion
    14.9 Significance of Kinetic Equivalence
    14.10 Equivalent Dynamic System: Graphical Determination
    14J I Correction Couple Required for Arbitrary’ Choice of Both
    the Mass Locations
    1412 The Effective Force and the Inertia Force 644 14.13 Reversed Effective (Inertia) Force and Force Analysis 646 14.14 Dynamic Force Analysis of a Four-link Mechanism 64S 14.15 Analytical Expressions for Velocity and Acceleration of Slider in Slider-Crank Mechanism 654 1416 Piston Effort, Crank Pin Effort and Crank Effort 657
    14.17 Inertia Forces and Torques in Slider-Crank Mechanism 659
    14.15 Dynamic Force Analysis of a Slider-Crank Mechanism 663
    14.19 Turning Moment Diagram {Crank Effort Diagram) 675
    14.20 Fluctuation of Crank Shaft Speed 678
    14.21 The Flywheel 682
    14.22 Flywheel for Punching Press 683
    Review Questions 701
12. Governors
    15*1 Introduction 705
    J 5.2 Functions of a Governor 705
    15.3 Types of Governors 707
    15.4 Terms Used in Governors 708
    15.5 The Watt Governor 709
    15.6 Effect of Mass of Amis in Watt Governor 111
    15.7 The Porter Governor 713
    15.8 Effect of Friction 7/ 7
    15.9 Proell Governor 724
    15.10 Spring Controlled Governors 729
    15.11 Hartnell Governor 729
    15.12 Governor with Spring Connected Balls (Wilson-Hartodl Governor) 732
    15.13 Governor with Gravity and Spring Control 742
    15.14 Hartung Governor 744
    15.15 Pickering Governor 746
    15.16 inertia Governors 747
    15.17 Characteristics of Centrifugal Governors 747
    15.18 Quality of Governor: Definitions 748
    15.18.1 Controlling Force 748
    15.18.2 Stability and Isochroitism 749
    15.18.3 Sensitiveness 752
    15 *18.4 Hunting 752
    15.19 Governor Effort and Power 752
    15.20 Effect of Friction: Insensitiveness 754
    Review Questions 763
    705-766xii Contents
13. Balancing 767-849
    16.1 Introduction 767
    16.2 Balancing of Rotating Masses 767
    J 6J Static and Dynamic Balancing Problem 76#
    \6A Unbalanced Rotating Mass 769
    16.5 Balancing of Several Masses Revolving in the Same Plane 772
    16.6 Analytical Approach for Several Rotating Masses in Same Plane 775
    J 6.7 Balancing of Several Masses Revolving in Different Planes 775
    16.7.1 First Method 775
    16.7.2 Second Method (Dalby’s Method) 779
    16.8 Balancing of Rotors 789
    16.9 Static and Dynamic Balancing 790
    16.10 Static Balancing Machines 790
    16.11 Dynamic Balancing Machines 791
    16.11.1 Pivoted Cradle Balancing Machine 792
    16.12 Field Balancing 794
    16.12. ) Balancing of a Twin Disc 795
    16.12.2 Balancing by Four Observations 796
    16.13 Balancing of Reciprocating Masses 798
    16.14 Inertia Effects of Reciprocating Masses in Engine Mechanism 799
    16.15 Primary and Secondary Unbalanced Forces due to
    Reciprocating Masses 801
    16.16 Inertia Effects of Crank and Connecting Rod 802
    16.17 Partial Balancing of Primary Inertia Forces 804
    16.18 Partial Balancing of Locomotives 807
    16.19 Effect of Partial Balancing in Locomotives 807
    16.20 Primary Balance of Multi-Cylinder In-Line Engine 822
    16.2 i Secondary Balance of Multi-Cylinder In-Line Engines 823
    16.22 Balancing of 2-Stroke and 4-Stroke Tn-Ltne Engines 824
    16.23 Firing Order 827
    16.24 Direct and Reverse Cranks 836
    16.25 Balancing V-Engines 841
    Review Exercises 845
14. Vibration Analysis
    17.1 Introduction
    17.2 Definitions
    17.3 Simple Harmonic Motion and Rotating Vectors
    17.4 Work Done in Harmonic Motion
    17.5 Elements of Discrete ( Lumped Parameter) Vibratory System
    Single Degree of Freedom Problems
    17.6 Undamped Free Vibrations
    17.6, 1 Method Based on Newton’s Second Law of Motion
    850-935
    850
    850
    852
    853
    855
    856
    856Contents xiijj
    17.6.2 Energy Method 859
    17.6.3 Rayleigh’s Method 860
    17.7 Equivalent Springs and Dashpots 864
    17.8 Equivalent Length of Shaft 867
    17.9 Damped Free Vibrations 868
    17.10 Logarithmic Decrement 572
    17.11 Forced Vibrations with Harmonic Excitation 877
    17.12 Vibration Isolation and Transmissibility 55J
    17.13 Vibration Isolation without Dampers 883
    17.14 Vibration Isolation Using Dampers 885
    17.15 Motion Transmissibility 889
    17.16 Whirling of Shafts 895
    17.17 Critical Speed of Light Vertical Shaft with Single DISC
    (without Damping) 896
    17.18 Critical Speed of Light Vertical Shaft Having
    Single Disc with Damping 900
    17.19 Longitudinal and Transverse Vibrations 905
    17*20 Natural Frequency of Free Transverse Vibrations due to a
    Point Load on a Simply-Supported Shaft 906
    17
    *21 Transverse Vibration of a Uniformly Loaded Shaft 907
    17.22 Transverse Vibrations of Shaft Canying Several Loads 911
    Torsional Vibrations
    17.23 Single Rotor System 917
    17.24 Free Torsional Vibrations: Two Rotor System 918
    17.25 Free Torsional Vibrations: Three Rotors 920
    1726 Torsional Vibration of Geared System 927 Review Questions 931 Appendix I Units Appendix it Mathematics Appendix HI 5-/- and M.K.S Units
    Bibliography
    937-938
    939-941
    942-974
    975-976
    Index 977-986
    I N D E X
    Absolute motion, 28
    Absorption dynamometer. 604. 605
    Acceleration. 87
    absolute, 95
    angular. 87-90, 92-99, 103. 106. 406. 410
    centripetal. 89
    Coriolis. 94. 103
    equation. 91
    gyroscopic. 409. 410
    image. 90, 91
    normal. 88
    of piston. 96. 112. 115
    analytical. II5-117
    polygon, 94. 95. 103
    relative, 89-92
    rigid link, 88
    tangential. 88. 90. 92
    Acceleration analysis, 61, 89-94, 135
    analytical approach. 773
    cam and follower, 287-293
    complex mechanism. IIS
    of direct contact mechanisms. 232, 300
    four-bar linkage. 99
    Raven’s method, 135
    return mechanism. 103-104
    slider-crank mechanism. 101, 136
    slotted lever, 104
    Accuracy points. 205-208
    Ackerman steering gear. 32. 181-183
    Addendum of tooth. 306
    modification. 328
    standard. 327
    Art. 428
    Amplitude of vibration. 920
    damped vibration, 868
    forced vibration. 851. 877
    Angle of approach
    friction. 446
    heel. 424
    lap. 517. 518. 519. 520
    obliquity, 308
    repose, 446
    Approximate straight line motion mechanisms, 162—
    163
    Grasshopper. 168
    Robert’s, 171
    Tchcbichcff. 169
    Amhold-Kennedy’s theorem, 82
    Arc of action contact. 320
    Allas, Urones-Nelson, 228. 230
    Automotive differential, 362
    Axial pilch. 356
    Back cone bevel gear. 360
    Backlash. 307
    Balancing by four-observations, 796
    Balancing, definition, 767
    dynamic, 768-769
    partial. 804
    static, 768
    Balancing of cranks, 806
    locomotives, 807-812
    multicylinder in-line engines. 822-823
    reciprocating masses. 801
    revolving masses. 772, 775
    rotors, 789
    secondary forces. 839
    V-engines. 841
    Ball hearing. 507
    Band brake. 583
    Band and block brake. 587
    977978 Index
    Band brake, differential 584
    simple, 584
    Ba.se circle of cam. 247

• 270
  Ba.se circle of involute gear, 316* 312
  Bearn engine mechanism. 32. 33
  Bearing
  ball. 507
  horse shoe-shaped* 470* 471
  journal. 504. 505
  Michel thrust
• 505
  Needle rotten 507-508
  roller
• 507-508
  Belt drive
  catenary effect 538. 540
  centrifugal tension. 525
  creep, 539
  Hat 519
  initial lension. 526
  law of (helling), 519-522
  length of, 51SJ13
  limiting ratio of tensions. 519-522
  material, 533
  maximum HP transmitted. 522
  maximum tension, 526, 532
  power transmitted, 526, 535
  slip* 515^516
  timer helt 553
  V-bclt 455, 52 J
  velocity ratio. 513-515
  Belt transmission dynamometer. 609
  Bevel gears. 303* 362* 372
  miter
• 3.62
  pitch angle. 362
  pilch cone, 16ft. 362
  pitch surface, 360* 362
  shaft angle, 361* 362
  tooth thickness. 307
  Ircdgold’s approximation. 360
  Zctol. 304. 362
  Bevis Gibson torsion dynamometer. 604. 612
  Binary links. 22. 54
  minimum number in chain* 53
  Block brake. 560-56*
  Boundary friction, 444. 501
  Bow of a ship. 430
  Brakes, band. 559. 583
  band and block. 587
  block, 560, 561
  external. 559
• 566
  internal. 573
  long shoe* 566-570
  pivoted shoe. 560
  self energization. 561-563
  self locking. 565
  short shoe. 561-563
  Braking of vehicles. 596
  Bush roller chain, 553, 554
  Cams, advantages. 24J
  Cams, analysis* 287
  analytical design, 280
  angle of action. 244, 290
  angle of retum/descent. 265. 27 J , 274
  angle of rise/assent/outstrnke, 265. 271. 274
  angle of dwell, 21L 111
  base circle
  273. 274
       circular arc. 287
       cylindrical, 243
       disc, 242. 244. 247
       displacement diagram* 248, 249, 25.1. 253
       flat. 245
       follower, oscillating, 243. 284, 285
       jerk, 287
       layout of, 27{)
       master, 287
       pitch circle, 248
       pitch curve, 247
       pitch point 248
       plate cam. 242, 253
       pressure angle, 244, 260
       prime circle* 248
       profile, 248, 263, 266
       radial* 242* 243
       specified contours, 270. 287
       specified follower motion, 269r-287
       tangent. 287. 292
       types, 244
       undercutting, 269
       Centre of percussion. 636
       Centre distance
       spiral gears, 347, 350
       worm gears* 355
       Chain
       constrained* 40
       double slider. 35
       drive, 553-554
       Ibur-bar, 29
       kinematic, 21
       pitch* 553-554
       pitch quadric cycle, 28
       roller, 554
       silent
• 555
  slider-crank* 33
  sprocket* 554
  Chcbyshcv spacing. 206. 218index 979
  Circular Frequency, 893
  Circular pitch, 306
  Clearance, 307
  Closed chain. 21
  Closed pair, 27, 242
  Closure, loop equation. 131
  Clutches, cone. 475
  disc, 479
  multi-disc, 48 L
  single plate* 479
  Coefficient of rolling friction. 461-462
  sliding friction, 443
  Coefficient of energy fluctuation, 680
  Coefficient insensitiveness, 755
  Coefficient of speed fluctuation, 680
  Cognate linkages. 232
  Collar friction. 463
  Collars and pivots, 463
  Complex algebra. 135
  Complex mechanisms. 118
  Complex polar notations, 9
  Compound gear train, 368
  Conical clutch, 475
  Conjugate tooth profiles, 312-314
  Constrained mechenism, 38
  Constraint. 38-40
  motion, 38, 59
  Contact, arc of, 320
  path of 318
  Contact ratio. 307. 321
  Coriolis acceleration. 103, 104. 126
  Correction couple, 640. 643
  Coupler, 29
  Coupler curves. 228-230
  equation of, 229
  for 5-bar linkage. 235-236
  Couple, gyroscopic, 410, 411
  reaction, 411
  representation vectorial. 405
  swaying, 809
  Cradle balancing machine. 792
  Cramer’s rule, 878
  Crank effort, 657, 675
  Cranks, direct and reverse, 836
  Crank-pin effort. 657
  Crank-rocker mechanisms, 30, 31, 32
  Crankshaft balancing, 806
  Crank-slotted lever mechanism. 33
  Critical damping coefficient. 869, 870, 876
  Critical speed in rope dynamometer, 604. 606
  Crosby indicator. 172
  Crossed belt, 5H, 518
  Curvilinear motion of translation, 3
  Cycloidal follower motion. 258, 268
  Cycloidal gear teeth. 314
  Cycloidal and involute tooth comparison, 342
  Cylindrical cams. 243, 244
  pairs, 25
  D’Alembert’s principle, 618-620
  Dal by’s method, 779-781
  ldamping factor/ratio coefficient, 869
  Damped vibrations. 868
  critical, 870
  overdamped, 870
  undeFdamped, 871
  Davis steering gear. 178
  Dedcndum, 306
  Degrees of freedom, 4, 23, 26, 38, 45
  of chains, 38. 39
  effect of
  multiple joint, 41
  spring connection, 41
  even/odd number of links, 50
  of mechanisms, 38
• 39
  of pairs, 25* 26, 45
  redundant. 43
  Diametral pitch. 306
  Diagrams, free body, 620
  schematic, 21
  Differential mechanism, 398
  Dimensional synthesis, 204. 208
  Direct contact mechanism. 48
  Direct and reverse cranks. 836
  Displacement finite and infinitesimal, 79
  Displacement of
  particle, 11
  rigid body, 11, 12
  Displacement, relative, 12, 13
  Displacement-time curve
  in follower motion. 250-254
  in quick return motion mechanism, 158. 159
  in slider crank mechanism. 654. 659, 663
  Displacement vector, 11
  Dobbic-Mclnnes indicator mechanism. 175
  Double block brake, 563
  Double-crank mechanism, 29
  Double helical gear,
  Double Hooke’s joint. 192, 193
  Double lever mechanism, 29
  Drag link mechanism. 29
  Drive, belt, 518. 529, 531, 532
  chain, 513
  305980 ^dex
  cam. 242
  clutch
• 475
  friction, 474, 5H
  rope, 300, 513, 521, 526
  Dry friction, 444
  Dunkcrley’s method* 911
  Dwell period in cams. 245, 246
  Dynamic balancing, 768-769
  Dynamic machines* 790
  Dynamics, defined* 623, 679, 681
  Dynamically equivalent two-mass system* 634, 639
  Dynamometers, 604
  absorption. 604-605
  belt transmission. 609
  epicyclic gear train* 608
  Prony brake, 60S
  rope brake* 606
  torsion, 611
  transmission, 604. 608
  Face of gear tooth. 307
  width of helical gear. 345
  Face cam, 243
  Ferguson’s parados* 386
  Field balancing. 794
  Fillet radius, 307
  Film lubrication. 502, 504
  Firing order. 827
  Flat face follower, 280
  Flat pair, 24
  Fluctuation of crank shaft speed, 678
  Fluctuation of energv, 680
  Flywheel, 682
  energy, 683, 684
  speed! 683. 684
  Foettinger torsion dynamometer, 613
  Follower, classiftcation, 244-246
  Follower, flat raced, 247. 273. 283
  cycloidal* 248. 258
  knife edge. 246
  lift 248
  modified constant velocity, 249
  motions types. 244
  mushroom, 246
  offset, 244
  oscillating, 244
  parabolic, 248, 254
  radial
• 244
  roller
• 246
  simple harmonic* 250-251
  spherically seated, 246
  stroke. 248
  uniform velocity, 249, 250
  Force analysis
  dynamic, 646
  static, 62
  Force analysis of
  four-bar mechanism slider. 648
  crank mechanism. 659, 663
  Force closure in cams, 242
  Force, controlling
  effective, 644
  inertia, 644. 646
  Fore of ship, 428
  acceleration polygon, 94
  instantaneous centre. 78^79
  inversions, 29
  mechanical advantage. 36
  pressure angle, 37
  transmission angle. 36
  Free body diagram, 620
  Freedom, degrees of, 4
  Effect of friction on governors. 717, 724, 754
  Effect, gyroscopic, 404, 405, 406, 414. 427
  Effect of partial balancing of locomotives* BG7-810
  Effective force, 619, 644
  tension. 522
  Efficiency of inclined plane
  helical gears, 344, 350
  spiral gears, 347, 350
  worm gears. 355
  Effort at crank
• 657
  Effort of governor* 752
  piston. 657
  Element* definition of* 20
  Elliptical trammel* 35
  Energy fluctuation* flywheel, 680, 681, 682. 684
  Enumeration of chains, 53-57
  Epicyclic dynamometer, 608
  gear train, 366
  torque and tooth loads. 384
  Epicycloid. 342
  Equilibrium, dynamic, 415
  Equilibrium, static. 618-619
  Equivalent linkage. 48
  Equivalent two-mass system dynamic* 634-635
  Error in function generator structural* 204—205
  Euler’s theorem. 4
  Exact straight line motion
  condition for
  . 163
  Hart
  , 165
  Peaucellier, 164
  Scim-Russcl, 166Index 981
  Frequency of vibration
  cyclic, 677
  damped. 768
  fundamental, 907, 910
  natural. 906
  Freundenstein’s equation. 217
  Friction. 443
  angte. 446
  axis, 495-496. 499
  boundary. 444. 501
  circle, 495
  clutches. 474
  coefficient. 445
  dry, 443, 444
  film, 444. 502
  greasy. 444. 501
  rolling, 444. 461
  skin. 444, 501
  solid. 443, 444
  moment, 464, 496
  viscous, 444, 502
  Friction in governors, 603, 664
  pivot and collar. 463
  roiling. 444. 461
  Full depth tooth. 327
  Function generation, 217, 219
  algebraic method, 219, 373
  graphical method, 208
  Function generator, 204. 205
  Gear trains, 366
  algebraic method, 373
  bevel gear differential, 397
  compound, 368
  epicyclic, 37L 372
  formula (algebraic) method, 376
  ordinary (simple), 366
  reverted. 370
  tabulation method. 379
  train value, 368
  Globular pair, 24
  Governors, 705
  centrifugal, 707
  controlling force, 707
  definitions, 708
  effort. 752
  emergency. 707
  friction, 717, 754
  gravity control. 708
  Hartnell, 729
  Harfung. 744
  isochronous, 757
  inertia. 708, 747
  insensitiveness. 754-757
  pendulum. 709
  pickering, 746
  porter, 713
  power, 752
  Proell. 724
  quality, 748
  sensitiveness. 752
  spring controlled. 729
  stability. 749
  watt, 709
  Wilson Hartnell. 729, 732
  Graphical cam design, 275
  Graphical differentiation. 64—66
  GrashoFs chain, 29
  Grashoff’s law, 29
  Grubler’s criterion inconsistencies. 43
  Gyroscope, definition. 404
  Gyroscopic acceleration. 407
  Gyroscopic action. 439
  Gyroscopic action in grinding mill. 437
  Gyroscopic couple. 410
  Gyroscopic effects on
  air planes. 414
  four wheeler. 415
  naval ship. 427
  two wheeler. 423
  Gyroscopic ship stabilisation, 432
  Gear, definition, 300
  Gear ratio, 307
  Gears, 301
  bevel, 304
  classification. 301
  helical. 302, 344
  Herringbone. 303
  hypoid, 304
  rack and pinion. 303
  spur, 301, 302, 305
  spiral, 304. 305. 347
  worm. 305
  Gear teeth
  base circle, 316
  conjugate. 312
  cycloidal profile, 314
  face. 307
  Hank, 307
  involute, 315
  module, 306, 327
  proportions, 327
  [ 1 I982 index
  Hammer blow, 807
  Hand pump mechanism. 34
  Han mechanism, 165
  Harmonic motion, simple. 625
  Hartnell governor, 729
  Helical gear. 302, 344
  normal circular pilch, 346-347
  Helix angle. 303
  Herringbone gear, 303
  Higher pair, 25, 28, 24J
  effect on d ^o.f-. 40
  Hooke’s joint, 185
  double. 192
  HP transmitted by belt and rope, 522
  Hrones and Nelson atlas, 228
  Hunting governor. 752
  Hypoide gearing, 304
  Jaw dutches, positive, 475
  Jerk, 248. 253, 254, 255
  Jockey pulley’s, 540
  Joints, simple. 41
  multiple, 41
  Journal bearing, 503-504
  friction in, 495-496
  pressure distribution, 503
  Tower’s experiment, 502
  Kennedy’s theorem, 82
  Kinematics, 19
  Kinematic
  chain. 21
  enumeration. 53
  pairs. 23
  synthesis, 203
  Klein’s construction. 109
  Idler pulleys. 540 Kutzbach’s criterion, 40
  Images, velocity and acceleration. 68, 69, 88. 89
  Inclined planes. 446
  efficiency of. 447-448
  friction of, 446-448
  Indicator diagrams for engines. 171, 675
  Inertia effects of
  crank and connecting rod. 802
  reciprocating masses, SOL
  Inertia force, 646
  determination. 639
  Inertia torque, 619, 620. 649
  Inscnsitiveness Instantaneous centres , governor , 78, 754—757
  Aronhold Kennedy’s theorem. 82
  Locations of, 80, S3
  method for velocity, 85
  notation, 81
  number of. 82
  properties. 79
  Interference in involute teeth. 324
  mcihods of elimination, 343
  minimum number of teeth to avoid. 328. 336
  Internally expanding shoe brakes. 573
  Inversion. 28
  of four-bar chain, 212
  of double-slider chain, 35
  of slider-crank chain, 33
  Inversion, importance of, 28
  properties of, 28
  Inverted tooth chain, 555
  Involute teeth, 312-315
  Isochronous governors, 757
  Law of gearing. 310
  Laws of motion. 618
  Laws of solid friction. 444
  Length of arc of contacts, 320
  Length of path of contact 318
  approach. 318
  recess, 318
  Limiting angle of friction, 445. 446
  Limiting coefficient of friction. 445
  Linear motion lower pairs. 40
  Links, classification. 22
  conventional representation. 22
  Linkage. 28
  Locomotives,
  effects in, 807
  partial balancing of. 807
  Logarithmic decrement, 872
  I
  -ong shoe brakes. 566
  shorter method, 570
  Longitudinal vibrations. 905
  Loop closure equation. 39. 131
  Lower pairs. 25
  equivalent. 45
  Lubrication. 444. 502, 504
  film, 502
  hydrostatic, 506
  of journal hearing. 503-504
  of plane surfaces. 500-501
  viscous. 502Index 983
  Machine, definition. 19. 27
  magnification factor 830
  Manipulators, 58
  Master earn. 287
  Materials for belt and rope. 552
  Mechanical advantage. 36, 77
  Mechanism, definition. 22, 27
  Michel thrusl bearing, 505
  Minimum number of pinion teeth, 336
  Miter gear. 362
  Mobility. 38
  Mobility equalion. 40
  Mode of vibration. 907
  Module, standard values. 306, 308
  Motor car steering gear. 177
  Ackerman
  , 181
  Davis, 178
  condition of correct steering. 177
  Motion generation, 204, 205. 208
  Motion of the follower. 244, 245
  Motion of translation. 3
  curvilinear. 3
  rectilinear. 3
  Motion transfer fink, 52
  Motion, simple harmonic, 625
  Movabiltty. 40. 50
  Multile joint, 4J
  higher. 25
  lower. 25
  prismatic, 23
  redundant, 43
  revoltilc. 23
  rolling. 21 45
  screw, 23
  turning, 23
  Pantograph, 32, 160-162
  Parabolic follower motion, 254
  Parallel, helical geats. 302. 344
  Partial balancing of locomotives, 8117-812
  Particle, motion of, 3
  Path generation. 204-205. 230-241
  Peaucdlier mechanism, 164
  Pendulum, compound. 628, 631. 636
  simple, 626
  torsional, 629, 633
  Percussion, centre, 636
  Periodic time. 850
  Phase angle, 793, 8U9. 853
  Pickering governor. 746
  Pinion. 303. 306
  Piston effort, 657
  Pitch circle, 248. 302
  cone. 360-363
  tine. 336
  Pitching motion of ships, 428
  Pivot bearing, friction, 463
  Plane of gyracouple, 405
  precession. 406
  spin, 406
  Planar motion, 24
  Planar pair. 24
  Planetaiy gear trains, 17-1
  Plate clutch, 479
  Poles. 208. 212
  Port 428
  Position vector, ID
  Preeessional motion. 406
  Precision points, 205
  Pressure angle of.
  earns, 244, 260-263
  Ibur-bar mechanism. 17
  spur gears. 305
  Primary and secondary unbalanced forces, SfiI-833
  Primary balancing of multicylinder in-line engines.
  822, 824
  Prismatic pairs, 23
  Properties of 79T41G
  Pulleys, idler and Jockey, 540
  Pure rolling. 45, 177. 300
  Notation, static forces. 621
  Number of instantaneous centres, 79
  Number synthesis, 49, 203
  Offset follower motion, 244, 263
  Offset slider-crank mechanism, 158
  condition of rotatibility of crank, L6G
  Oldham’s coupling, 3.6
  Open chain. 21
  Oscillating cylinder engine mechanism. 33
  Oscillating follower with fial face. 245
  Oscillating follower with roller. 245, 284
  Overdamped vibration. 870
  Pairs, classification, 23
  Pairing dements. 2Q
  Pairs,
  cylindrical, 23
  definition. 20
  flat, 24
  globular. 24
  i984 index
  Quadric cycle chain* 28
  Quaternary link* 22
  Quick T\Mum mechanism. 31
  drag-link type* 31
  offset slider crank type, 158
  slotted lever, 33
  ^ 3.4
  Whit-Worth mechanism. 33* 106
  Skeleton diagram, 20
  Slider-crank mechanism. 34, 58, 132
  acceleration. 654
  displacement, 655
  force analysis, 646* 659
  inversions* 655
  velocity, 655
  Sliding pair* 23
  Slotted lever quick return motion mechanism* 33, 34
  Spacing of accuracy points, 205
  Spatial mechanism, 57
  Specified cam profiles, 287
  follower motion
• 248, 263
  Speed regulation* 706
  Spherical pair, 24
  Spiral hevcl gear, 304
  Spring constant, 891, 892
  Sprocket, 553
  Spur gears, 302. 303, 305
  addendum
• 306
  arc. of contact, 307
  backlash. 307
  base circle
• 315
  circular pitch. 306
  clearance. 307
  conjugate action. 310
  contact ratio, 307
  dedendum* 306
  face width. 307
  fillet radius. 307
  hilt-depth tooth* 327
  interchangeable, 327
  interference, 324
  length of path of contact* 3IS
  minimum number of teeth for pinion, 328. 336
  pitch circle, 306
  pilch circle diameter, 306
  pitch line. 336
  pressure angle. 308
  stub tooth, 327
  tooth face, 307
  tooth proportions 327
  tooth thickness. 307
  undercutting, 324
  working depth. 307
  Stability of
  2-wheeler, 423
  A-wheeler 415
  governors* 748
  Stabilization, gyroscopic, 432
  Star hoard, 427
  Static balance, 768
  Static balancing machines, 790
  Rack. 326
  Radial Hat faced cam follower, 244
  Radial roller earn follower. 244
  Raven’s method, 135
  Rayleigh s method, 912
  Rectilinear motion
• 2
  Rectilinear translation, 3
  Relative displacement* 12
  Relative velocity, 67* 68
  acceleration, 88
  Relative poles* 208, 212
  Reverted gear trains, 370
  Revolute pair. 23
  Rigid body displacement, II
  guidance. 205
  motion, 2
  Robert’s Chehyehev theorem, 232
  Rolling contact. 300, 506. 508
  Rolling friction* 461
  Rolling of ships, 428
  Rolling contact, bearing, 506* 508
  Rotation, motion* 4
  Roio-centrcs, 212
  Rubbing velocity* 75
  Scott Russel’s mechanism. 166
  Screw friction
• 450
  jack. 450
  pair, 23
  Secondary force balancing of multi-cylinder in-line
  engines. 823
  Secondary couples, 829
  Self actuating brake, 562
  Self-closed pairs, 27
  Self energisation, 562
  Self locking, 454
  Sensitiveness of governors, 752
  Shaking farce, 650
  Simple harmonic motion* 625
  Simple pendulum, 626
  Simplex indicator, 171
  Singular link, 2 L

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