Theory of Machines – S S Rattan

Theory of Machines – S S Rattan
اسم المؤلف
S S Rattan
التاريخ
13 ديسمبر 2023
المشاهدات
261
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Theory of Machines
S S Rattan
Professor of Mechanical Engineering
National Institute of Technology
Kurukshetra
CONTENTS
Preface xv
List of Reviewers xvii
Visual Walkthrough xviii

  1. Mechanisms and Machines 1
    1.1 Mechanism and Machine 1
    1.2 Types of Constrained Motion 2
    1.3 Rigid and Resistant Bodies 3
    1.4 Link 3
    1.5 Kinematic Pair 3
    1.6 Types of Joints 5
    1.7 Degrees of Freedom 5
    1.8 Classification of Kinematic Pairs 6
    1.9 Kinematic Chain 6
    1.10 Linkage, Mechanism and Structure 7
    1.11 Mobility of Mechanisms 7
    1.12 Equivalent Mechanisms 14
    1.13 The Four-bar Chain 18
    1.14 Mechanical Advantage 23
    1.15 Transmission Angle 23
    1.16 The Slider-crank Chain 27
    1.17 Double Slider-crank Chain 30
    1.18 Miscellaneous Mechanisms 32
    Summary 34
    Exercises 35
  2. VelocityAnalysis 38
    2.1 Absolute and Relative Motions 38
    2.2 Vectors 38
    2.3 Addition and Subtraction of Vectors 39
    2.4 Motion of a Link 40
    2.5 Four-link Mechanism 41
    2.6 Velocity Images 42
    2.7 Angular Velocity of Links 43
    2.8 Velocity of Rubbing 43
    2.9 Slider-crank Mechanism 44
    2.10 Crank- and Slotted-lever Mechanism 54
    2.11 Algebraic Methods 62
    2.12 Instantaneous Centre (I-Centre) 64
    2.13 Kennedy’s Theorem 65viii Contents
    2.14 Locating I-Centres 66
    2.15 Angular-velocity-ratio Theorem 68
    2.16 Centrode 74
    Summary 76
    Exercises 76
  3. Acceleration Analysis 79
    3.1 Acceleration 79
    3.2 Four-link Mechanism 81
    3.3 Acceleration of Intermediate and Offset Points 83
    3.4 Slider-crank Mechanism 85
    3.5 Coriolis Acceleration Component 97
    3.6 Crank and Slotted-lever Mechanism 99
    3.7 Algebraic Methods 110
    3.8 Klein’s Construction 112
    3.9 Velocity and Acceleration from Displacement-time Curve 113
    3.10 Centre of Curvature 114
    3.11 Hartmann Construction 115
    3.12 Euler-Savary Equation 116
    3.13 Bobillier Construction 118
    3.14 Cubic of Stationary Curvature 120
    Summary 121
    Exercises 122
  4. Computer-aided Analysis of Mechanisms 124
    4.1 Four-link Mechanism 124
    4.2 Use of Complex Algebra 131
    4.3 The Vector Method 132
    4.4 Slider-crank Mechanism 136
    4.5 Coupler Curves 140
    Summary 142
    Exercises 143
  5. Graphical and Computer-aided Synthesis of Mechanisms 144
    Part A: Graphical Methods
    5.1 Pole 144
    5.2 Relative Pole 146
    5.3 Function Generation by Relative Pole Method 148
    5.4 Inversion Method 151
    5.5 Function Generation by Inversion Method 151
    5.6 Path Generation 155
    5.7 Motion Generation (Rigid-body Guidance) 158
    Part B: Computer-aided Synthesis of Mechanisms
    5.8 Function Generation 159
    5.9 Chebychev Spacing 166
    5.10 Path Generation 169
    Contents ix
    5.11 Motion Generation (Rigid-body Guidance) 175
    Summary 179
    Exercises 179
  6. Lower Pairs 181
    6.1 Pantograph 181
    6.2 Straight-line Mechanisms 182
    63 Engine Indicators 190
    6.4 Automobile Steering Gears 194
    6.5 Types of Steering Gears 195
    6.6 Hooke’s Joint 198
    6.7 Double Hooke’s Joint 205
    Summary 206
    Exercises 207
  7. Cams 209
    7.1 Types of Cams 209
    7.2 Types of Followers 212
    73 Definitions 213
    7.4 Follower Displacement Programming 214
    7.5 Derivatives of Follower Motion 215
    7.6 High-speed Cams 216
    7.7 Undercutting 216
    7.8 Motions of the Follower 217
    7.9 Layout of Cam Profiles 223
    7.10 Cams with Specified Contours 232
    7.11 Analysis of a Rigid Eccentric Cam 241
    7.12 Analysis of an Elastic Cam System 244
    7.13 Spring Surge, Unbalance and Wind Up 246
    Summary 247
    Exercises 247
  8. Friction 250
    8.1 Kinds of Friction 250
    8.2 Laws of Friction 251
    8.3 Coefficient of Friction 251
    8.4 Inclined Plane 252
    8.5 Screw Threads 256
    8.6 Screw Jack 262
    8.7 Wedge 265
    8.8 Pivots and Collars 268
    8.9 Friction Clutches 274
    8.10 Rolling Friction 285
    8.11 Anti-friction Bearings 285
    8.12 Greasy Friction 286
    8.13 Greasy Friction at a Journal 286X Contents
    8.14 Friction Axis of a Link 287
    8.15 Film Friction 290
    8.16 Mitchell Thrust Bearing 291
    Summary 292
    Exercises 293
  9. Belts, Ropes and Chains 296
    9.1 Belt and Rope Drives 296
    9.2 Open- and Crossed-belt Drives 298
    9.3 Action of Belts on Pulleys 298
    9.4 Velocity Ratio 299
    9.5 Slip 299
    9.6 Material for Belts and Ropes 301
    9.7 Crowing of Pulleys 301
    9.8 Types of Pulleys 302
    9.9 Law of Belting 304
    9.10 Length of Belt 304
    9.11 One (Stepped) Pulleys 307
    9.12 Ratio of Friction Tensions 310
    9.13 Power Transmitted 312
    9.14 Centrifugal Effect on Belts 315
    9.15 Maximum Power Transmitted by a Belt 316
    9.16 Initial Tension 320
    9.17 Creep 324
    9.18 Chains 325
    9.19 Chain Length 326
    9.20 Angular Speed Ratio 327
    9.21 Classification of Chains 328
    Summary 329
    Exercises 330
  10. Gears 332
    10.1 Classification of Gears 333
    10.2 Gear Terminology 337
    10.3 Law of Gearing 342
    10.4 Velocity of Sliding 343
    10.5 Forms of Teeth 343
    10.6 Cycloidal Profile Teeth 343
    10.7 Involute Profile Teeth 345
    10.8 Interchangeable Gears 348
    10.9 Non-standard Gears 348
    10.10 Path of Contact 349
    10.11 Arc of Contact 350
    10.12 Number of Pairs of Teeth in Contact (Contact Ratio) 351
    10.13 Interference in Involute Gears 354
    10.14 Minimum Number of Teeth 355Contents xi
    10.15 Interference Between Rack and Pinion 360
    10.16 Undercutting 361
    10.17 Comparison of Cycloidal and Involute Tooth Forms 362
    10.18 Helical and Spiral Gears 362
    10.19 Terminology of Helical Gears 364
    10.20 Velocity Ratio and Centre Distance of Helical Gears 364
    10.21 Helical Gear Forces and Efficiency 365
    10.22 Worm and Worm Gear 369
    10.23 Terminology of Worm Gears 370
    10.24 Velocity Ratio and Centre Distance of Worm Gears 370
    10.25 Efficiency of Worm Gears 371
    10.26 Bevel Gears 372
    Summary 374
    Exercises 375
  11. Gear Trains 378
    11.1 Simple Gear Train 378
    11.2 Compound Gear Train 379
    11.3 Reverted Gear Train 380
    11.4 Planetary or Epicyclic Gear Train 381
    11.5 Analysis of Epicyclic Gear Train 382
    11.6 Torques in Epicyclic Trains 390
    11.7 Sun and Planet Gear 394
    11.8 Bevel Epicyclic Gear 397
    11.9 Compound Epicyclic Gear 399
    11.10 Automotive Transmission Gear Trains 400
    11.11 Differentials 405
    Summary 407
    Exercises 407
  12. Static Force Analysis 410
    12.1 Constraint and Applied Forces 410
    12.2 Static Equilibrium 410
    12.3 Equilibrium of Two- and Three-force Members 411
    12.4 Member With Two Forces and a Torque 412
    12.5 Equilibrium of Four-force Members 412
    12.6 Force Convention 413
    12.7 Free-body Diagrams 413
    12.8 Superposition 414
    12.9 Principle of Virtual Work 426
    12.10 Friction in Mechanisms 428
    Summary 431
    Exercises 432
  13. Dynamic Force Analysis 434
    13.1 D’alembert’s Principle 434xii Contents
    13.2 Equivalent Offset Inertia Force 435
    13.3 Dynamic Analysis of Four-link Mechanisms 435
    13.4 Dynamic Analysis of Slider-crank Mechanisms 437
    13.5 Velocity and Acceleration of a Piston 437
    13.6 Angular Velocity and Angular Acceleration of Connecting Rod 439
    13.7 Engine Force Analysis 440
    13.7 Turning Moment on Crankshaft 441
    13.8 Dynamically Equivalent System 445
    13.9 Inertia of the Connecting Rod 446
    13.10 Inertia Force in Reciprocating Engines (Graphical Method) 449
    13.11 Turning-moment Diagrams 458
    13.12 Fluctuation of Energy 460
    13.13 Flywheels 461
    13.14 Dimensions of Flywheel Rims 469
    13.15 Punching Presses 471
    Summary 474
    Exercises 474
  14. Balancing 477
    14.1 Static Balancing 477
    14.2 Dynamic Balancing 480
    14.3 Transference of a Force From One Plane to Another 480
    14.4 Balancing of Several Masses in Different Planes 481
    14.5 Force Balancing of Linkages 488
    14.6 Balancing of Reciprocating Mass 490
    14.7 Balancing of Locomotives 492
    14.8 Effects of Partial Balancing in Locomotives 492
    14.9 Secondary Balancing 496
    14.10 Balancing of Inline Engines 497
    14.11 Balancing of V-engines 509
    14.12 Balancing of W, V-8 and V-12 Engines 513
    14.13 Balancing of Radial Engines 575
    14.14 Balancing Machines 520
    14.15 Field Balancing 524
    Summary 526
    Exercises 527
  15. Brakes and Dynamometers 530
    15.1
    15.2
    15.3
    15.4
    15.5
    15.6
    15.7
    15.8
    Types of Brakes 530
    Block or Shoe Brake 530
    Band Brake 536
    Band and Block Brake 541
    Internal Expanding Shoe Brake 544
    Effect of Braking 547
    Types of Dynamometers 549
    Prony Brake Dynamometer 550Contents xiii
    15.9 Rope Brake Dynamometer 550
    15.10 Belt Transmission Dynamometer 551
    15.11 Epicyclic-train Dynamometer 552
    15.12 Bevis-Gibson Torsion Dynamometer 553
    15.13 Automotive Propulsion 553
    Summary 556
    Exercises 556
  16. Governors 559
    16.1 Types of Governors 559
    16.2 Watt Governor (Simple Conical Governor) 560
    16.3 Porter Governor 562
    16.4 Proell Governor 566
    16.5 Hartnell Governor 569
    16.6 Hartung Governor 574
    16.7 Wilson-Hartnell Governor (Radial-spring Governor) 575
    16.8 Pickering Governor 578
    16.9 Spring-controlled Gravity Governor 579
    16.10 Inertia Governor 580
    16.11 Sensitiveness of a Governor 582
    16.12 Hunting 582
    16.13 Isochronism 583
    16.14 Stability 583
    16.15 Effort of a Governor 583
    16.16 Power of a Governor 585
    16.17 Controlling Force 589
    Summary 594
    Exercises 594
  17. Gyroscope 597
    17.1 Angular Velocity 597
    17.2 Angular Acceleration 597
    17.3 Gyroscopic Torque (Couple) 599
    17.4 Gyroscopic Effect on Aeroplanes 601
    17.5 Gyroscopic Effect on Naval Ships 602
    17.6 Stability of an Automobile 605
    17.7 Stability of a Two-wheel Vehicle 610
    17.8 Rigid Disc at an Angle Fixed to a Rotating Shaft 612
    Summary 613
    Exercises 613
  18. Vibrations
    18.1 Definitions 615
    18.2 Types of Vibrations 616
    18.3 Basic Features of Vibrating Systems 616
    18.4 Degrees of Freedom 617
    615xiv Contents
    Section-I (Longitudinal Vibrations) 618
    18.5 Free Longitudinal Vibrations 618
    18.6 Displacement, Velocity and Acceleration 623
    18.7 Inertia Effect of the Mass of Spring 624
    18.8 Damped Vibrations 629
    18.9 Logarithmic Decrement 633
    18.10 Forced Vibrations 636
    18.11 Forced-damped Vibrations 638
    18.12 Magnification Factor 641
    18.13 Vibration Isolation and Transmissibility 644
    18.14 Forcing Due to Unbalance 646
    18.15 Forcing Due to Support Motion 648
    Section II (Transverse Vibrations) 650
    18.16 Single Concentrated Load 650
    18.17 Uniformly Loaded Shaft 651
    18.18 Shaft Carrying Several Loads 654
    18.19 Whirling of Shafts 657
    Section III (Torsional Vibration) 659
    18.20 Free Torsional Vibrations (Single Rotor) 659
    18.21 Inertia Effect of Mass of Shaft 660
    18.22 Multifilar Systems 661
    18.23 Free Torsional Vibrations (Two-rotor System) 666
    18.24 Free Torsional Vibrations (Three-rotor System) 667
    18.25 Torsionally Equivalent Shaft 668
    18.26 Free Torsional Vibrations of Geared System 671
    Summary 673
    Exercises 674
  19. Automatic Control 677
    19.1 Open and Closed-loop Control
    (Unmonitored and Monitored Control) 677
    19.2 Amplification 678
    19.3 Actuator (Servomotor) 678
    19.4 Transducer 678
    19.5 Block Diagrams 678
    19.6 Lag in Response 679
    19.7 Damping 680
    19.8 First-order System Response 680
    19.9 Second-order System Response 682
    19.10 Transfer Function 682
    19.11 Transfer Function Relationships 685
    Summary 686
    Exercises 686
    Appendix I
    Appendix II
    Index
    687
    702
    705INDEX
    Absolute motion 38
    Absorption dynamometer 549
    Accelerating force
    primary 490
    secondary 490
    Acceleration 79
    centripetal 80
    Coriolis component 97
    image 84
    of intermediate points 83
    of offset points 83
    of piston 437,438
    radial 80
    tangential 80
    Ackermann steering gear 194, 196
    Actuator 678
    Addendum 339
    Addendum circle 339
    Addendum coefficient 356
    Adsorbed film 286
    Amplification 678
    Analysis of mechanisms 1, 124
    Andrew variable stroke engine 53
    Angle
    of action 213, 341
    of ascent 213
    of dwell 213
    of descent 213
    of friction 25
    helix 364
    lead 370
    of obliquity 340
    pressure 340
    repose 252
    Angular acceleration 597, 599
    of connecting rod 439
    of links 83
    Angular velocity of links 43
    Angular velocity of
    precession 599
    Angular velocity ratio theorem 68
    Anti-friction bearings 284
    Applied forces 410
    Arc of approach 341
    Arc of contact 341, 350
    Arc of recess 341
    Automatic control 677
    closed-loop 677
    monitored 677
    open-loop 677
    unmonitored 677
    Automobile steering gears
    Ackeramann 194, 196
    Davis 194
    types 194
    Automotive propulsion 553
    Balancing 477
    dynamic 480
    field 524
    In different planes 481
    machines 520
    static 520
    dynamic 521
    of in-line engines 497
    two-cylinder 498
    four-cylinder 499
    six-cylinder 500
    of linkages 488
    of locomotives 492
    of radial engines 515
    of reciprocating mass 490
    ofV-engines 509
    of V-8 engines 513, 514
    of V-12 engines 513, 514
    ofW-engines 513
    secondary 496
    static 477
    Ball bearings 284
    Ball’s point 121
    Band brake 536
    Band and block brake 541
    Base circle
    cam 212
    gear 346
    Bearings
    anti-friction 284
    ball 284
    collar 267
    footstep 267
    Mitchell thrust 290
    pivot 267
    roller 285
    thrust on 441
    Belt
    action on pulleys 298
    centrifugal effect on 315
    creep in 324
    crossed drive 298
    flat 310
    initial tension in 320
    law of (belting) 304
    length of crossed 306
    length of open 304
    material 301
    maximum power
    transmitted 316
    open drive 298
    power transmitted 312
    ratio of friction tensions 310
    slip 299
    V 311
    velocity ratio 299, 324
    Bevel gears 334,372
    epicyclic 397
    spiral 334
    straight 334706 Index
    zerol 334 tangent 231 frustrum of cone 270
    Block diagrams 678 trace point 212 Collar bearing 267
    Bobillier construction 118 types 208 Complex numbers 63, 111
    Bobillier theorem 118 unbalance in 245 Compound epicyclic gear 399
    Body centrode 74 undercutting 215 Computer-aided analysis of
    Body guidance 175 wedge 208 four link mechanism 124
    Brakes 530 wind up in 245 slider crank mechanism 136
    band 536 with specified contours 231 Computer-aided synthesis 144
    band and block 541 Centre of curvature 114 Constraint forces 410
    block 530 Centre distance of Constrained motion
    effect of (braking) 547 helical gears 364 completely 2
    internal expanding shoe 544 worm gears 370 incompletely 2
    self energised 531 Centrifugal governors 559 successfully 2
    self locking 531 Centrifugal clutch 275 types 2
    shoe 530 Centripetal acceleration 80 Cone clutch 275
    types 530 Centrode Cone pulley 307
    Braking effect 547 body 74 Configuration diagram 38
    moving 74 Conical collar 268, 270
    Cam fixed 74 Conjugates 115
    angle of action 208 space 74 Conjugate point 115, 119
    angle of ascent 213 Chain 327 Connecting rod
    angle of decent 213 block 328 angular acceleration of 439
    angle of dwell 213 classification 328 angular velocity of 439
    barrel 210 conveyor 328 force (thrust) along 441
    base circle 212 hoisting 328 inertia of 446
    circular arc 233, 234 inverted tooth 329 Contact length 340
    conjugate 210 length of 326 Contact ratio 341, 351
    convex 233, 234 power transmission 328 Control, automatic 679
    cylindrical 209 roller 328 Convex cams 233, 234
    disc 209 silent 329 Coriolis acceleration
    drum 210 speed ratio 327 component 97
    eccentric 240 sprocket 326 Correction couple 448
    elastic 243 Chebychev spacing 168 Coupler 18
    flat 208 Circular-arc cams 233, 234 Coupler curves 140
    globoidal 210 Circular pitch 338, 364 Cramer’s rule 160
    gravity 211 Clearance 339 Crank-crank mechanism 19
    high speed 215 Closed pair 4 Crank effort 441
    jump 241, 245 Clutches 273 Crank effort diagrams 458
    pitch curve 212 centrifugal 275 Crank-lever mechanism 20
    pitch circle 213 cone 275 Crank-rocker mechanism 20
    pitch point 213 disc 274 Crank and slotted lever
    positive drive 211 multi plate 274 mechanism 28
    pre-loaded 211 single plate 274 Critical speed 657
    pressure angle 212 Coefficient of Crowning of pulleys 301
    prime circle 213 fluctuation of energy 460 Cubic of stationary curvature 120
    profile, layout of 222 fluctuation of speed 460 Cycloidal motion 220
    radial 209 friction 250 Cycloidal profile teeth 343
    rigid eccentric 240 Coincident points 62
    spiral 209 Collar 267 D’Alembert’s principle 434
    spherical 210 Conical 268, 270 Damped vibrations 629
    spring surge in 245 flat 268, 269 Damping 680Index 707
    Damping coefficient 629
    Damping factor 630
    Damping ratio 630
    Davis steering gear 194
    Dead angle 288
    Dead centre position 288
    Dedendum 339
    Dedendum circle 339
    Degree of freedom 5
    Deltoid linkage 20
    Differentials 405
    Differential gear 406
    Direct and reverse cranks 575
    Double lever mechanism 20
    Double Hooke’s joint 204
    Double parallelogram linkage 10
    Double rocker mechanism 20
    Double slider crank chain 30
    Drag crank mechanism 19
    Dunkerley’s method 655
    Dynamic balancing 480
    Dynamic force analysis 434
    Dynamically equivalent
    system 445
    Dynamics 1
    Dynamometers 530, 549
    absorption 549
    belt transmission 557
    Bevis-Gibson torsion 553
    epicyclic train 552
    prony brake 550
    rope brake 550
    transmission 549
    types 549
    Eccentric cam 240
    Effective driving force 440
    Efficiency of
    helical gears 365
    spiral gears 365
    worm gears 371
    Elastic cam system 243
    Element 3
    Elliptical trammel 30
    Equilibrium of members with
    two forces 477
    two forces and a torque 472
    three forces 411
    four forces 472
    Energy method 655
    Engine indicator 189
    Crosby 190
    Dobbie mclnnes 192
    Simplex 190
    Thomson 191
    Epicyclic gear 381
    bevel 397
    compound 399
    Epicyclic train dynamometer 552
    Equilibrium of
    two-force member 411
    three-force member 411
    four-force member 472
    Equilibrium method 618
    Equivalent mechanism 74
    Equivalent offset inertia force 435
    Error detector 677
    Euler-Savary equation 116
    Feedback 677
    Ferguson’s paradox 408
    Film friction 249, 289
    Field balancing 524
    First order system response 680
    Fluctuation of energy 460
    coefficient of 460
    maximum 460
    Fluctuation of speed 459
    coefficient 460
    maximum 460
    Flywheels 460
    Flywheel rims 469
    Follower
    displacement
    programming 213
    flat faced 272
    knife edge 277
    mushroom 272
    offset 272
    oscillating 272
    radial 272
    reciprocating 272
    roller 277
    spherical faced 272
    types 277
    Follower motions 276
    constant accel, and decel. 218
    constant velocity 219
    cycloidal 220
    SHM 216
    Footstep bearing 267
    Force analysis
    dynamic 434
    static 410
    Forced vibrations
    damped 638
    harmonic 637
    periodic 637
    step input 63
    Forces
    constraint 410
    applied 410
    Forcing due to
    unbalance 646
    support motion 648
    Forms of teeth 343
    Four-bar chain 18
    Four-link mechanism 41, 81, 124,
    148, 151, 435
    Free-body diagrams 413
    Free longitudinal vibrations 618
    Free torsional vibrations 666, 667
    of geared system 671
    Friction
    angle of 257
    axis 286
    boundary 249, 285
    circle 286
    clutches 273
    coefficient of 250
    dry 249
    film 249, 289
    greasy 249, 285
    in mechanisms 428
    kinds 249
    laws of 250
    limiting angle of 257
    rolling 249, 284
    skin 249
    solid 249
    tension 310
    wheels 332
    Freudenstein’s equation 159
    Function generation 744, 148,
    151, 159
    Fundamental frequency 667
    Gear ratio 338
    Gear box
    sliding 400
    pre-selective 401
    Gears
    bevel 334, 372708 Index
    classification 333
    conjugate 343
    contact ratio 341, 351
    crossed helical 335, 336
    differential 405
    double helical 333
    epicyclic 381
    for intersecting shafts 334
    for parallel shafts 333
    for scew shafts 334
    helical 333, 336, 362
    Herringbone 333
    Humpage 409
    hypoid 337
    Interchangeable 348
    Interference in involute 354
    law of (gearing) 342
    mitre 334
    non-standard 348
    pairs of teeth in contact 351
    pressure angle 340
    spur 333
    spiral 335, 362
    rack and pinion 360
    worm 336
    zerol bevel 334
    Gear teeth
    bottom land 340
    comparison of teeth forms 362
    cycloidal 343
    face 340
    face width 340
    flank 340
    forms of 343
    involute 343, 345
    left-handed 362
    minimum number of 355
    right-handed 362
    space width 339
    top land 340
    Gear trains
    automotive transmission 400
    bevel epicyclic 397
    compound 379
    compound epicyclic 399
    epicyclic 381
    planetary 381
    reverted 380
    simple 378
    sun and planet 394
    torques in 390
    Geared system 671
    Governor 559
    Centrifugal 559
    coefficient of
    insensitiveness 590
    controlling force 589
    effort of 583
    Hartnell 569
    Hartung 574
    height of 560
    hunting 582
    inertia 560, 580
    isochronous 583
    Pickering 578
    Porter 562
    Proell 566
    power of 585
    radial spring 575
    sensitiveness of 582
    spring-controlled gravity 579
    stability of 583
    types 559
    Watt 560
    Wilson-Hartnell 575
    Graphical differentiation 111
    Graphical methods of
    synthesis 144
    Grass-Hopper mechanism 185
    Grashof’s law 20
    Gruebler’s criterion 8
    Gyroscope 597
    Gyroscopic couple 599
    Gyroscopic effect on
    aeroplanes 601
    naval ships 602
    Gyroscopic torque 599
    Hammer-blow 492
    Hand pump 29
    Harmonic forcing 637
    Hartmann construction 115
    Hart mechanism 183
    Hartnell governor 569
    Hartung governor 574
    Height of governor 560
    Helical gears 333, 336, 362
    centre distance of 364
    crossed 335, 336
    double 333
    efficiency of 365
    forces in 365
    helix angle 364
    herringbone 333
    spur 333
    velocity ratio 364
    Helical pair 5
    Helix angle 364
    Herringbone gear 333
    Higher pair 4
    High speed cam 215
    Hooke’s joint 197
    acceleration of driven
    shaft 201
    double 204
    polar velocity diagram 200
    velocity ratio 199
    Humpage reduction gear 409
    Hypoid gears 337
    Inclined plane 251
    Indexing mechanisms 33
    Indicators, engine 189
    Inertia effect 624
    Inertia force 449
    Inertia governor 560, 580
    Inertia of connecting rod 446
    Initial tension 320
    Instantaneous centre 64
    Interchangeable gears 348
    Intermediate pulley 302
    Internal expanding shoe brake 544
    Interference in gears 354
    Inversion method of synthesis 151
    Inverted slider-crank
    mechanism 57
    Inversions of mechanisms 27
    Involute profile teeth 343, 345
    Joints 5
    Kempe’s mechanism 188
    Kennedy’s theorem 65
    Kinematics 1
    Kinematics chain 6
    Kinematic derivatives 214
    Kinematics link 3
    Kinematics pair 3
    classification 6
    types 3
    Kinetics 1
    Klein’s construction 112
    Kutzback’s criterion 8Index 709
    Lag in response 679
    Law of
    belting 304
    gearing 342
    Laws of friction 250
    Lazy tongs 189
    Lead 370
    Lead angle 370
    Least square technique 161
    Limiting angle of friction 251
    Line of action 340
    Line of centres 338
    Linear system 780
    Link 3
    Linkage 7
    Logarithmic decrement 633
    Longitudinal vibrations 616
    damping coefficient 629
    damping factor 630
    energy method 622
    equilibrium method 618
    inertia effect of mass 624
    magnification factor 641
    Rayleigh’s method 623
    Loose and fast pulley 303
    Lower pairs 4
    Machine 1
    Magnification factor 641
    Mechanical advantage 23
    Mechanism
    crank-crank 19
    crank-lever 20
    crank-rocker 20
    double-crank 19
    double-lever 20
    double-rocker 20
    drag-crank 19
    of zero order 7
    oscillating-oscillating 20
    rotary-oscillating 20
    rocker-rocker 20
    rotary-rotary 19
    Mechanisms 1, 7
    classification 7
    degree of freedom 8
    mobility 7
    Mitchell thrust bearing 290
    Motion
    absolute 38
    of a link 40
    relative 38
    Motion generation 144
    Multifilar systems 661
    bifilar suspension 661
    trifilar system 662
    Multiplate clutch 274
    Natural frequency 615
    Non standard gears 348
    Number synthesis 8
    Oldham’s coupling 31
    Oscillating cylinder engine 28
    Oscillating-oscillating
    converter 20
    Pair 3
    Pantograph 180
    Parallel-crank four bar linkage 20
    Parallel linkages 188
    Parallel ruler 188
    Path generation 144
    Path of approach 340
    Path of contact 340
    Path of recess 340
    Paucellier mechanism 181
    Periodic forcing 637
    Physical derivatives 214
    Pickering governor 578
    Pinion 333, 338
    Piston
    acceleration 437, 438
    effort 440
    velocity 437, 438
    Pitch
    axial 370
    circle 213, 337
    circular 338, 364
    curve 212
    cylinder 337
    diametral 338
    diameter 338
    line 338
    module 338
    normal circular 364
    point 213, 338
    surface 338
    Pivots 267, 271
    conical 268, 272
    flat 268, 272
    Pivot bearing 267
    Planetary gear train 381
    Polar velocity diagram 200
    Pole 144
    Porter governor 562
    Pre-selective gear box 401
    Prime circle 213
    Principle of virtual work 426
    Pressure angle 212, 340
    Primary accelerating force 490
    Proell governor 566
    Pulleys
    cone 307
    crowning of 301
    guide 303
    idler 302
    intermediate 302
    loose and fast 303
    stepped 307
    types 302
    Quadric-cycle mechanism 41
    Quick return mechanisms
    crank and slotted lever 28
    Whitworth quick return 27
    Rack 333
    Rayleigh’s method 623
    Redundant chain 7
    Redundant degree of freedom 10
    Redundant link 10
    Relative motion 38
    Relative pole 146
    Relative pole method 148
    Relative velocity method 383
    Resistance
    aerodynamic 554
    frictional 554
    gradient 554
    road 553
    rolling 553
    tractive 554
    Resistant body 3
    Resonance 641
    Rigid body 3
    Rigid-body guidance 175
    Rigid disc at an angle 612
    Robert mechanism 207
    Rocker-rocker mechanism 20
    Roller bearing 285
    Rolling pair 5
    Rolling friction 249, 284710 Index
    Root circle 339
    Rope drive 296, 297, 311
    Rope material 301
    Rotary engine 27, 28
    Rotary-oscillating converter 20
    Rubbing velocity 43
    Scotch yoke 31
    Scott-Russel mechanism 185
    Screwjack 261
    Screw pair 5
    Screw threads 255
    Secondary accelerating force 490
    Secondary balancing 496
    Servomotor 678
    Sewing machine mechanism 73
    Shaking force 490
    Shaking couple 490
    Simple conical governor 560
    Simple harmonic motion 216
    Single plate clutch 274
    Slider-crank mechanism 44, 85,
    136, 151, 288, 437
    Sliding gear box 400
    Sliding pair 4
    Slip 299
    Snap action mechanisms 32
    Space centrode 74
    Speed ratio 327
    Spherical pair 5
    Spiral gears 362
    Spring surge 245
    Sprocket 326
    Spur gears
    addendum 339
    addendum circle 339
    addendum coefficient 356
    angle of action 213, 341
    angle of obliquity 340
    arc of approach 341
    arc of contact 341
    arc of recess 341
    backlash 340
    base circle 346
    circular pitch 338, 364
    clearance 339
    contact length 340
    contact ratio 341, 351
    cycloidal tooth profile 343
    dedendum 339
    dedendum circle 339
    diametral pitch 338
    face 340
    face width 340
    flank 340
    forms of teeth 343
    gear ratio 338
    interference in 354
    involute tooth profile 343, 345
    line of action 340
    line of centres 338
    minimum number of teeth 355
    module 338
    path of approach 340
    path of contact 340
    path of recess 340
    pinion 333, 338
    pitch 338
    pitch circle 337
    pitch diameter 338
    pitch line rack 338
    pitch point 338
    pitch surface 338
    pressure angle 340
    pressure line 340
    rack 338
    rack and pinion 333, 360
    top land 340
    tooth thickness 340
    velocity of sliding 343
    undercutting 361
    Square threads 256
    Stability of automobile 605
    Stability of two-wheel vehicle 610
    Static balancing 477
    Static equilibrium 410
    Static force analysis 410
    Statics 1
    Steering gears
    Ackermann 194, 196
    Davis 194
    Straight line mechanisms 181
    Structure 7
    Sun and planet gear 394
    Superposition of loads 414
    Superstructure 7
    Swaying couple 493
    Synthesis of mechanisms 144
    Tangential acceleration 80
    Tchebicheff mechanism 187
    Thrust
    along connecting rod 441
    on bearings 441
    on sides of cylinder 441
    Torsional system 681
    Torsionally equivalent shaft 668
    Torsional vibrations 659
    geared system of 671
    inertia effect of mass 660
    three-rotor system 667
    two-rotor system 666
    Trace point 212
    Tractive force 492
    Tractive resistance 554
    Transducer 678
    Transfer function 682
    open loop 685
    closed loop 685
    Transmission angle 23
    Transmissibility 644
    Transverse vibrations 650
    Dunkerley’s method 655
    energy method 655
    shaft carrying several
    loads 654
    single concentrated load 650
    uniformly-loaded shaft 651
    Turn buckle 260
    Turning pair 4
    Turning-moment diagrams 458
    Turning moment on
    crankshaft 441
    Unbalance 245
    Unclosed pair 4
    Undercutting
    cam 215
    gear 361
    Uniform pressure theory 268
    Uniform wear theory 268
    Universal drafting machine 189
    Universal joint 197
    V-belt 311
    Vector approach 62, 111
    Velocity
    Angular 43
    from displacement curve 111
    image 42
    of piston 437,438
    of rubbing 43
    of sliding 343Index 711
    ratio 339, 364 of three-rotor system 667 Whipping speed 657
    Vibrations 615 of two-rotor system 666 Whirling of shaft 657
    cycle 615 period of 615 Whirling speed 657
    damped 615, 229 resonance in 615 Whitworth quick return
    degree of freedom 617 torsional 616 mechanism 27
    free 615 transmissibility of 644 Wilson-Hartnell governor 575
    frequency of 615 transverse 616 Wind up 245
    forced 615 types 616 Worm gears
    forced damped 638 Virtual work 426 axial pitch of 372
    isolation 644 V-threads 259 centre distance 372
    logarithmic decrement 633 efficiency of 373
    longitudinal 616 Watt governor 560 lead 372
    magnification factor 641 Watt mechanism 186 lead angle 372
    natural 615 Wedge 264 velocity ratio 372

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