Theory of Machines – Kinematics and Dynamics
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Loading...Theory of Machines – Kinematics and Dynamics
B.V.R. GUPTA
Principal
Simhadhri Educational Society
Group of Institutions
&
Formerly Professor & Dean
Faculty of Engineering
Andhra University
Visakhapatnam, A.P.
CONTENTS
Abbreviations, Notations and Symbols
- Simple Mechanisms
1.1 Introduction
1.2 Kinematic Link or Element
1.3 Kinematic Pair
Nature of Relative Motion between the Elements
Nature of Contact between the Elements
Nature of the Mechanical Arrangement for Complete or
Successful Constraint between the Elements
1.4 Kinematic Chain
1.4.1 First Equation Using Pairs
1.4.2 Second Equation Using Joints
1.4.3 According to the Type of Closure between Elements
1.4.4 Degrees of Freedom
1.5 Mechanism
1.6 Inversion
1.6.1 Single Slider Crank Chain
1.6.2 Double Slider Crank Chain
1.6.3 Four-Bar Mechanisms
1.7 Exercise
1.7.1 Short Answer Questions
1.7.2 Problems
1.7.3 Multiple Choice Questions
lX
Xl
xxxiii
viixx Contents - Mechanisms with Lower Pairs 25
2.1 Introduction 27
2.2 Pantograph 27
2.3 Mechanisms for Straight Line Motions 28
2.3.1 Peaucellier Mechanism 29
2.3.2 Hart Mechanism 29
2.3.3 Scott-Russell Mechanism 30
2.4 Approximate Straight Line Mechanism 31
2.4.1 Watt Mechanism 31
2.4.2 Grasshopper Mechanism 32
2.4.3 Tchebicheff Straight Line Motion 32
2.4.4 Roberts Mechanism 33
2.5 Steering Gear Mechanism 33
2.5.1 Davis Steering Gear (Exact) 34
2.5.2 Ackermann Steering Gear (Approximate) 35
2.6 Hooke’s Joint (or) Universal Joint 36
2.7 Double Hooke’s Joint 41
2.8 Exercise 43
2.8.1 Short Answer Questions 43
2.8.2 Problems 45
2.8.3 Multiple Choice Questions 46 - Velocities and Accelerations in Mechanisms 49
3.1 Introduction 51
3.2 Motion 51
3.2.1 Translatory Motion 51
3.2.2 Rotary Motion 51
3.2.3 Speed 51
3.2.4 Angular Displacement (6) 52
3.2.5 Radian 52
3.2.6 Angular Velocity (w) 52
3.2.7 Relation between Linear Velocity and Angular Velocity 53
3.3 Instantaneous Centre Method 53
3.3.1 Properties of Instantaneous Centres 54
3.3.2 Number of Instantaneous Centres in a Mechanism 55
3.3.3 Types of Instantaneous Centres 55Contents xxi
3.3.4 Location of Instantaneous Centres 55
3.3.5 Kennedy’s Theorem or Three-centres-in-line Theorem 56
3.3.6 Application of Instantaneous Centre to Any Mechanism 57
3.3.7 Steps in Determining the Unknown Instantaneous Centres 57
3.4 Relative Velocity Method 64
3.5 Acceleration in Mechanisms 70
3.5.1 Introduction 70
3.5.2 Angular Acceleration 70
3.5.3 Vector form between Linear and Angular Acceleration 70
3.5.4 Various Steps to be Followed in the Acceleration Analysis 71
3.6 Coriolis Component of Acceleration 78
3.7 Exercise 83
3.7.1 Short Answer Questions 83
3.7.2 Problems 83
3.7.3 Multiple Choice Questions 88 - Inertia Forces in Reciprocating Parts 91
4.1 Introduction 93
4.1.1 Terms Used in Static 93
4.1.2 D-Alembert’s Principle 94
4.2 Analytical Method for Reciprocating Mechanism 95
4.2.1 Displacement of Piston (Xp) 96
4.2.2 Velocity of Piston (vp) 97
4.2.3 Acceleration of Piston (ap) 97
4.2.4 Angular Velocity of Connecting Rod (cot) 98
4.2.5 Angular Acceleration (ac) 98
4.3 Klien’s Construction for Reciprocating Mechanisms 100
4.3.1 Klien’s Velocity Diagram 100
4.3.2 Klien’s Acceleration Diagram 101
4.4 Forces on the Reciprocating parts of an Engine 104
4.4.1 Neglecting the Weight of the Connecting Rod 104
4.4.2 Considering the Weight of the Connecting Rod 109
4.5 Equivalent Dynamical System 110
4.5.1 Dynamically Equivalent System 110
4.5.2 Determination of Dynamically Equivalent System of Two Masses Placed
Arbitrarily (Analytically) 111xxii Contents
4.5.3 Determination of Dynamically Equivalent System of Two Masses Placed
Arbitrarily (Graphically) 112
4.6 Inertia Forces in a Reciprocating Engine 113
4.6.1 Graphical Method 113
4.6.2 Analytical Method 114
4.7 Exercise 120
4.7.1 Short Answer Questions 120
4.7.2 Problems 120
4.7.3 Multiple Choice Questions 122 - Turning Moment Diagrams and Design of Flywheel 125
5.1 Introduction 127
5.2 Single-Cylinder Double-Acting Steam Engine 127
5.3 Four-Stroke Cycle Internal Combustion Engine 128
5.3.1 Fluctuation of Energy 129
5.4 Flywheel 130
5.4.1 Coefficient of Fluctuation of Speed 131
5.4.2 Energy Stored in the Flywheel (E) 131
5.4.3 Design of Flywheel 132
5.5 Typical Worked Examples 133
5.6 Flywheel in Punching Press 141
5.7 Exercise 144
5.7.1 Short Answer Questions 144
5.7.2 Problems 144
5.7.3 Multiple Choice Questions 145 - Friction 147
6.1 Introduction 149
6.2 Laws of Friction 150
6.2.1 Friction between Dry Surfaces 151
6.2.2 Friction between Rough Surfaces 151
6.2.3 Friction is Self Adjusting 151
6.2.4 Angle of Friction (0) 151
6.2.5 Rolling Friction 152
6.3 Equilibrium of Body on a Rough Inclined Plane 153
6.3.1 Motion Up the Plane 154Contents xxiii
6.3.2 Motion Down the Plane 154
6.3.3 Maximum Efficiency 155
6.4 Screw Friction 156
6.4.1 Square Thread 156
6.4.2 Relation Between Effort and Weight Lifted by a Screw Jack 157
6.4.3 V-Thread 158
6.4.4 Mechanical Advantage 158
6.5 Pivot and Collar Friction 159
6.5.1 Uniform Intensity of Pressure 161
6.5.2 Uniform Rate of Wear 162
6.6 Clutches 164
6.6.1 Single-plate Clutch 165
6.6.2 Multi-plate Clutch 165
6.6.3 Cone Clutch 166
6.7 Brakes and Dynamometers 168
6.7.1 Introduction 168
6.7.2 Types of Brakes 168
6.7.3 Dynamometers 176
6.7.4 Types of Frictions 178
6.8 Exercise 181
6.8.1 Short Answer Questions 181
6.8.2 Problems 182
6.8.3 Multiple Choice Questions 185 - Governors 187
7.1 Introduction 189
7.2 Centrifugal Governors 189
7.3 Various Parts and Terms Used in Governors 191
7.3.1 Height of the Governor (h) 191
7.3.2 Equilibrium Speed 191
7.3.3 Sleeve Lift 191
7.4 Simple Watt Governor 191
7.4.1 Analytical Method 192
7.4.2 Graphical Method 193
7.5 Porter Governor 194
7.5.1 Analytical Method 195
7.5.2 Graphical Method 197xxiv Contents
7.6 Proell Governor 197
7.6.1 Analytical Method 198
7.6.2 Graphical Method 199
7.6.3 Comparison between Flywheel and Governor 209
7.7 Hartnell Governor 209
7.8 Hartung Governor 213
7.9 Definitions 218
7.9.1 Sensitiveness 218
7.9.2 Stable and Unstable 218
7.9.3 Isochronous/Isochronism 218
7.9.4 Hunting 218
7.9.5 Effort 218
7.9.6 Power 218
7.9.7 Controlling Force 218
7.9.8 Coefficient of Insensitiveness 219
7.10 Wilson-Hartnell Governor 219
7.11 Exercise 221
7.11.1 Short Answer Questions 221
7.11.2 Problems 221
7.11.3 Multiple Choice Questions 223 - Belt, Rope and Chain Drives 225
8.1 Introduction 227
8.2 Types of Belts 227
8.2.1 Flat Belt 228
8.2.2 V-belt 228
8.2.3 Circular Belt or Rope 229
8.3 Types of Belt Drives 230
8.3.1 Compound Belt Drives 231
8.3.2 Stepped or Cone Pulley 232
8.4 Speed Ratio or Velocity Ratio of a Belt Drive 232
8.4.1 Velocity Ratio of a Compound Belt Drive 233
8.4.2 Slip of the Belt 234
8.4.3 Effect of Creep on Velocity Ratio 235
8.5 Length of an Open Belt 235
8.6 Length of a Crossed Belt 237
8.7 Ratio of Tensions 239Contents xxv
8.7.1 Power Transmitted by a Belt 241
8.7.2 Effect of Centrifugal Tension Tc on Power Transmitted 241
8.7.3 Condition for Maximum Power 242
8.7.4 Effect of Initial Tension (To) 243
8.8 Rope Drive 243
8.8.1 Ratio of Tensions 243
8.9 Chain Drives 245
8.9.1 Types of Chains 246
8.10 Exercise 248
8.10.1 Short Answer Questions 248
8.10.2 Problems 249
8.10.3 Multiple Choice Questions 251 - Gyroscope 255
9.1 Introduction 257
9.2 Gyroscopic Couple and its Effect 258
9.3 Effect of Gyroscopic Couple on an Aeroplane 259
9.4 Special Terms Used in Ships 263
9.4.1 Effect of Gyroscopic Couple on the Ship During Steering 264
9.4.2 Effect of Gyroscopic Couple on the Ship During Pitching 265
9.4.3 Effect of Gyroscopic Couple on the Ship During Rolling 266
9.5 Stability of Four-Wheeler 268
9.5.1 Effect of the Gyroscopic Couple 269
9.5.2 Effects of the Centrifugal Couple 270
9.6 Stability of a Two-wheeler 273
9.6.1 Effect of the Gyroscopic Couple 274
9.6.2 Effects of the Centrifugal Couple 275
9.7 Exercise 278
9.7.1 Short Answer Questions 278
9.7.2 Problems 279
9.7.3 Multiple Choice Questions 280 - Cams 283
10.1 Introduction 285
10.2 Classification of Followers 286
10.2.1 Based on the Surface in Contact 287xxvi Contents
10.2.2 Based on the Type of Movement of the Follower 287
10.2.3 Based on the Line of Motion of Follower 287
10.2.4 Based on the Desired Mathematical Motions 288
10.3 Types of Cams 288
10.3.1 Based on Follower Motion 288
10.3.2 Based on the Shape of the Cam 288
10.4 Terminology 289
10.4.1 Cam Profile 289
10.4.2 Base Circle 289
10.4.3 Trace Point 289
10.4.4 Pitch Curve 290
10.4.5 Prime Circle 290
10.4.6 Pressure Angle 290
10.4.7 Cam Angle 290
10.4.8 Pitch Point 290
10.4.9 Lift or Stroke(s) 290
10.4.10 Pitch Circle 291
10.5 Analysis of Motion of the Follower 291
10.5.1 Uniform Velocity 292
10.5.2 Simple Harmonic Motion (SHM) 294
10.5.3 Uniform Acceleration and Retardation 296
10.5.4 Cycloidal Motion 297
10.6 Construction of Displacement Diagrams 299
10.6.1 Displacement Diagram for Uniform Velocity 300
10.6.2 Displacement Diagram for Simple Harmonic Motion (SHM) 300
10.6.3 Displacement diagram for Uniform Acceleration and Retardation (UAR) 301
10.6.4 Displacement Diagram for Cycloidal Motion 302
10.7 Construction of Cam Profiles 303
10.7.1 Cam Profile with Radial Knife Edge Follower Having Outward Cycloidal
Motion and Return Uniform Velocity Motion 303
10.7.2 Cam Profile with a Radial Knife Edge Follower Having Outward SHM and
Return Uniform Acceleration and Retardation (UAR) 305
10.7.3 Cam Profile with an Offset Knife Edge Follower Having Outward SHM and
Return UAR 305
10.7.4 Cam Profile with the Radial Roller Follower with Outward Cycloidal Motion
and Return Uniform Velocity 306
10.7.5 Cam Profile with an Offset Roller Follower with Outward Cycloidal Motion
and Return with Uniform Velocity 308Contents xxvii
10.7.6 Cam Profile for Radial Flat Faced Radial Follower with Outward Cycloidal
Motion and Return Uniform Velocity 309
10.8 Cams with Specified Contours 312
10.8.1 Circular Arc Cam with Flat-faced Reciprocating Follower 312
10.8.2 Tangent Cam with Reciprocating Roller Follower 315
10.9 Exercise 318
10.9.1 Short Answer Questions 318
10.9.2 Problems 319
10.9.3 Multiple Choice Questions 320 - Toothed Gearing 323
11.1 Introduction 325
11.2 Classification of Toothed Gearing 325
11.2.1 According to Axes 325
11.2.2 According to the Range of Peripheral Velocity 326
11.2.3 According to Position of Teeth on the Gear Surface 326
11.2.4 According to Type of Gearing 327
11.2.5 According to Materials Used for Gears 328
11.3 Terminology Used in Gears 328
11.3.1 Pitch Circle 328
11.3.2 Addendum (a) 329
11.3.3 Addendum Circle 329
11.3.4 Dedendum (d) 330
11.3.5 Dedendum Circle 330
11.3.6 Clearance 330
11.3.7 Face 330
11.3.8 Flank 330
11.3.9 Face Width 331
11.3.10 Top Land 331
11.3.11 Tooth Profile 331
11.3.12 Circular Pitch (Pa) 331
11.3.13 Pitch Point (P) 331
11.3.14 Diametral Pitch (Pa) 331
11.3.15 Module (m) 331
11.3.16 Pressure Angle or Obliquity (p) 332
11.3.17 Path of Contact 332
11.3.18 Length of Path of Contact 332xxviii Contents
11.3.19 Arc of Contact 332
11.4 Condition for Constant Velocity Ratio or Law of Gearing 332
11.5 Length of the Arc of Contact 335
11.6 Minimum Number of Teeth on the Pinion to Avoid Interference 340
11.7 Interference in Involute Gears 344
11.8 Methods of Avoiding Interference 344
11.9 Forms of Teeth 344
11.9.1 Cycloidal Teeth 345
11.9.2 Involute Tooth 346
11.10 Helical Gears 346
11.11 Bevel Gears 347
11.12 Spiral Gears 348
11.13 Exercise 348
11.13.1 Short Answer Questions 348
11.13.2 Problems 349
11.13.3 Multiple Choice Questions 351 - Gear Trains 353
12.1 Introduction 355
12.2 Simple Gear Train or Simple Gear Drive 355
12.2.1 Speed Value or Speed Ratio or Velocity Ratio (VR) 356
12.2.2 Train Value 356
12.2.3 Power Transmitted by a Simple Gear Train 357
12.3 Compound Gear Train 358
12.4 Reverted Gear Train 359
12.5 Epicyclic Gear Train 362
12.6 Torque in Epicyclic Gear Trains 369
12.7 Compound Epicyclic Gear Train 371
12.8 Epicyclic Gear Trains with Bevel Gears 375
12.9 Exercise 380
12.9.1 Short Answer Questions 380
12.9.2 Problems 382
12.9.3 Multiple Choice Questions 386Contents xxix - Balancing of Rotating Masses 389
13.1 Introduction 391
13.2 Checking of a Rotating Element 391
13.3 Types of Balancing of Rotating Elements 392
13.3.1 Balancing of a Single Unbalanced Rotating Mass 392
13.3.2 Balancing of Several Unbalanced Rotating Masses 392
13.4 Balancing of a Single Unbalanced Rotating Mass 393
13.4.1 By a Single Balancing Mass Rotating in the Same Plane 393
13.4.2 By Two Balancing Masses in Two Different Planes 394
13.5 Balancing of Several Unbalanced Masses Rotating in the Same Plane 399
13.5.1 Analytical Method 400
13.5.2 Graphical Method 400
13.6 Balancing of Several Unbalanced Masses Rotating in Several Planes 402
13.7 Exercise 410
13.7.1 Short Answer Questions 410
13.7.2 Problems 410
13.7.3 Multiple Choice Questions 412 - Balancing of Reciprocating Masses 413
14.1 Introduction 415
14.2 Partial Balancing 416
14.3 Effect of Partial Balancing in Two-Cylinder Locomotives 417
14.3.1 Tractive Force (FT) 418
14.3.2 Swaying Couple 419
14.3.3 Hammer Blow 419
14.3.4 Types of Locomotives 420
14.4 Multi-cylinder In-line Engines 428
14.5 Radial Engines 434
14.5.1 Direct and Reverse Crank Method 435
14.5.2 Analytical Method 436
14.6 V-Engines 439
14.6.1 Analytical Method 440
14.6.2 Direct and Reverse Crank Method 441
14.7 Exercise 443
14.7.1 Short Answer Questions 443
14.7.2 Problems 443
14.7.3 Multiple Choice Questions 445xxx Contents - Longitudinal and Transverse Vibrations 447
15.1 Introduction 449
15.2 Basic Elements of Any Vibratory System 449
15.2.1 Inertial Element or Mass 449
15.2.2 Restoring Element or Spring 449
15.2.3 Damping Elements or Damper 450
15.3 Various Terms Used in Vibration and their Meanings 450
15.3.1 Period 450
15.3.2 Cycle 450
15.3.3 Frequency 450
15.3.4 Resonance 450
15.4 Types of Vibrations 450
15.4.1 Free or Natural Vibrations 450
15.4.2 Forced Vibrations 450
15.4.3 Damped Vibrations 450
15.5 Types of Vibrations Based on the Deflection 451
15.5.1 Longitudinal Vibrations 451
15.5.2 Transverse Vibrations 451
15.5.3 Torsional Vibrations 451
15.6 Natural Frequency of Free Longitudinal Vibrations 451
15.6.1 Equilibrium Method 452
15.6.2 Energy Method 453
15.6.3 Rayleigh’s Method 454
15.7 Natural Frequency of Free Transverse Vibrations 459
15.7.1 Energy (Rayleigh’s) Method of a Shaft Subjected to Number of Point Loads 464
15.7.2 Dunkerley’s Method for a Shaft Subjected to a Number of Point Loads 464
15.8 Critical Speed or Whirling Speed of a Shaft 468
15.9 Frequency of Free Damped Vibrations (Viscous Damping) 471
15.9.1 When the Roots are Real (Overdamping or Large Damping) 473
15.9.2 When the Roots are Equal (Critical Damping) 473
15.9.3 When the Roots are Complex Conjugate (Underdamping or Small Damping) 473
15.9.4 Logarithmic Decrement 474
15.10 Frequency of Forced Damped Vibration 476
15.10.1 Magnification Factor or Dynamic Magnifier (D) 478
15.11 Exercise 480
15.11.1 Short Answer Questions 480
15.11.2 Problems 481
15.11.3 Multiple Choice Questions 483Contents xxxi - Torsional Vibrations 485
16.1 Introduction 487
16.2 Natural Frequency of Free Torsional Vibrations 487
16.3 Torsional Vibrations of a Shaft with Number of Rotors 488
16.3.1 Free Torsional Vibrations of a Single Rotor System 488
16.3.2 Free Torsional Vibrations of a Two-Rotor System 490
16.3.3 Free Torsional Vibrations of a Three Rotor System 493
16.4 Torsionally Equivalent Shaft 499
16.5 Free Torsional Vibrations of a Geared System 505
16.6 Exercise 509
16.6.1 Short Answer Questions 509
16.6.2 Problems 509
16.6.3 Multiple Choice Questions 510
Bibliography 513
Index 515
Index
A
Accelerating force, 487
Acceleration, 51, 291, 415
Ackermann steering gear, 18, 35
Addendum, 329
Addendum circle, 329
Aeroplane, 259
Aft, 263
Air pump, 19
Angle of friction, 151
Angular acceleration, 40, 98, 259
Angular displacement, 32, 267, 487
Angular velocity, 13, 98, 415
Anti-friction bearing, 178
Approximate straight line mechanism, 31
Arc of approach, 332
Arc of contact, 332
Arc of recess, 332
B
Balancing, 391, 416
Band and block brake, 168, 174
Band brake, 168, 170
Beam engine, 18
Bed plate, 3
Belts, 152, 227
Bevel gears, 347
Binary, 4
Block or shoe brake, 168
Bow, 265
Brakes, 168
Bull engine, 14
C
Cam angle, 290
Cam profile, 289
Cams, 285, 288
Centre of mass, 93, 391
Centrifugal couple, 270
Centrifugal governor, 189
Centrifugal tension, 241
Centroid, 93
Chain, 4, 29, 227
Circular arc cam, 312
Circular belt, 229
Circular pitch, 331
Clearance, 330
Clutches, 164
Coefficient of fluctuation of speed, 131, 215
Collar bearing, 162
Complex conjugates, 473
Compound belt drive, 231
Compound gear train, 358
Compound mechanism, 12, 23
Cone clutch, 166
Cone pulley, 232
Connecting rod, 12, 96, 415
Constraint, 5, 286, 509
Contact ratio, 337
Coriolis component, 78
Couple, 419, 488
Coupled, 420
Coupling rod, 18
Crank-pin, 116, 421
Crankshaft, 3,127, 416
Creep , 235
Critical damping, 473
Critical speed, 468
Cross belt drive, 230
Cross head, 4, 105, 415
Cycle, 450
Cycloidal gears, 344
Cycloidal motion, 288, 309
Cylinder head, 3
D
D-Alembert’s principle, 94
Damped vibrations, 450
Damper, 450516 Index
Four-bar mechanism, 11, 121
Free vibrations, 450
Frequency, 450
Friction, 5, 149
Friction circle, 180
Davis steering gear, 34
Dedendum, 330
Dedendum circle, 330
Degrees of freedom, 11, 264
Design of flywheel, 132
Diametral pitch, 331
Differential band brake, 170
Direct crank method, 435
Displacement diagram, 299, 309
Double hooke’s joint, 41
Double slider crank chain, 15
Dry surfaces, 151
Dunkerlay’s method, 464
Dynamic friction, 150
Dynamic magnifier, 478
Dynamically equivalent system, 111
Dynamics, 3, 93
Dynamometers, 168, 176
E
Effort, 218
Element, 3, 209, 415
Ellipse trammel, 15
Energy method, 453
Energy stored, 131
Epi-cyclic gear train, 362, 369
Equal roots, 473
Equilibrium method, 452
Equilibrium of body, 153
Equilibrium speed, 191
External gearing, 327
G
Gear train, 355
Geared system, 488, 505
Governor, 189
Grass hopper mechanism, 32
Greasy friction, 180
Gyroscope, 259
Gyroscopic couple, 258, 259
H
Hammer blow, 419
Hart mechanism, 30
Hartnell governor, 209
Hartung governor, 213
Height of governor, 193
Helical gears, 346
High velocity, 326
Higher pairs, 5, 20
Hooke’s joint, 36, 41
Hunting, 218
Hydraulic brakes, 4
Hydraulic jacks, 4
F
Face, 330
Face width, 331
Flank, 330
Flat belt, 228
Flat faced, 309
Fluctuation of energy, 129
Fluids, 4
Flywheel, 3, 127, 488
Followers, 286, 358
Foot step bearing, 10
Forced closed pair, 10
Forced vibration, 476
Fore-end, 263
Four stroke cycle internal combustion engine,
I
Idlers, 356
Indexing mechanism, 11
Inertia force, 113, 416
Inertial element, 449
Initial tension, 243
Instantaneous centre method, 53, 100
Interference, 340
Internal brake, 168
Internal expanding shoe brake, 176
Internal gearing, 327
Intersecting axes, 326
Inversion, 12, 27, 86
Inverted chain, 247
128 Involute gears, 344Index 517
Inward, 319
Isochronism, 218
Isochronous, 218
K
Kennedy’s theorem, 56
Kinematic chain, 7, 11
Kinematic link, 3, 56
Kinematic pair, 5, 7, 23
Kinematics, 3, 53
Kinetic energy, 505
Kliens construction, 100
Knife edge, 287
L
Large damping, 473
Law of gearing, 333
Laws of friction, 150
Left turn, 261
Length of a crossed belt, 237
Length of an open belt, 235
Length of path of contact, 332
Length of the arc of contact, 335
Lift, 290
Linear velocity, 53, 259
Link, 3,121, 245
Locomotives, 420
Logarithamic decrement, 474
Longitudinal vibration, 451
Low velocity, 326
Lower pairs, 6, 27
M
Machine, 3,141,443
Magnification factor, 478
Main bearings, 3
Mass, 93, 242, 415
Matter, 93
Maximum efficiency, 155
Maximum power, 242
Mechanical advantage, 158
Mechanism, 3, 248, 415
Medium velocity, 326
Minimum number of teeth, 340
Modified uniform velocity, 293
Module, 331
Motion, 3, 149, 488
Multi plate clutch, 165
Multi-cylinder in-line engines, 428
N
Natural frequency , 451
Natural vibrations, 450
Non-intersecting and non-parallel, 326
0
Offset, 287
Oldham coupling, 16
Open belt drive, 230
Oscillating mechanism, 11
Outward, 291
Over damping, 473
P
Pairs, 4, 166, 337
Pantograph, 27
Parallel axes, 326
Partial balancing, 416
Peaucellier mechanism, 29
Pendulum engine, 14
Period, 450
Piston, 3, 176, 428
Piston rod, 3, 84,105
Pitch circle, 290
Pitch curve, 290
Pitch point, 290
Pitching, 264
Pivot bearing, 162
Port side, 265
Porter governor, 194
Power, 218
Power transmitted, 241
Pressure angle, 290
Pressure angle, 332
Primary forces, 416, 429
Prime circle, 290
Proell governor, 197
Proney brake, 176
Punching press, 17518 Index
Q
Quarternary, 4
Quick return mechanism, 12, 22
R
Rack and pinion, 327
Radial engines, 434
Radial follower, 287, 309
Radian, 52
Ratio of tensions, 239
Rayleigh’s method, 454
Real roots, 473
Reciprocating mass, 415
Reciprocating mechanism, 10, 95, 415
Reference plane, 403, 423
Relative velocity method, 51, 99
Resonance, 450
Restoring element, 449
Restoring force, 487
Reverse crank method, 435
Reverted gear train, 359
Right hand screw rule, 53, 259
Right turn, 261
Rigid, 3, 245, 489
Rigid frame, 8
Roborts mechanism, 33
Roller chain, 246
Rolling, 264, 345
Rolling friction, 150-152, 178
Rolling pair, 5, 9, 22
Rope, 4, 227, 355
Rope brake dynamometer, 177
Rotary internal combustion, 14
Rotary motion, 6, 51, 325
Rotating masses, 392, 416
Rough surfaces, 151
S
Scotch yoke mechanism, 16
Screw friction, 156
Screw pair, 5, 22
Secondary forces, 429
Self closed pair, 10
Sensitiveness, 218
Several masses, 393
Shaping machine, 13, 49
Silent chain, 247
Simple band brake, 172
Simple gear train, 355, 357
Simple harmonic motion (SHM), 288
Simple mechanism, 3, 12
Simple watt governor, 191
Single cylinder double acting steam engine, 127
Single mass, 410
Single plate clutch, 165
Single rotor system, 488
Single slider crank chain, 16
Sleeve lift, 191
Sliding friction, 150
Sliding pair, 5, 27
Slip, 234
Slotting machine, 12
Small damping, 473
Specified contour, 312
Speed, 17, 93, 416
Speed ratio, 232
Speed value, 356
Spherical pair, 5
Spiral gears, 348
Spring, 449
Square thread, 156
Stability, 219, 268
Stable, 218
Star board, 264
Static, 3, 151, 420
Static friction, 149
Steering gear mechanism, 33
Stepped pulley, 232
Stern, 263
Straight line motion, 27
Strain energy, 505
Stroke, 290
Swaying couple, 419
T
Tabular method, 364
Tangent cam, 315
Tchebicheff straight line motion, 32
Tensile force, 4
Ternary, 4
Three rotor system, 493
Three-centres-in-line theorem, 56
Tooth profile, 331
Toothed gearing, 325Index 519
Top land, 331
Torque, 369, 420
Torsional vibrations, 451
Torsionally equivalent shaft, 499
Tractive force, 418
Train value, 356
Transformation, 11
Translatory motion, 51
Transverse vibrations, 449
Turning moment diagram, 127
Turning pair, 4, 28
Two cylinder locomotives, 417
Two rotor system, 490
Two way brand brake, 172
Types of frictions, 178
U
Uncoupled, 420
Under damping , 473
Uniform acceleration and retardation,
Uniform pressure, 163
Uniform velocity, 153, 288
Uniform wear, 163
Universal joint, 36, 43
Unstable, 218
V
V-belt, 228
Velocity – 13, 134, 291
Velocity of sliding, 334
Velocity ratio, 232
Velocity ratio, 325
V-Engines, 439
Viscous damping, 471
V-thread, 158
w
Watt mechanism, 31
Weight, 93, 315, 510
Weight lifting jack, 19
288 Whirling speed, 468
Work, 3, 241, 435
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