A Text Book of Theory of Machines

A Text Book of Theory of Machines
(In S.I. Units)
[For Degree, U.P.S.C. (Engg. Services), A.M.I.E. (India)]
Dr. J.S. BRAR
B.E., M.E., Ph.D. ([IT, Delhi)
Head Department of Mechanical Engineering
Delhi College of Engineering, Delhi.
By
Dr. R.K. BANSAL
B.Sc. Engg. (Mech.), M. Tech., Hons. (I.I.T., Delhi)
Ph.D., M.I.E. (India)
Department of Mechanical Engineering
Delhi College of Engineering, Delhi
Chapters
�duction
1.1. Definition
1.2. Mechanism and Machine
1.3. Link
1.4. Kinematic Pair
1.5. Degrees ofFreedom
1.6. Kinematic Chain
Solved Problems 1.1-1.5
Contents
1.7. Binary, Ternary, Quaternary Joints
1.8. Binary, Ternary and Quaternary Links
1.9. Degrees ofFreedom for Plane Mechanism
1.10. Inversion ofMechanism
1.11. Different Types ofKinematic Chains and Their Inversions
1.11.1. Four Bar Chains
1.11.2. Single-Slider Crank MechanisIJ?,
1.11.3. Double-Slider Crank Chain
Solved Problems 1.6-1.15
Highlights
Exercise–1
on ofInertia
2.1. Introduction
2.2. Displacement
2.3. Velocity
2.4. Acceleration
2.5. Acceleration ofa Particle Moving along a Circular Path
2.6. Angular Displacement
2.7. Angular Velocity
2.8. Angular Acceleration
2.9. Force, Mass and Weight
2.10. Centripetal and Centrifugal Force
2.11. Mass Moment oflnertia
2.12. Angular Momentum
2.13. Torque
2.14. Work
2.15. Power
2.16. Energy
2.16.1. Potential Energy
2.16.2. Strain Energy
2.16.3. Kinetic Energy
Solved Problems 2.1-2.16
2.17. Law ofConservation ofEnergy
2.18. Impulse and Impulsive Force
2.19. Law ofConservation ofMomentum
2.20. Impact ofTwo Bodies
Pages
Chapters
2.20.1. Co-efficient ofRestitution
Solved Problems 2.17-2.20
(x)
2.20.2. Loss ofKinetic Energy during Impact
Solved Problems 2.21-2.25
2.21. Simple Harmonic Motion
2.21.1. Definitions ofsome terms used with S.H.M.
Solved Problems 2.26-2.28
2.21.2. Oscillation ofthe bodies having S.H.M.
Solved Problems 2.29-2.30
2.21.3. OsciHation ofa Simple Pendulum
Solved Problems 2.31-2.35
Highlights
Exercise-2
ity of Points in Mechanism
3.1. Introduction
(A) INSTANTANEOUS CENTRE METHOD
3.2. Instantaneous Centre Method
Solved Problem 3.1
3.3. Analysis ofReciprocating Engine Mechanism
by Instantaneous Centre Method
Solved Problems 3.2-3.3
3.4. Analysis ofFour Bar Mechanism by Instantaneous Centre Method
Solved Problems 3.4-3.5
3.5. Number and Types oflnstantaneous Centres in a Mechanism
3.6. Method for Locating an Instantaneous Centre
3.7. Kennedy Theorem (or Three Centres-in-line Theorem)
3.8. Procedure of Locating Instantaneous Centres
Solved Problems 3.6-3.7
(B) RELATIVE VELOCITY METHOD
3.9. Relative Velocity Method
3.9.1. Relative Velocity oftwo bodies moving in straight lines
3.9.2. Relative Velocity ofa rigid link
3.10. Velocities in Four Bar Chain
3.11. Velocities in Slider Crank Mechanism
Solved Problems 3.8-3.9
3.12. Rubbing Velocity at a Pin-Joint
Solved Problems 3.10-3.15
3.13. Forces Acting in a Mechanism
3.14. Mechanical Advantage
/ Solved Highlights Problems 3.16-3.17
,./Acceleration in Mechanism
J ·4.1. Introduction
4.2. Acceleration ofa Body Moving along a Circular Path
4.3. Acceleration Diagram for a Link
4.4. Acceleration Diagram for a Slider Crank Mechanism
Solved Problems 4.1-4.5
4.5. Coriolis Acceleration Component
Solved Problems 4.6-4.11
Pages
143
148(xi)
Chapters
Highlights
/ Exercise-4
� Mechanism with Lower Pairs
5.1. Introduction
5.2. Pantograph
5.3. Straight Line Mechanism
5.4. Exact Straight Line Motion Mechanisms
Solved Problem 5.1
Approximate Straight Line Motion Mechanism
5.5.1. Watt’s Straight Line Mechanism
5.5.2. Modified Scott-Russel Mechanism
5.5.3. Gross-Hopper Mechanism
5.5.4. Tehebichetrs Mechanism
5.5.5. Robert’s Mechanism
Solved Problems 5.2-5.3
Application ofStraight Line Motion in Engine Indicators
5.6.1. Simplex Indicator
Solved Problems 5.4
5.6.2. Crosby Indicator
5.6.3. Thomson Indicator
5.6.4. Double Mclnnes Indicator
Steering Gears
5.7.1. Davis Steering Gear
Solved Problem 5.5
5.7.2. Ackermann Steering Gear
Universal or Hooke’s Joint
5.8.1. Analysis of Hooke’s Joint
5.8.2. Ratio ofAngular Velocities ofthe shafts
5.8.3. Conditions for equal speeds ofdriven and ring shafts
5.8.4. Maximum and Minimum speeds ofdriven shaft
Solved Problems 5.6-5.10
Double Hooke’s Joint
Solved Problem 5.11
Highlights
Exercise-5
�ction
6.1. Introduction
6.2. Definitions
6.2.1. Co-efficient offriction
6.2.2. Angle offriction
6.2.3. Cone of friction
6.3. Types of Friction
6.3.1. Dry friction
6.3.2. Greasy friction
6.3.3. Film friction
6.4. Law:s of Dry Friction
Solved Problems 6.1-6.6
Pages
213(xii)
Angle of Repose
Chapters
6.5.
6.6. Equilibrium ofa Body lying on a Rough Inclined Plane
Solved Problems 6.7-6.11
6.7.
6.8.
6.9.
Screw Threads Friction
Screw-Jack
Solved Problems 6.12-6.17
V-Threads Friction
Solved Problem 6.18
Pivot and Collar Bearing
6.10.1. Flat pivot
Solved Problem 6.19
6.10.2. Conical pivot
6.10.3. Truncated conical pivot
Solved Problems 6.20-6.21
L6.10.4. Friction Clutches Solved Flat collar Problems 6.22-6.23
6.11.1. Disc clutch or single plate clutch
Solved Problems 6.24-6.30
6.11.2. Multi plate clutch
Solved Problems 6.31-6.33
6.11.3. Cone clutch
‘ Solved Problems 6.34-6.35
6.12. Greasy Friction
6.12.1. Greasy friction ofa journal
6.12.2. Greasy friction ofa slider-crank mechanism
6.13. Film Friction or Viscous Friction
Highlights
Exercise-6

7. .n’e1ts, Ropes and Chain Drives
   V7.1. Introduction
   7.2. Open Flat Belt Drive
   7.2.1. Velocity Ratio of Open Belt Drive
   Solved Problems 7.1-7.2
   7.2.2. Slip of the Belt
   7.2.3. Creep ofthe Belt
   Solved Problems 7.3-7.5
   7.3. Cross Belt Drive
   7.4. Compound Belt Drive
   Solved Problem 7.6
   7.5. Length of Belt
   7.5.1. Length ofan Open Belt Drive
   7.5.2. Length ofa Cross-Belt Drive
   Solved Problems 7.7-7.8
   7.6. Ratio of Belt Tensions
   7.7. Power Transmitted by Belt
   Solved Problems 7.9-7.10
   Pages
   304(xiii)
   Centrifugal Tension
   Chapters
   7.8.
   7.9. Maximum Power Transmitted by a B�lt
   Solved Problems 7.11-7.14
   7.10. Initial Tension in the Belt
   Solved Problems 7.15-7.17
   7.11. V-Belt Drive and Rope-Drive
   Solved Problems 7.18-7.23
   7.12. Chain Drive
   7.13. Relative Advantages and Disadvantages ofChain and Belt
   (or Rope) Drives
   Highlights
   Exercise-7
8. �es and Dynamometers
   ../”‘”8.1. Introduction 8.2. Types ofBrakes 8.2.1. Simple Block or Shoe Brake Solved Problems 8.1-8.5 8.2.2. Band Brake Solved Problems 8.6-8.11 8.2.3. Band and Block Brake Solved Problems 8.12-8.13 8.2.4. Internal Expanding Shoe Brake Solved Problem 8.14 8.3. The Braking ofa Vehicle Solved Problems 8.15-8.16 8.4. Dynamometer 8.5. Absorption Dynamometer 8.5.1. Prony_Brake Dynanometer 8.5.2. Rope Brake Dynamometer Solved Problem 8.17 8.6. Transmission Dynamometer 8.6.1. Epi-cyclic Train Dynamometer 8.6.2. Belt Transmission Dynamometer Solved Problem 8.18 8.6.3. Torsion Dynamometer Highlights / Exercise-8 !)/Gears 9.1. Introduction 9.2. Classification ofGears 9.3. Definition ofthe terms used in Gears Solved Problems 9.1-9.2 9.4. Law ofGearing or Condition for Constant Velocity Ratio ofGear Wheels. 9.5. Velocity ofSliding 9.6. Forms ofTeeth 9.7. Cycloidal Profile Teeth 9.7.1. Formation ofa Cycloid Rack Tooth Profile 405Chapters (xiv) 9.7.2. Formation ofa Cycloid Teeth ofaGear 9.7.3. Involute Profile Teeth 9.7.4. InvoluteGear Teeth 9.7.5. Important Points for Involute Profile ToothedGears in Mesh 9.7.6. System ofGear Teeth 9.8. Length ofPath ofContact 9.9. Length ofArc ofContact 9.10. Number ofPairs ofTeeth in Contact (or Contact ratio) Solved Problems 9.3-9.5 9.11. Interference in InvoluteGears Solved Problems 9.6-9..8 9.12. The Minimum Number ofTeeth required on the Pinion in Order to Avoid Interference 9.13. The Minimum Number ofTeeth required on the Wheel in order to avoid Interference Solved Problems 9.9-9.11 9.14. Interference between Rack and Pinion and Minimum Number ofTeeth on a Pinion for Involute Rack in order to avoid Interference Solved Problem 9.12 9.15. HelicalGears 9.16. Important Terms for HelicalGears 9.17. SpiralGears 9.18. The Efficiency ofthe SpiralGears Solved Problems 9.13-9.15 Highlights Exercise-9 Introduction Types ofGear Trains 10.2.1. Simple Gear Train 10.2.2. CompoundGear Train 10.2.3. Reverted Gear Train 10.2.4. EpicyclicGear Train 10.3. Velocity Ratio ofGear Trains 10.3.1. Velocity Ratio ofa SimpleGear Train Solved Problems 10.1-10.4 10.3.2. Velocity Ratio ofa CompoundGear Train Solved Problems 10.5-10.6 10.3.3. Velocity Ratio ofRevertedGear Train 10.3.4. Velocity Ratio ofEpicyclicGear Train Solved Problems 10.7-10.12 10.4. Sun and PlanetGear Solved Problems 10.13-10.15 10.5. Torques and Tooth Loads in EpicyclicGear Train Solved Problems 10.16–10.18 10.6. Compound EpicyclicGear Train Solved Problem 10.19 Pages Chapters ✓- 10.7. Epicyclic Gear Train with Bevel Gear Solved Problems 10.20-10.25 Highlights / Exercise-IO Inertia Forces in Reciprocating Parts 1 1. 1. Introduction 1 1.2. D-Alembert’s Principle 1 1’.3. Effect of a Number of Forces Acting on a Rigid Body Solved Problems 1 1 . 1-11.2 1 1.4. Velocity and Acceleration of the Piston 11.4. 1. Analytical method 11.4.2. Angular velocity and angular acceleration ofconnecting rod Solved Problems 1 1.3-1 1.7 11.4.3. Graphical method for velocity and acceleration of reciprocating parts Solved Problems 1 1.8-11 . 10 11 .5. Torque Exerted on the Crank-shaft when Friction and Inertia of Moving Parts are Neglected Solved Problem 1 1. 1 1 1 1.6. Forces on the Reciprocating Parts of an Engine Considering Friction and Inertia ofMoving Parts but Neglecting Weight ofthe Connecting Rod 1 1.6.1 . Piston effort 1 1.6.2. Force acting along the connecting rod 1 1.6.3. Thurst on the sides ofcylinder walls 1 1.6.4. Cank effort 1 1.6.5. Thurst on crank-shaft bearing 1 1.7. Torc;,ue on the Crank-shaft or Turning Moment on Crank-Shaft Solved Problems 11. 12-11.19 1 1.8. Dynamically Equivalent System Solved Problems 11.20-11.22 1 1.9. Magnitude of Correction Couple Applied to Two Mass System which is Dynamically Equivalent to Rigid Body Solved Problem 11.23 1 1. 10. Torque Exerted on the Crank-shaft, Considering the Weight of the Connectin.g Rod Solved Problems 1 1.24-1 1.28 Highlights Exercise–1 1 1 9 �ing Moment Diagrams ¼;.u Introduction 12.2. Turning Moment Diagrams for Different Types of Engines 12.3. Fluctuation ofEnergy and Fluctuation ofSpeed ofCrank-shaft 12.4. Co-efficient of Fluctuation of Energy (Ke) 12.5. Co-efficient of Fluctuation ofSpeed (K5) 12.6. Flywheels Solved Problems 12. 1-12.12 Pages Chapters 12.7. Flywheel’s Rim Dimensions Solved Problems 12.13-12.14 12.8. Operation of a Flywheel in a Punching Press Solved Problems 12.15-12.19 Highlights _ / Exercise-12
   �-a�ancing ofRotatingMasses
   13.1. Introduction
   13.2. Balancing of Rotating Masses
   13.2.1. Balancing ofa Single Rotating Mass
   Solved Problem 13.1
   13.2.2. Balancing ofSeveral Masses Rotating in the same plane
   Solved Problem 13.2
   13.2.3. Balancing ofSeveral Masses Rotating in different planes
   Solved Problems 13.3-13.9
   Highlights
   / Exercise-13
   �alancing ofReciprocating Masses
   14.1. Introduction
   14.2. Balancing ofReciprocating Engine
   14.3. Partial Balancing of Primary Force
   Solved Problem 14.1
   14.4. Partial Balancing of Locomotives
   14.5. Effect ofPartial Balancing ofLocomotives
   14.5.1. Variation ofTractive Force (or Effort)
   14.5.2. Swaying Couple
   14.5.3. Hammer Blow
   Solved Problems 14.2-14.5
   14.6. Coupled Locomotives
   Solved Problem 14.6
   14.7. Primary Balance ofMulti-cylinder In-line Engines
   14.8. Secondary Balance of Multi-cylinder In-line Engines
   Solved Problems 14.7-14.10
   14.9. Method ofDirect and Reverse Cranks
   Solved Problems 14.11-14.12
   14.10. V-Engines Balancing
   Solved Problem 14.13
   Highlights
   Exercise-14
   Introduction
   15.2. Types ofGovernors
   15.3. Types ofCentrifugal Governors
   15.4. Watt Governor
   Solved Problems 15.1-15.2
   15.5. Porter Governor
   Solved Problems 15.3-15.7
   Pages
   768Chapters
   15.6. ProellGovernor
   Solved Problems 15.8-15.9
   15.7. BartnellGovernor
   Solved Problems 15.10-15.13
   15.8. Wilson-HartnellGovernor
   Solved Problems 15.14-15.15
   15.9. Some Important Definitions
   15.9.1. Sensitiveness
   15.9.2. Stability
   15.9.3. Isochronism
   15.9.4. Hunting
   15.10. Governor Effort and Power
   Solved Problem 15.16
   15.11. Controlling Force
   Solved Problems 15.17-15.18
   15.12. Friction and Insensitiveness
   Solved Problems 15.19-15.21
   Highlights
   Exercise-15
   (xvii )
   fbrations (Longitudinal and Transverse)
   16.1. Introduction
   16.2. Types ofVibration
   16.3. Important Definitions for Vibrating Motion
   16.4. Free Vibrations
   16.5. Methods of Finding the Natural Frequency of Free
   Longitudinal Vibrations
   16.5.1. Equilibrium method
   16.5.2. Energy method
   16.5.3. Rayleigh’s method
   16.6. Method for Natural Frequency of Free Transverse Vibrations
   Solved Problem 16.1
   16.7. Effect ofthe Inertia of Shaft on Longitudinal and Transverse Vibrations
   16.8. Natural Frequency ofTransverse Vibrations ofShafts or Beams
   under Different Types of Loads and End Conditions
   16.8.1. Natural frequency ofa shaft carrying a single concentrated load
   Solved Problems 16.2-16.3
   16.8.2. Natural frequency ofa shaft carrying a uniformly distributed load …
   16.9. Natural Frequency ofTransverse Vibrations ofa System
   of Several Loads attached to the Same Shaft
   16.9.1. Energy method
   16.9.2. Dunkerley’s method
   Solved Problems 16.4-16.5
   16.10. Whirling Speeds or Critical Speeds
   Solved Problems 16.6-16.8
   16.11. Damped Vibrations
   16.11.1. Expression for displecement for over-damped, under-damped
   and critical-damped system
   Solved Problems 16.9-16.11
   Pages
   Chapters
   1 6.12. Logarithmic Decrement
   Solved Problems 16.12-16.16
   1 6.13. Forced-Damped Vibrations
   16.14. Magnification Factor
   Solved Problems 16.17-16.20
   1 6.15. Vibration Isolation and Transmissibility
   Solved Problems 16.21-16.22
   Highlights
   Exercise-16
   �orsional Vibrations
   17.1. Introduction
   17.2. Natural Frequency ofFree Torsional Vibrations
   Solved Problem 17.1
   17.3. Effect ofInertia ofShaft on Torsional Vibrations
   17.4. Free Torsional Vibrations ofa Single Rotor System
   17.5. Free Torsional Vibrations ofa Two Rotor System
9. 6. Free Torsional Vibrations ofa Three Rotor System
   17.7. Torsionally Equivalent Shaft
   ms
   Solved Problems 17.2-17.6
   Free Torsional Vibrations ofa Geared System
   Solved Problems 17.7-17.9
   Highlights
   Exercise-17
   18.1. Introduction
   18.2. Types ofFollowers
   18.3. Nomenclatures for Cam Profile
   18.4. Motions ofthe Follower
   18.5. Uniform Motion or UniformVelocity ofa Follower
   18.6. Simple Harmonic Motion ofFollower
   18.7. Uniform Acceleration and Uniform Retardation
   18.8. Cycloidal Motion
   18.9. Cam Profile Construction
   Solved Problems 18.1-18.4
   18.10. Cam Profile for Roller Followers
   Solved Problems 18.5-18.10
   18.11. Cams with Specified Contours
   18.12. Circular Arc Cam with Flat-faced Follower
   Solved Problems 18.11-18.12
   18.13. Tangent Cam with Roller-follower
   Solved Problem 18.13
   Highlights
   Exercise-18
10. Computer-Aided Analysis ofMechanisms
    19.1. Introduction
    19.2. Coupler Curve
    19.3. Coupler Curve for Slider Crank Chain
    Pages
    Chapters
    19.3.1. Computer programme for coupler curve in FORTRAN
    19.3.2. Computer programme for coupler curve for
    reciprocating engine mechanism in C++
    Problem 19.1
    19.4. Coupler Curve for Four Bar Kinematic Chain
    19.4.1. Computer programme for coupler curve in FORTRAN
    19.4.2. Computer programme for coupler curve for four bar
    kinematic chain in C++
    Problem 19.2
    19.5. Computer-Aided Analysis ofMechanism
    19.6. Computer-Aided Analysis ofSlider Crank Mechanism
    19.6.1. Expression for displacement
    19.6.2. Expression for velocity
    19.6.3. Expression for acceleration
    19.7. Computer Programme for a Slider Crank Mechanism in FORTRAN
    19.7.1. Computer programme for a slider crank mechanism in C++
    Problem 19.3
    19.8. Computer Aided Analysis ofFour Bar Kinematic Chain
    19.8.1. Expression for displacement
    19.8.2. Expression for velocity
    19.8.3. Expression for acceleration
    19.9. Computer Programme for a Four Bar Kinematic Chain
    Problem 19.4
    \ ~ /Exercise-19 1
    �thesis of M;echanism
    20.1. Introduction
    20.1.1. Number synthesis
    20.2. Degrees ofFreedom ofa Planar Kinematic Chain (Griibler Criterion)
    20.2.1. Minimum number ofbinary links in a constrained mechanism
    with simple hinges
    20.2.2. Fully constrained motion ofa kinematic chain
    20.3. Dimensional Synthesi3
    20.3.1. Graphical method
    20.3.2. Analytical method
    Problems 20.1-20.2
    20.4. Mechanisms for Position Guidance
    20.5. Summary
    Highlights
    Exercise-20
    �yroscopic Effects and Gyroscope
    21.1. Introduction
    21.2. Spinning and Precession
    21.3. Gyroscopic Couple
    Problems 21.1-21.5
    2:J..4. Effect ofGyroscopic Couple on the Stability ofAutomotive Vehicles
    21.4.1. Stability offour wheelers
    Problems 21.6-21.9
    Pages
    Chapters
    21.4.2. Stability of two wheelers
    Problem 21.10
    21.5. Gyroscopic Effects on Ships and Aeroplanes
    21.5.1. Gyroscopic effects on Ships
    21.5.2. Gyroscopic effects on aeroplanes
    21.6. Gyroscopic Analysis of Grinding Mill
    21.7. Gyroscope
    Problems 21.11-21.13
    Exercise-21
    Objective Type Questions
    Index
    Pages
    1066
    1068
    1069
    1069
    1070
    1070
    1072
    1072
    1077
    … 1079-1126
    … 1127-1131 ·Subject Index
    A _
    Absorption dynamometers, 378
    Acceleration, 33
    Acceleration diagram for a link, 129

• for a slider crank mechanism, 130
  Ackerman steering gear, 192
  Addendum, 399
  Addendum circle, 399
  Angle of friction, 210
• repose, 217
  Angular displacement, 35
  Angular momentum, 39
  Angular velocity, 35
  Angular acceleration, 35
  Arc of contact ofa gear, 410
  length of, 409
• recess of a gear, 409
  B
  Balancing of rotating masses, 658
  Balancing of reciprocating masses, 704
  Band brake, simple, 340
• and block brake, 357
  Belt drive, 284
• velocity ratio of, 285
• transmission dynamometers, 381
  Bennett’s construction, 547
  Bevel gears, 397
  Bevis-Gibson flash light torsion dynamometer, 385
  Binary joint, 8
  Binary link, 9
  Brakes, 331
  Braking of a vehicle, 370
  c
  Cams, 928
  Cam profile construction, 944
  Cam profile for roller followers, 954
  Cams with specified contours, 968
  Centrifugal force, 39
• governors, 759
• tension, 305
  Chain drives, 284, 326
  Circular arc cam with a flat-faced follower, 968
• pitch, 399
  Clearance, 400
  Co-efficient of fluctuation of energy, 611
  friction, 210
• speed, 612
• restitution, 56
  Compound belt drive, 292
  Compound gear train, 451
  Compound epicyclic gear train, 497
  Completely constrained motion, 7
  Computer-Aided analysis of Mechanism, 992
  Cone of friction, 211
  Cone clutch, 267
  Conical pivot, 242
  Construction of cam profiles, 944
  Controlling force, 808
  Coriolis acceleration, 143
  Coupled locomotives, 724
  Coupler curve, 992
• for four bar mechanism, 993
• for slider crank mechanism 992
  Crank and lever mechanism, 12
  Crank effort, 555
  Creep ofbelt, 289
  Critical damping, 855
  Critical speed, 849
  Cross-belt drive, 291
• length of, 296
  Cross by indicator, 185
  Cycloidal motion, 941
  Cycloidal teeth, 404
  D _
  D’Alembert’s principle, 523
  Damped vibrations, 858
  Damping factor or ratio, 857
  Davis steering gear, 189
  Dedendum, 399
  Dedendum circle, 399
  Degrees offreedom, 4
• of a planer kinematic chain, 1003
  Design of spur gears, 434
  Diametral pitch, 399
  Differential equation of simple harmonic
  motion, 67
  Differential band brake, 348
  Differential gear of an automobile, 511
  Dimensions of the flywheel rim, 639
  1 1271 128
  Dimensional synthesis, 1006
• Analytical method, 1011
• Graphical method, 1006
  Direct cranks, 741
  Disc clutches, 253
  Displacement, 33
  Displacement, velocity and acceleration diagrams
  when follower moves with uniform velocity, 931
  with simple harmonic motion, 934
  with uniform acceleration and retardation, 937
  with cycloidal motion, 941
  Double block or shoe brake, 340
  crank mechanism, 18
  Hooke’s joint, 205
  lever mechanism, 18
  slider crank chain, 18
  Dry friction, 213
  Dunkerley’s method, 846
  Dynamics, 1
  Dynamometers, 331, 378
  Dynamometer, 378
  absorption type, 378
• transmission type, 381
  E _
  Effect ofgyroscopic couple
• on automotive vehicles, 1030
• on ships and aeroplane, 1054
  Efficiency screw jack, 231
  Efficiency of spiral gears, 436
  Effort of a governor, 804
  Elliptical trammel, 18
  Energy, 43
  Energy Method, 833, 845
  Epicyclic gear train, 452
• torques in, 485
• train dynamometer, 381
  Epicyclic gear train with Bevel Gear, 501
  Equivalent dynamical system, 572
  Exact straight line motion mechanisms made up
  of turning pairs, 171
• consiating of one sliding pain, 176
  F _
  Face of the tooth, 399
  Film friction, 212
  Flank ofthe tooth, 400
  Flash light torsion dynamometer, 386
  Flat belt, 3 16
• collar, 248
• pivot, 238
  Fluctuation of energy, 610
• speed, 610
  Flywheel, 613
• energy stored in, 613
  THEORY OF MACHINES
  rim dimensions of, 639
  in punching press, 645
  Force, 39
• acting along a connecting rod, 549
• on reciprocating parts of an engine, 548
  Forced vibrations, 869
  Forms of teeth, 404
  Four bar chain, 11
  Free vibrations, 830
• types of, 829
  Frequency, 826
  Free torsional vibrations ofsinglerotorsystem, 897
  oftwo rotor system, 898
• of three rotor system, 900
• of geared system, 914
  Friction ofpivot and collar bearing, 239
  Friction circle, 276
  Friction clutches, 255
  Friction wheels, 394
  G
  Gears, 394
  Gear ratio, 400
  Gear train, 450
  simple, 450
  compound, 450
  Reverted, 451
  Epicylic, 451
  Governors, 758
  Hartnell, 784
  Porter, 763
  Proell, 778
  Watt, 760
  Wilson-Hartnell, 797
  effort and power, 804
  types of, 758
  Grasshopper mechanism, 178
  Greasy friction, 212
  Grubler’s equation, 10
  Grubler criterion, 1003
  Gyroscopic effects and Gyroscope, 1022
  Gyroscopic couple, 1022
  Gyroscopic effects on aeroplanes, 1055
• on ships, 1054
  Gyroscopic analysis of Grinoling Mill, 1055
  Gyroscope, 1057
  H _
  Hartung governor, 758
  Hammer blow, 711
  Hartnell governor, 784
  Hart’s mechanism, 174
  Helical gears, 396
  Helix angle, 433INDEX
  Herringbone gears, 397
  Higher pair, 3
  Hooke’s joint, 193
  Humpage’s gear, 511
  Hunting ofgovernors, 803
  ! _
  Impulse, 54
  Impulsive force, 54
  Incompletely constrained motion, 7
  Inertia forces in reciprocating parts of an engine,
  523
  Initial tension in the belt, 312
  Instantaneous centre method, 87
• centre of rotation, 88
  Instantaneous centre, 96
  Instantaneous method, 87
  Insensitiveness of Governor, 816
  Interference in involute gears, 415
  Internal expanding brake, 362
  Inversion of mechanism, 11
  four bar chain, 12
• of single slider crank chain, 14
• of double slider crank chain, 18
  Involute teeth, 407
  Isochronous governors, 803
  K _
  Kennedy Theorem, 99
  Kinetic energy, 43
  Kinematics, 1
  Kinematic chain, 5
• pair, 2
  Klien’s construction, 536
  L _
  Law of conservation of energy, 53
• momentum, 55 .,,
  Laws of dry friction, 213
  Low of gearing, 402
  Length of cross belt drive, 296
  of open belt drive, 294
• of arc of contact, 410
• of path of contact, 409
  Limiting friction, 210
• angle of friction, 211
  Link, 2
  Linear acceleration, 33
• displacement, 33
• velocity, 33
  Location of instantaneous centres, 97
  Logarithmic decrement, 863
  Longitudinal vibrations, 829
• natural frequency of, 831
  1 129
  Loss of kinetic energy during elastic impact, 60
  Lower pair, 3
  M
  Machine, 2
  Magnification factor, 875
  Mass, 38
• moment of inertia, 40
  Maximum efficiency of a screw jack, 232
• fluctuation of energy, 610
• fluctuation of speed, 610
  Maximum and minimum speeds of the driving
  shaft, 197
  Mechanical advantage, 121
  Mechanism, 2
  Mechanism for position guidance, 1020
  Method of direct and reverse crank, 741
  Minimum no. ofteeth on the pinion in order to avoid
  interference, 422
• for involute rack, 431
• on wheel, 424
  Modified Scott-Russel mechanism, 177
  Module, 399
  Motion of follower, 931
  Motion of Rotation, 87
• Translation, 87
  Multiple disc clutch, 266
  N _
  Natural frequency of free longitudinal vibrations,
  831
• transverse vibrations, 835
  Nomenclatures for cam profile, 930
• torsional vibrations, 895
  Number of degrees of freedom for plane mechanisms, 9
  Number synthesis, 1003
  o _
  Oldham’s coupling, 20
  Open belt drive, 285
• length of, 294
  Oscillating cylinder engine, 16
  Over-damping, 855
  P _
  Pantograph, 170
  Partial balancing of locomotives, 708
  Partial Balancing ofprimary force, 706
  Path of approach, 400
• contact, 400
• recess, 400
  Path of contact length of, 409
  Peaucellier mechanism,· 173
  Period of vibration, 8301 1 30
  Periodic time, 830
  Pickering governor, 759
  Pinion, 400
  Pitch diameter, 398
  Pitch point, 398
  Plate clutches, 2153
  Porter governor, 763
  Potential energy, 43
  Power, 42
• of a governor, 804
• transmitted by a belt, 303
  Precession and spinning, 1022
  Pressure angle, 400
  Pressure line, 400
  Principle of conservation of energy, 57
• momentum, 60
  Proell governor, 778
  Profile, 400
  Prony brake dynamometer, 378
  Q
  Quaternary joint, 8
  Quaternary link, 9
  R
  Rack, 400
  Radial engines, balancing of, 741
  Radius of gyration, 40
  Ratio of.angular velocities, 195
• belt tensions, 301
  Rayleigh’s method, 834
  Relative velocity method, 104
  Restitution, co-efficient of, 56
  Reverse cranks, 741
  Reverted gear train, 451
  Ritte·rha-gs’s construction, 545
  Robert’s mechanism; 180
  Rolling pair, 4
  Rope drive, 284, 318
  · – ratios of driving tensions for, 319
• brake dynamometer, 379
  Rotary engine, 16
  Rubbing velocity at a pin joint; 110
  s
  Scott Russell’s mechanism, 176
• modified, 177
  Screw tread friction, 225
  Screw jack, 226
  Screw pair, 4
  Scotch yoke mechanism, 20
  Sensitiveness of governors, 803
  Simple shoe brake, 331
  ·
  harmonic motion, 65, 934
  ._ pendulum, 74
• gear train, 450
  Simplex indicator, l83
  THEORY OF MACHINES
  Single block or shoe brake, &31
• disc clutch, 253
  Single slider crank mechanism, 13
  Sliding friction, 212
• pair, 3
  Slip of belt, 287
  Solid friction, laws of, 212
  Spherical pair, 4
  Spinning and precession, 1022
  Spiral gears, 434
• centre distance for a pair of, 434
• · efficiency of, 436
  Spur gear, 396
  Stability of governors, 803
• offour wheelers, 1031
• of two wheelers, 1051
  Statics, 1
  Steering gears, 190
  Straight line mechanism, 171
• con”sisting ofone sliding pair, 176
• made up ofturning pairs, 171
  Strain energy, 43
  Structure, 6
  Successfully constrained motion, 7
  Sun and planet wheel, 479
  Swaying couple, 710
  Synthesis of mechanism, 1003
  System of gear teeth, 409
  T
  Tangent cam with roller follower, 977
  Tchebichefe’s mechanism, 178
  Ternary joint, 8
  Ternary link, 9
  Thompson indicator, 186
  Three centres-in-line Theorem, 99
  Thrust on the sides of the cylinder walls, 550
• on crankshaft bearings, 550
  Time period, 830
  Torque, 41
• on the crank shaft, 548
• in epicyclic gear trains, 486
  Torsion dynamometer, 384
  Torsional pendulum, 80
• vibrations, 894
  Torsionally equivalent shaft, 903
  Transmissibility, 882
  Transverse vibrations, 829
  Trifilar suspension, 80
  Truneated conical pivot, 242
  Turning pair, 4
  Tu•ning moment diagram, 605INDEX
  for different types of engines, 605
  Types ofvibrations, 829
  gear train, 450
  followers, 928
  brakes, 331
  u …, Under damping, 855 Universal joint, 193 Unstable governor, 813 v
  Variation oftractive force, 709
  V-belt, 318
• drive, 318
• V-Engines, balancing, 748
  Velocity, 33
  Velocity ratio ofgear trains, 453
• simple gear train, 454
  compound gear train, 459
  Reverted gear train, 462
  Epicyclic gear train, 463
  Velocity of sliding, 404
  Vibration isolation, 882
  Viscous damping, 849
  Viscous friction, 211
  1 1 3 1
  w
  Watt’s straight line mechanism, 176
  Watt governor, 760
  Weight, 38
  Whirling speed, 849
  Whitworth’s quick return motion mechanism, 14
  Wilson Hartnell governor, 797·
  Work, 41

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