اسم المؤلف
P. L. Ballaney
التاريخ
20 ديسمبر 2023
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643
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Theory of Machines and Mechanisms
P. L. Ballaney
Contents
Chap.
- DEFINITIONS AND BASIC CONCEPT
SJ. Units ; Fundamental Units or S.I. Base Units and
S.I. Supplementary Units-I
Machine
The Science of Mechanics
Kinematics of Machine
Kinematic Link or Element
Structure
Difference: bet-�een a Machine and a Structure
Kinematic Pair
Types of Kinematic Pairs
Kinematic Chain
Mechanism
Difference between Machine and Mechanism
Skeleton Outline ofa Machine or Kinematic
Representation of a Machine
Expansion ofPairs (Limit and Disguise of Revolute Pairs)
Inversions of Mechanism
Four-bar Chain or Quadratic Cycle Chain
(a) Application ofQuadric Cycle Chain
Grashofs Law
Special Cases of Four Bar Chains
Tasks performed by Four Bar Chain
Slider Crank Mechanism
Inversions of Slider Crank Chain
Double Slider Crank Chain
Binary, Ternary, Quatenary Links
Compound Chain
(a) Linkage of more than Four Bars with Constraint
Six-Bar Chains
Degrees of Freedom or Criteria of Constraint
Test Your Comprehension
Test Questions
Practice Problems - MOTION AND INERTIA
Displacement
Velocity
Acceleration
Acceleration of a Particle Moving Along a Circular Path
Angular Di8placement
Angular Velocity
Angular Acceleration
Force
Mass
Force
Pages
Centripetal Force
Centrifugal Force
Mass Moment ofInertia
Couple
Angular Momentum
Work, Power and Energy
Conservation of Energy and Conservation ofMomentum
Impulse, Impact
Harmonic Motion
Simple Harmonic Motion
Compound Pendulum
Kinetically Equivalent System-Case I
Kinetically Equivalent System-Case II
D’Alembert’s Principle
D’Alembert’s Principle
Rolling without Slipping
Acceleration of Geared System
Test Your Comprehension
Test Questions
Practice Problems
Pages - VELOCITIES IN MECHANISM: INSTANTANEOUS CENTRE .MEI’HOD 104-139
The Relative Linear Velocities of Points in a Link
Methods ofTransmitting Motion
(a) Line ofTransmission-
(b) Transmission Angle
(c) Deviation Angle
Angular Velocity Ratio Theorem
Instantaneous Centre ofRotation
Properties ofInstantaneous Centre ofRotation
Mathematical Deduction
Special Cases of Instantaneous Centre ofRotation
Types ofInstantaneous Centres of Mechanisms
The Three Centres in-line Theorem (Kennedy’s Theorem)
Procedure to be Followed for Locating Instantaneous Centres
Important Suggestions
Space Centrode, Body Centrode
Test Questions
Test Your Comprehension
Practice Problems - VELOCITIES IN MECHANISMS: VELOCITY POLYGONS
Introduction
Relative Velocities ofPoints in Kinematic Link
Relative Angular Velocities ofTwo Kinematic Lin.ks or Rigid Bodies
Relative Velocities ofPoints on the Same Link
Relative Velocity of Coincident Points in Two Kinematic Links having
Plane Motion and Successful Constraint
Applications
Relative Angular Velocities of Links in Mechanism
and Rubbing Velocities on the Pin at the Pin Joints
Mechanical Advantage and Power Transmission in Mechanism
150Chap. Pages
4.9 Kinematic Analysis ofComplex Mechanism 172
4.10 Trial Solutions 188
TestYour Comprehension 190
Practice Problems 192 - ACCELERATION IN MECHANISM-ACCELERATION POLYGON
METHOD 201-269
5.1 Acceleration Analysis 201
5.2 Acceleration diagram for a Link 201
5.3 The Acceleration Centre of a Link 203
5.4 Klein’s Construction for Determining the Acceleration ofthe Piston 205
5.5 Special Cases ofKlein’s Construction
207
5.6 Ritterhau’s Construction for Finding the Acceleration ofPiston 209
5.7 5.8 Bennet’s Approximate Construction Analytical for Method Finding ofthe Finding Acceleration the ofthe Piston 210
Displacement, Velocity and Acceleration of the Piston 212
5.9 Acceleration Polygon for a Four-bar Chain Mechanism
215
5.10 Corioli’s Law 232
5.11 AccelerationAnalysis ofLink Sliding in a Swivelling Pin 245
5.12 The Geneva Wheel or Maltese Cross 255
Test Your Comprehension 259
Practice Problems 262 - MECHANISM WITH LOWER PAIRS: STRAIGHT LINE AND
COPYING DEVICES 270-296
6.1 Introduction 270
6.2 Pantograph 270
6.3 Straight Line Motions 272
6.4 Mathematically Exact Straight Line Mechanism ; Paucellier’s Mechanism 272
6.5 Paucellier-Lipkin Exact Straight Line Mechanism 274
6.6 Paucellier-Lipkin Exact Straight Line Mechanism (Alternative) 274
6.7 Hart’s Straight Line Mechanism 276
6.8 Hart Exact Straight Line Mechanism (Alternate) 277
� 6.9 Hart Exact Straight Line Mechanism (Alternate) 277
6.10 Hart Exact Straight Line Mechanism (Alternate) 278
6.11 Kempe’sMechanism 278
6.12 Bricard Exact Straight Line Mechanism 279
6.13 Bricard Exact Straight Line Mechanism (Alternate) 279
.- – – 6.14 Scott-Russel Mechanism, Straight Line
Mechanism with a Sliding Pair 280
6.15 (a) Straight Line Mechanism having a Link with Rectilinear Translation 280
(b) Straight Line Mechanism having a Link with Rectilinear Translation 280
(c) Straight Line Mechanism with a Link having Rectilinear Translation
(Perrolotz Principle) 281
6.16 Approximate Straight line Mechanism : Watt-Straight Line Mechanism 281
6.17 Modified Scott-Russel Mechanism 282
6.18 Grass-Hopper Mechanism 283
6.19 The Tchebiehoff Straight Line Motion 283
�:.,.. 6.20 The Robert’s Straight Line Motion 284
I- 6.21 6.22 Crosby StraightIndicator Line Mechanism Mechanism ofEngine indicator 286 284
6.23 Thomson Indicator Mechanism 287
6.24 Dobbie Mcinnes Indicator Mechanism 287
�:;. tChap.
Test Your Comprehension
Test Questions
Practice Problems
7.CAMS
Definition
Types of Followers
Types of Cams
Terminology
Types of Motion of the Follower
Analysis of the Motion of Follower
Analysis of the Motion of Follower for Cams with Specified Countours
Analysis of Motion of Follower : Simple Harmonic Motion
Analysis of Motion of Follower : Uniform Acceleration and Deceleration
Analysis of Motion of Follower : Cycloidal or Sine Acceleration Motion Curve
Analysis of the Motion of the Follower for Can;is with Spec”‘”ifiedContour�
Cam with Concave Flank, Circular Nose and Roller Follower ,
Convex Circular Arc Cam with Roller Follower
r
Circular Arc Cam with Flat-facedMushroom Follower
Circular Arc Cam with Oscillating Roller Follower
Eccentric Circle Cam with Translating Flat Footed Follower
Test Your Comprehension
Test Questions
Practice Problems
8.GYROSC�
8.1 A Gyroscope
8.2 Principles of Gyroscope
8.3 Gyroscopic Couple
8.4 (a)Forced Directions Precession of Spin Vector, Precession V.ector and Torque Vector with
(b) Analysis of the Forces on Bearing due to the Forced Precessing of Rotating
Disc Mounted on Shafts
8.5 Effects of Gyroscopic Couples on the Stability of an Automobile
Negotiating a Curve
8.6 Gyroscopic Effects on Two Wheel Vehicle
8.7 Gyroscopic Stabilization
8.8 Stabilization of Sea Vessels
8.9 Analysis of Gyroscopic Effects on Sea Vessels
8.10 Gyroscopic Analysis for a Body Fixed to Rotating Shaft at Certain Angle
8.11 Gyroscopic Analysis of Grinding Mills
Test Your Comprehension
Test Questions
Practice Problems
9.FRICTION
Force of Friction
Types of Friction
Laws of Dry or Solid Friction
The Limiting Angle of Friction
Experimental Verification of the Limiting Angle of Friction
Minimum Force Required to Move a Body on Horizontal Plane
The Inclined Plane
Maximum Efficiency
_Pages
288 Chap. Pages
9.9 The Inclined Plane with Guide Friction 443
9.10 Wedge 445
9.11 Friction of Screw and Nut 447
9.12 Screw Jack 452
9.13 V-Threads 457
9.14 Pivot and Collar Friction 463
9.15 Flat Pivot 464
9.16 Flat Coller Pivot 465
9.17 Conical Pivot 467
9.18 Development-Of Clutches for Automobiles 475
9.19 Single Plate Clutch 476
9.20 Multiple Plate Clutch 476
9.21 Theory of Plate Clutches 477
9.22 The Cone Clutch 492
9.23 Theory of Cone Clutch 493
9.24 Centrifugal Clutch 499
9.25 Theory of Centrifugal Clutches … 499
9.26 Friction in Turning Pair�Friction Circle 502
9.27 Power Loss in Friction at a Bearing 503
9.28 FrictionAxis of a Link 503
9.29 Friction in_a Slider Crank Mechanism 504
9.30 Film Lubrication in Rotating Shafts 508
Test Your Comprehension 512
Test Questions 516
Practice Problems 517 - BELT, ROPE AND CHAIN DRIVE 521-573
10.1 Belt, Rope and Chain Drives· 521
10.2 Flat Belts 521
10.3 (a) Angular Velocity Ratio 521
(b) Effect of Belt Thickness on Velocity Ratio 522
10.4 Effect of Slip on Velocity Ratio 523
1.0.5 (a) Length of Flat Belts 524
p (b) Angle of Contact 526
10.6 Law of Belting 527
10.7 Cone Pulleys -527
10.8 Graphical Method 530
I 10.9 Crowning of Pulleys . 530
,, …._ 10.10 Ratio of Belt Tensions 531
10.11 Power Transmitted by Belt Drive … 531
10.12. Effect of Centrifugal Tension on ihe Power Transmitted 532
10.13 Design of Belt Dimensions 533
10.14 Maximum Power Transmitted by Belt Drive 533
10.15 Phenomenon of Creep in Belts 534
10.16 Allowance for Creep of Belts . 534
10.17 (a) Initial Tension in Belts 535
(b) Effect of Initial Belt Tension on Maximum Power 536
10.18 V-Belts 536
.�?: 10.19 Timing Belts 537
10.20 Ratio of Tension in a V-Belt and Rope Drive 537
10.21 Chain Drive 538
10.22 Kinematics of Chain Drive 538
10.23 Angular Velocity Ratio 539
� 10.24 Construction ofBush and Roller Chain .j40Chap.
10.25 Mean Velocity Ratio and the Length of the Chain
10.26 Power Transmitted by Chain
10.27 Impact Loading
10.28 Other Classified Chains
Test Your Comprehension
Test Questions
Practice Problems - BRAKES AND DYNAMOMETERS
Definition
(a) Types of Brakes
(b) External Shoe Brakes or Block Brakes
Block Brakes ; Angle of lap > 45°
Double Shoe Block Brakes
Graphical solution of the Pivoted Shoe Brake
Heat Generated in Braking
(a) Band Brakes
Different Arrangement ofBand Brakes
Simple Band Brakes
Differential Band Brakes
Two-Way Band Brakes
Band and Block Brake
Internal Expanding Shoe Brakes ; Pin Anchored Shoe Brake
Vehicle Brakes
Vehicle Braking
Mechanical Brakes
Hydraulic Brakes
Force Multiplication Ratio
Brake Dive
Braking Effectiveness Relations
Internal Expanding Shoe Brakes (A Detailed Description on Different Types
of Internal Expanding Shoe Brakes)
(a) Pressure Distribution
(b) Torque equation about the brake centre
Force Multiplication Ratio �n Cam to Drum
Articulated Link Anchored Brakes (Huck Brake)
Duo-Serve Brake (Bendix Type Brake)
Disc Brakes
Locomotive Train Brakes ; Vacuum Braking System
Dynamometers
Absorption Dynamometers (Mechanical)
Transmission Dynamometers ; Belt Transmission Type
Water Brake Dynamometers
Hydraulic Dynamometer (Froude’s Dynamometers)
Epicyclic Train Dynamometer
Torsion Dynamometer
Devis-Gibson Flash Light Torsion Dynamometer
Test Your Comprehension
Test Questions
Practice Problems - TOOTHED �ARS
12.1 Introduction \
12.2 Claseificatior. ofGears
Pages
Terminology Used in Gears
Law of Gearing or Conditions of Correct Gearing
Velocities of Sliding in the Mating Teeth ofthe Gear Wheels
Forms ofTeeth
(a) Construction ofan Involute
(b) Properties ofthe Involute ofa Circle (Involut,e Function)
(a) Involute GearTeeth
(b) Involute Gear Teeth
Cycloidal Teeth
Effect ofCenter Distance Variation on the Velocity Ratio for Involute Profile
Tooth Gears
Properties ofInvolute Profile Toothed Gears in Mesh
Standard Interchangeable Tooth Profile
Length ofthe Path of Contact and Number ofTeeth in Contact
Interference and Undercutting in Involute Gears
Maximum Number ofTeeth on Gear Wheel
Minimum Number of Teeth on Pinion to Avoid Interference
Minimum Number ofTeeth for Involute Rack and Pinion
Unequal-Addendum Tooth Forms
Interference-Further Comments
Comparison of Cycloidal and Involute Tooth Forms
Friction between Gear Teeth
Path ofContact for Cycloidal Gear Teeth
Internal Gears
Manufacture ofSpur Gears
Strength ofGearTeeth (Involute)
Wear of Gear Teeth (Involute)
Strength and Resistance to Wear of Cycloidal Teeth
Helical Teeth
Terminology for Helical Teeth
Spiral Gears
Efficiency of Spiral Gears
Worm and Worm Gears
Test Questions
Test Your Comprehension
Practice Problems
13/QEAR TRAINS
¼.1 Definition
13.2 <5′::rmple Trains of Gears and Velocity Ratio
13.3 ;c;mpound Trains ofGear
13.4 _Reverted Gear Train
13.5 Epicyclic or Planetary Gear Train
13.6 Tooth Loads and Torques in Epicyclic Gear Trains
13.7 Ferguson’s Paradox
13.8 Compound Epicyclic Gear Train
13.9 The Motor Car Gear Box
13.10 Cyclometer Mechanism
13.11 The Wilson Gear Box
13.12 Differentials
Test Your Comprehension
Test Questions
Practice Problems
Pages
815Chap. - INERTIA FORCE ANALYSIS IN MACHINES
14.1 r …1echanics of Principal Moving Part-PistonConnected Rod-Crank System
14.2 Piston Side-Thrust and Connecting Rod Force5
14.a Force Along the Connecting Rod
14.4 Force Perpendicular to the Crank or Rotative Force
14.5 Effective Driving Force for Piston Effort
14.6 Inertia Force Analysis in a Reciprocating Engine (Considering the Mass of
the Connecting Rod)
Test Your Comprehension
Test Questions
Practice Problems - TURNING :MOMENT DIAGRAMS AND FLYWHEEL
Turning Moment Diagrams for Steam Engine
Turning Moment Diagram for Four.Stroke Internal Combustion Engine
Turning Moment Diagram for Multi-cylinder Engines
Flywheel
Fluctuation of Energy and Speed in Flywheels
Determination ofMaximum Fluctuation ofEnergy
(a) Co-efficient of Fluctuation of Energy
(b) Co-efficient of Fluctuation of Speed
15.8 Size of Flywheel
15.9 DimensionofFlywheel Rim
15.10 The flywheel in punching press
Test Your Comprehension
Test Questions
Practice Problems
��OVERNORS
Vi;_·l Function ofGovernor
16.2 Comparison between Functions ofFlywheel and Governor
16.3 (a) Classification ofGovernors
(b) Simple Governor
(c) Terminology
(d) Watt Governor
16.4 Porter Governor
16.5 Proel Governor
16.6 Hartnell Governor
16.7 Spring Controlled Governor&
16.8 Wilson Hartnell Governor
16.9 Definitions
16.10 Governor Effort and Power - 1l__;flartung Governor
16.12 PickeringGovernor
16.13 Inertia Governors
. 16.14 Controlling I<“orce
16.15 Stability ofSpring Controlled Governors
16.16 Friction and Insensitiveness
i6.17 Influence of.Governor on SpeedTorque Characteristics ofan Engine
Test Questions
Test Your Comprehension
Practice Problems
Pages
972Chap. - BALANCING OF ROTATINGAND RECIPROCATING MASSES
Balancing ofRotating Masses
Balancing of Single RevolvingMass
·BalancingofSeveral Masses Revolving the Same Plane
·Reference Plane
Balance of Several Masses in Different Planes
Application ofthe Reference Plane Method to the Solution of Problems
The Effect of the Inertia Force ofthe Reciprocating Mass on the Engine Frame
Partial Primary Balance
(a) Partial Balance ofLocomotives
Effects of Partial Balancing in Locomotives
Coupled Locomotives
Trailing Wheels
(a) Balancing ofV-Engines
Direct and Reverse Cranks
Application ofDirect and Reverse Cranks
Six Cylinder In-Line Engine
Radial Engine
Single Cylinder Reciprocating Engine
Balancing ofIn-line Engine with N Cylinder
Balance ofIn-line Four-Cylinder Four-stroke Petrol Engine
Balance ofSix-Cylinder Four-Stroke Engine
Ten-Cylinder Oil Engines Symmetrical about the Mid-Plane
V-Engine
V-8 Engine
V-12 Engine
W-Engine
Radial Engine with N-Cylinders
Test Your Comprehension
Practice Problems
Pages - MECHANICALVIBRATION
Introduction
Defmitions
Und E_qu Ener!· · rium ped Method Free MethVibratiorua od
Rayleigh’_s Method
Transverse Free Vibrations
Longitudinal and Transverse Vibrations Considering the Mass ofthe Shaft
Natural Frequency of Free Transverse Vibrations
Tran�verse Vibration : Uniformly Loaded Shaft
Transverse Vibration : One LoadActing on the Shaft
Energy Method (Lord Rayleigh) or Maxwell’s Theorem ofReciprocal Deflection
Dunkerley’s Empirical Equation
Critical or Whirling Speed ofthe Shaft
Secondary Critical Speed
TorsionalVibration : Two Rotor System
(a) Torsional Vibration : Three Rt>tor System
Torsional Vibration of Geared System
Free Vibration with Viscous Damping or Damped Free Vibrations
Logarithmic Decrement
Additional Comment onWhirling of Shaft
1121Chrr.p,.
18.� 1 Forced Vibrations
18.22 Reciprocating and Rotating Unbalance
18.23 Vibration Isolation and Transmissibility
18.24 Vibration ofMass Supported to Foundation Subject toVibration
Test Your Comprehension
Test Questions
Practice Problems - HOOKE’S JOINT STEERING GEARS-TRIFILAR SUSPENSION
19.1 Hooke’s Joint
19.2 Hooke’s Joint Analysis
19.3 Trifilar Suspension
19.4 Motor Car Steering Gear
19.5 The Davis Steering Gear
19.6 TheAckermann Steering Gear
Test Your Comprehension
Practice Problems - AUTQMOTIVE-VEIDCLE PROPULSION
Power Requiredfor Propulsion
Power Available
Gradient Performance
Power Available (Manual and Automatic Transmission)
Calculation ofEquivalent weight-We
Relative Drive Effectiveness for Four wheel, Front wheel and Rear wheel Drives - INTRODUCTION TO AUTOMATIC CONTROL
Introduction
Un-monitored and Monitored Control Systems
Continuous and Discontinuous Controllers
System Response
Types ofInput
Response to First Order System to Step Input
Second Order System Response
System Stability
Control Action-Proportional Control
Integral Control
Transfer Functions
Transfer Function Relationships
Open Loop and Closed Loop Transfer Function
Remote Position Controller - . ANALYSIS OF MECHANISMS-_’\NALYTICAL APPROACH
22.1 Introduction : Review ofComplex Numbers
22.2 Loop-Closure Equatio?l
22.3 Freudenstein’s Equation : (Equation for Displacement)
22.4 Alternate Solution
22.5 Use ofCosine Law for Determining Angles for Four-bar Mechanism
22.5 (a) Slider CrankMechanism
22.6 Additional Useful Information on Complex Numbers
22.7 Coupler Curves
1240Chap.
22.8 Slider Crank Mechanism
22.9 The Geneva Wheel or Maltese Cross - INTRODUCTION TO KINEMATIC SYNTHESIS
Introduction
Type Synthesis
Tasks of Kinematic Synthesis
Scale Factor for Input and Output Motion
Chebyshev Spacing ofPrecision Po-ints
Two Position Synthesis ; Four Bar Mechanism
Three Position Synthesis ; Four Bar Mechanism
Bloch’s Synthesis Method
Freudensteins Equation for Three Point Function Generation
Complex-number Modellingin Kinematic Synthesis
Loop Closure-Equation Technique
23.11.1 Application of Loop Closure �ethod for Function Generator
Position, Velocity and Acceleration Specification for the Four-bar Function
Generator
Synthesis for Slider Crank Mechanism
Number Synthesis : Associated Link Concept
Synthesis ofSome Slider Mechanisms
Synthesis of Cam and Sliding Pivots
Synthesis of Some Gear Mechanism
Graphical Synthesis ofQuick Return Mechanism
Six-bar Quick-Return Mechanism
Crank Slider Quick Return
· Practice Problems
Test Your Comprehension - INTRODUCTION TO COMPUTER AIDED ANALYSIS OF
MECHANSIMS
24.1 Introduction
24.2 Four-bar Mechanism
24.3 Slider Crank Mechanism - INTRODUCTION TO COMPUTER-AIDED SYNTHESIS OF
MACHINES
25.1 Four Bar Mechanism
25.2 Least Square Technique
Test Papers
Interconversion Tables
Index
Pages
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