SUBJECT CODE

: 22438

As per Revised Syllabus of

MSBTE - I Scheme S.Y. Diploma Semester - IV Mechanical / Automobile Engineering (ME / AE)

Theory of Machines Manoj Y. Bhojane D.A.E., B.E. (Mech), M.E.(Heat Power) Formerly Worked as Visiting Lecturer in Automobile Engineering Department Government Engineering & polytechnic, Awasari (kd)

Shripad V. Kusnurkar BE (Mechanical) ME (Manufacturing Process) Ex. Principal MDA, Polytechnic, Latur Lecturer in Dr. DY Patil Soet. Poly. Charoli, br. Lohegaon, Pune

Prashant M. Patil BE (Mechanical) MBA (Marketing), ME (CAD / CAM) Senior Lecturer (Mechanical Department) Sanjay Ghodawat Polytechnic, Atgire, Kolhapur.

Ashish Bahendwar ME (Manufacturing Technology), M.B.A. Lecturer, Govt. Polytechnic, Gondia.

®

TECHNICAL

PUBLICATIONS SINCE 1993

An Up-Thrust for Knowledge

(i)

Theory of Machines Subject Code : 22438 Second Year Diploma Semester - IV Mechanical / Automobile Engineering (ME / AE)

First Edition : January 2019 Second Revised Edition : January 2020

ã Copyright with Authors All publishing rights (printed and ebook version) reserved with Technical Publications. No part of this book should be reproduced in any form, Electronic, Mechanical, Photocopy or any information storage and retrieval system without prior permission in writing, from Technical Publications, Pune.

Published by : ®

TECHNICAL

PUBLICATIONS SINCE 1993

An Up-Thrust for Knowledge

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ISBN 978-93-332-0009-7

9 789333 200097 9789333200097 [2]

MSBTE I (ii)

Syllabus Theory of Machines ( 22438 ) Teaching Scheme

Examination Scheme Credit

L

3

T

-

P

(L+T+P)

2

5

Paper Hrs.

3

Unit Unit - I Fundamentals and type of Mechanisms

Theory ESE

Practical

PA

Total

ESE

PA

Total

Max

Min

Max

Min

Max

Min

Max

Min

Max

Min

Max

Min

70

28

30*

00

100

40

25@

10

25

10

50

20

Unit Outcomes (UOs) (in cognitive domain)

Topics and Sub - topics

1.a

Identify various links in the given figure of the mechanism with justification.

1b.

Describe with sketches the constructional details of the given type of mechanism.

1c.

Select suitable mechanism for the given application with justification.

1d.

Select suitable material of the mechanism for the given application with justification.

1.1

Kinematics of Machines : Introduction to Statics; Kinematics, Kinetics, Dynamics : Kinematic links, joints, pairs, chain and its types, constrained motion and its types, Inversion, Mechanism, Machine and structure.

1.2

Inversions of Kinematic Chains and their materials : Four bar chain coupler, Beam Pantograph.

- Locomotive engine and

Single slider Crank chain Pendulum pump, Rotary I.C. engine mechanism, Oscillating cylinder engine, Whitworth quick return mechanism Quick return mechanism of shaper; Double slider chain - Scotch Yoke mechanism, Elliptical trammel, Oldham's Coupling.

(iv)

Marks

14

Unit - II Velocity and Acceleration in Mechanisms

Unit - III Cams and Followers

2a.

Use analytical method (without derivation) to calculate the velocity and acceleration of given links in the given slider crank mechanism

2b.

Estimate velocity and acceleration of any link at any instant in the given mechanism.

2c.

2.1

Concept of relative velocity and relative acceleration of a point on a link, angular acceleration, inter relation between linear and angular velocity and acceleration.

2.2

Analytical method and Klein's construction to determine velocity and acceleration of different links in single slider crank mechanism.

2.3

Drawing of velocity and acceleration diagrams for simple mechanisms. Determination of velocity and acceleration of point on link by relative velocity method (Excluding Coriollis component of acceleration).

3.1

Introduction to Cams and Followers. Cam and follower terminology, Classification of Cams and Followers. Applications of Cams and Followers.

3.2

Types of follower motions and their displacement diagrams Uniform velocity, Simple harmonic motion, uniform acceleration and retardation.

Describe with dimensioned sketch of the given mechanism.

2d.

Describe with velocity diagram for a given mechanism using relative velocity method.

2e.

Describe with acceleration diagram for the given mechanism.

2f.

Explain with velocity and acceleration diagram for the given mechanism using Klein's construction.

3a.

Identify the type of motion of follower in the given situation with justification.

3b.

Describe with dimensioned sketch of the given cam and follower arrangement.

3c.

Describe with cam profile for the given motion of knife - edge and roller follower with and without offset application using Graphical method.

3.3

(v)

Drawing of profile of a radial cam based on given motion of reciprocating knife - edge and roller follower with and without offset.

10

12

Unit - IV Belt, Chain and Gear Drives

Unit - V

4a.

Calculate velocity ratio, belt tensions, slip and angle of contact in the given belt drive.

4b.

Estimate power transmitted and condition for maximum power transmitted in the given belt drive for given data.

4c.

Select suitable belt for the application with justification.

4d.

Calculate Train value and velocity ratio for the given simple, compound, reverted and epicyclic gear trains using spur and helical gears. Select suitable gear for the application with justification.

4f.

Select suitable drives for the given application with justification.

5a.

4.2

Chain Drives - Introduction to chain drives, Types of chains and sprockets, Methods of lubrication, Merits, demerits and selection of chains for given applications.

4.3

Gear Drives - Introduction to gear drives, Classification of gears, Law of gearing, gear terminology, Types of gear trains, Train value and velocity ratio for simple, compound, reverted and epicyclic gear trains using spur and helical gears. Merits, demerits and selection of gear drives for given applications.

5.1

Introduction to Brakes - Types, Functions and Applications.

5.2

Construction and principle of working of i) Shoe brake, ii) Band brake, iii) Internal expanding shoe brake iv) Disk Brake.

5.3

Braking force, braking torque and power for shoe and band brake.

5.4

Clutches - Uniform pressure and Uniform Wear theories, Introduction to Clutch - Types, Functions and Applications, Construction and principle of working of :

given

Calculate braking force, braking torque and power lost in friction in the given shoe and band brake for the given data.

5b.

Explain with sketches the various parts of the given brakes with their functions and constructional details.

5c.

Describe with sketches the needs, functions and applications of the given clutches.

5d.

Belt Drives - Introduction to Flat belt, V - belt and its applications, materials used for flat and V belts. Introduction of timing belt and pulley, Angle of lap, length of belt, Slip and creep. Determination of velocity ratio of tight side and slack side tension, centrifugal tension and initial tension, condition for maximum power transmission, Merits, demerits and selection of belts for given applications.

given

4e.

Brakes and Clutches

4.1

Explain with sketches the various parts of the given clutch with their functions and constructional details.

a. Single - plate clutch b. Multi - plate clutch c. Centrifugal clutch d. Cone clutch e. Diaphragm clutch.

(vi)

14

08

Unit - VI Flywheels, Governors and Balancing

6a.

Explain with sketches the method of balancing a rotating mass as per the given conditions.

6b.

Estimate the balancing mass and position of plane analytically and graphically in the given situation for the given data.

6c.

Explain with sketches the turning moment diagram for the given single cylinder 4 - stroke I.C. Engine for the given data.

(vii)

6.1

Flywheel - Introduction to Flywheel - need, function and application of flywheel with the help of turning moment diagram for single cylinder 4 - Stroke I.C. Engine.

6.2

Coefficient of fluctuation of energy, coefficient of fluctuation of speed and its significance.

6.3

Governors - Introduction, types, functions and applications, Terminology of Governors, Comparison of Flywheel and Governor

6.4

Balancing - Need and types of balancing, Balancing of single rotating mass. Analytical and Graphical methods for balancing of several masses revolving in same plane.

12

Table of Contents Board Questions . . . . . . . . . . . . . . . . . . . . . . . 1 - 12

Unit - I Chapter - 1

Unit - II

Fundamentals and Type of Mechanisms (1 - 1) to (1 - 14)

Chapter - 2

Velocity and Acceleration Analysis in Mechanisms (2 - 1) to (2 - 22)

1.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 - 1

1.2

Theory of Machines . . . . . . . . . . . . . . . . . . . . . . 1 - 1

1.3

Kinematics of Machines . . . . . . . . . . . . . . . . . . 1 - 1

2.1

Basic Terms Related to Kinematics. . . . . . . . . . 2 - 1

1.4

Kinematic Link or Element . . . . . . . . . . . . . . . . 1 - 1 1.4.1 Types of Links . . . . . . . . . . . . . . . . . . . . . . 1 - 2

2.2

Relation between Linear Velocity, Angular Velocity and Linear Acceleration, Angular Acceleration. . . . . . . . . . 2 - 1

2.3

Relative Velocity Method . . . . . . . . . . . . . . . . . 2 - 2

2.4

Acceleration of a Point on Link . . . . . . . . . . . . . 2 - 2

2.5

Klein's Construction for Slider Crank Mechanism . . . . . . . . . . . . . . . . . . 2 - 6

2.6

Analytical Method to Find Velocity and Acceleration of a Slider Crank Mechanism . . . 2 - 7

2.7

Kennedy's Theorem . . . . . . . . . . . . . . . . . . . . . . 2 - 8

1.4.2 Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 - 2

1.5

Kinematic Pair . . . . . . . . . . . . . . . . . . . . . . . . . . 1 - 2 1.5.1 Classification of Kinematic Pairs . . . . . . . . 1 - 2

1.6

Types of Constrained Motions. . . . . . . . . . . . . . 1 - 4

1.7

Kinematic Chain and its Types . . . . . . . . . . . . . 1 - 5 1.7.1 Kinematic Chain . . . . . . . . . . . . . . . . . . . . . 1 - 5

1.8

Mechanism. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 - 6 1.8.1 Inversion of Mechanism . . . . . . . . . . . . . . . 1 - 6 1.8.2 Inversions of Kinematic Chains . . . . . . . . . 1 - 7

Board Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 - 18

1.8.3 Four Bar Chain or Quadric Cycle Chain. . . 1 - 7

Unit - III

1.8.4 Inversions of Four Bar Chain . . . . . . . . . . . 1 - 7 1.8.4.1 Beam Engine (Crank and Lever Mechanism). . . . . . . . . . . . . . . . . . . . 1 - 7

Chapter - 3

1.8.4.2 Coupling Rod of a Locomotive (Double Crank Mechanism) . . . . . . . 1 - 7

Cams and Followers (3 - 1) to (3 - 14)

3.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 - 1

3.2

Cam and Follower Terminology (Terms used in Cam Profile) . . . . . . . . . . . . . . . 3 - 1

1.8.5.1 Pendulum Pump or Bull Engine . . . . 1 - 8

3.3

Classification of Cam and Followers. . . . . . . . . 3 - 2

1.8.5.2 Oscillating Cylinder Engine . . . . . . . 1 - 9

3.4

Motion of the Follower . . . . . . . . . . . . . . . . . . . 3 - 4 3.4.1 Follower Moves with Uniform Velocity. . . 3 - 4

1.8.4.3 Watt’s Indicator Mechanism (Double Lever Mechanism) . . . . . . . 1 - 8

1.8.5 Single Slider Crank Chain. . . . . . . . . . . . . . 1 - 8

1.8.5.3 Rotary Internal Combustion Engine or Gnome Engine . . . . . . . . . . . . . . . 1 - 9

3.4.2 Follower Moves with Simple Harmonic Motion . . . . . . . . . . . . . . . . . . . . 3 - 4

1.8.5.4 Crank and Slotted Lever Quick Return Motion Mechanism . . . . . . . . 1 - 9

3.4.3 Follower Moves with Uniform Acceleration and Retardation . . . . . . . . . . . 3 - 5

1.8.5.5 Whitworth Quick Return Motion Mechanism . . . . . . . . . . . . . 1 - 10

3.4.4 Follower Moves with Cycloidal Motion. . . 3 - 5

1.8.6 Double Slider Crank Chain . . . . . . . . . . . . 1 - 11

3.5

1.8.6.1 Elliptical Trammels . . . . . . . . . . . . . 1 - 11

Construction of Cam Profile for a Radial Cam . 3 - 6 Board Questions . . . . . . . . . . . . . . . . . . . . . . . 3 - 12

1.8.6.2 Scotch Yoke Mechanism. . . . . . . . . 1 - 11 1.8.6.3 Oldham’s Coupling . . . . . . . . . . . . . 1 - 12 ®

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(ix)

4.25.2 Compound Gear Train. . . . . . . . . . . . . . . . 4 - 15

Unit - IV

4.25.3 Reverted Gear Trains . . . . . . . . . . . . . . . . 4 - 16

Chapter - 4

Belt, Chain and Gear Drives (4 - 1) to (4 - 28)

4.1

Part - I Belt Derive Selection of a Belt Drive : . . . . . . . . . . . . . . . . . 4 - 1

4.2

Types of Belts . . . . . . . . . . . . . . . . . . . . . . . . . . 4 - 1

4.3

Material used for Flat Belts and V-Belts . . . . . . 4 - 2

4.4

Timing Belts and Pulleys . . . . . . . . . . . . . . . . . . 4 - 2

4.5

Types of Belt Drives . . . . . . . . . . . . . . . . . . . . . 4 - 2

4.6

Difference between Open Belt and Cross Belt . 4 - 3

4.7

Angle of Lap or Angle of Contact . . . . . . . . . . . 4 - 3

4.8

Length of Belt . . . . . . . . . . . . . . . . . . . . . . . . . . 4 - 4

4.9

Slip and Creep of Belt . . . . . . . . . . . . . . . . . . . . 4 - 6 4.9.1 Slip of the Belt . . . . . . . . . . . . . . . . . . . . . . . 4 - 6

4.25.4 Epicyclic Gear Train . . . . . . . . . . . . . . . . 4 - 17

4.26 Applications of Each Drives . . . . . . . . . . . . . . 4 - 17 4.27 Solved Numerical. . . . . . . . . . . . . . . . . . . . . . . 4 - 17 Board Questions . . . . . . . . . . . . . . . . . . . . . . . 4 - 25

Unit - V Chapter - 5

Brakes and Clutches (5 - 1) to (5 - 20) Part A : Brakes

5.1

Introduction of Brakes . . . . . . . . . . . . . . . . . . . . 5 - 1 5.1.1 Types of Brake . . . . . . . . . . . . . . . . . . . . . . 5 - 1 5.1.2 Functions of Brake . . . . . . . . . . . . . . . . . . . 5 - 1 5.1.3 Applications of Brake . . . . . . . . . . . . . . . . . 5 - 1

4.9.2 Creep in Belt Drive . . . . . . . . . . . . . . . . . . . . 4 - 6

5.2

4.10 Velocity Ratio of Belt Drive . . . . . . . . . . . . . . . 4 - 6 4.11 Tight Side Tension and Slack Side Tension in Flat Belt :(Tension Ratio in Flat Belt) . . . . . . . . 4 - 7

Construction and Principle of Working of Brakes. . . . . . . . . . . . . . . . . . . . . 5 - 1 5.2.1 Single Shoe Brake. . . . . . . . . . . . . . . . . . . . 5 - 1 5.2.2 Double Shoe Brake . . . . . . . . . . . . . . . . . . . 5 - 2

4.12 Centrifugal Tension . . . . . . . . . . . . . . . . . . . . . . 4 - 7

5.2.3 Simple Band Brake . . . . . . . . . . . . . . . . . . . 5 - 2

4.13 Power Transition by Belt . . . . . . . . . . . . . . . . . . 4 - 7

5.2.4 Internal Expanding Shoe Brake . . . . . . . . . 5 - 3

4.14 Merits (Advantages) and Demerits (Disadvantages) of V Belt over Flat Belt . . . . . 4 - 8

5.2.5 Disc Brake. . . . . . . . . . . . . . . . . . . . . . . . . . 5 - 3

5.3

4.15 Compare Flat Belt and V Belt . . . . . . . . . . . . . . 4 - 8 Part - II Chain Drive

Braking Force Braking Torque . . . . . . . . . . . . . 5 - 5 5.3.1 Single Shoe Brake. . . . . . . . . . . . . . . . . . . . 5 - 5 5.3.2 Double Shoe Brake . . . . . . . . . . . . . . . . . . . 5 - 7

4.16 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 - 9

5.3.3 Simple Band Brake . . . . . . . . . . . . . . . . . . . 5 - 7

4.17 Advantages and Disadvantages of Chain Drive over Belt Drive. . . . . . . . . . . . . . . . . . . . . . . . . 4 - 10

5.3.4 Self Energizing and Self Locking Brake. . . 5 - 8 5.3.5 Numericals . . . . . . . . . . . . . . . . . . . . . . . . . 5 - 8

4.18 Selection of a Chain and Sprocket Wheel . . . . 4 - 10

Part B : Clutch

4.19 Methods of Lubricants . . . . . . . . . . . . . . . . . . . 4 - 10 5.4

4.20 Types of Chains . . . . . . . . . . . . . . . . . . . . . . . . 4 - 10 Part - III Gear Drive

Clutch. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 - 10 5.4.1 Introduction to Clutch . . . . . . . . . . . . . . . . 5 - 10

4.21 Gear Classification : (Types of Gears). . . . . . . 4 - 11

5.4.2 Types of Clutches . . . . . . . . . . . . . . . . . . . 5 - 11

4.22 Law of Gearing . . . . . . . . . . . . . . . . . . . . . . . . 4 - 12

5.4.3 Functions of Clutches . . . . . . . . . . . . . . . . 5 - 11 5.4.4 Applications of Clutches. . . . . . . . . . . . . . 5 - 11

4.23 Gear Terminology . . . . . . . . . . . . . . . . . . . . . . 4 - 13

5.4.5 Single Plate Clutch . . . . . . . . . . . . . . . . . . 5 - 11

4.24 Gear Trains. . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 - 14

5.4.6 Uniform Pressure Condition . . . . . . . . . . . 5 - 13

4.25 Types of Gear Trains . . . . . . . . . . . . . . . . . . . . 4 - 14 4.25.1 Simple Gear Train . . . . . . . . . . . . . . . . . . . 4 - 14 ®

5.4.7 Uniform Wear Condition . . . . . . . . . . . . . 5 - 13 TM

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Part B : Governor

5.4.8 Multiplate Clutch . . . . . . . . . . . . . . . . . . . 5 - 14 5.4.9 Cone Clutch. . . . . . . . . . . . . . . . . . . . . . . . 5 - 16

6.3

5.4.10 Centrifugal Clutch. . . . . . . . . . . . . . . . . . . 5 - 16 5.4.11 Diaphragm Clutch . . . . . . . . . . . . . . . . . . . 5 - 17

6.3.2 Types of Governor . . . . . . . . . . . . . . . . . . . 6 - 2

Unit - VI Chapter - 6

6.3.3 Function . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 - 3 6.3.4 Applications . . . . . . . . . . . . . . . . . . . . . . . . 6 - 3

Flywheels, Governors and Balancing (6 - 1) to (6 - 18)

6.3.5 Terminology of Governer . . . . . . . . . . . . . . 6 - 3 6.3.6 Comparison between Governor and Flywheel . . . . . . . . . . . . . . . . . . . . . . . . 6 - 3

Part A : Flywheels 6.1

Part C : Balancing

Flywheels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 - 1 6.1.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . 6 - 1

6.4

6.1.2 Need of Flywheel . . . . . . . . . . . . . . . . . . . . 6 - 1

6.4.3 Balancing of Single Rotating Mass. . . . . . . 6 - 4

6.1.4 Applications . . . . . . . . . . . . . . . . . . . . . . . . 6 - 1

6.4.4 Balancing of Several Masses Revolving In Same Plane . . . . . . . . . . . . . . . . . . . . . . . . . 6 - 4

Coefficent of Fluctuation of Speed and Energy. 6 - 2 6.2.1 Coefficient of Fluctuation of Speed . . . . . . 6 - 2

6.4.5 Numerical . . . . . . . . . . . . . . . . . . . . . . . . . . 6 - 6

6.2.2 Coefficient of Fluctuation of Energy . . . . . 6 - 2

®

Balancing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 - 4 6.4.1 Need of Balancing. . . . . . . . . . . . . . . . . . . . 6 - 4 6.4.2 Types of Balancing . . . . . . . . . . . . . . . . . . . 6 - 4

6.1.3 Function of Flywheel . . . . . . . . . . . . . . . . . 6 - 1

6.2

Governor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 - 2 6.3.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . 6 - 2

Solved Sample Papers

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(S - 1) to (S - 4)

Theory of Machines

1-1

Fundamentals and Type of Mechanisms

UNIT - I

1

Fundamentals and Type of Mechanisms 1.4 Kinematic Link or Element

1.1 Introduction What is Machine ?

Machine is a device which receives energy in some available form and utilizes it to do some particular type of work.



Each part of a machine, moves relative to some other part, is known as a kinematic link (or simply link) or element.



A link may consist of several parts, which are rigidly fixed together, so that they do not move relative to one another.



Example : In a reciprocating steam engine, as shown in Fig. 1.4.1, piston, piston rod and crosshead constitute one link ; connecting rod with big and small end bearings constitute a second link ; crank, crank shaft and flywheel a third link and the cylinder, engine frame and main bearings a fourth link.

Fig. 1.1.1 : Flow diagram of inputs and outputs to machine

1.2 Theory of Machines 

The subject Theory of Machines may be defined as that branch of Engineering-science, which deals with the study of relative motion between the various parts of a machine, and forces which act on them. The knowledge of this subject is very essential for an engineer in designing the various parts of a machine.

1.3 Kinematics of Machines

a) Kinematics : It is that branch of Theory of Machines which deals with the relative motion between the various parts of the machines. b) Dynamics : It is that branch of Theory of Machines which deals with the forces and their effects, while acting upon the machine parts in motion. c) Kinetics : It is that branch of Theory of Machines which deals with the inertia forces which arise from the combine defect of the mass and motion of the machine parts. d) Statics : It is that branch of Theory of Machines which deals with the forces and their effects while the machine parts are at rest. The mass of the parts is assumed to be negligible. TM

Technical Publications

Fig. 1.4.1 : Reciprocating steam engine 

A link or element needs not to be a rigid body, but it must be a resistant body.



Resistant body : A body is said to be a resistant body if it is capable of transmitting the required forces with negligible deformation.



Thus a link should have characteristics :

the following two

1. It should have relative motion, and 2. It must be a resistant body.

(1 --An1)up thrust for knowledge

Theory of Machines

1-2

1.4.1 Types of Links 

1.5 Kinematic Pair

In order to transmit motion, the driver and the follower may be connected by the following three types of links : a. Rigid link : A rigid link is one which does not undergo any deformation while transmitting motion.

The two links or elements of a machine, when in contact with each other, are said to form a pair.  If the relative motion between them is completely or successfully constrained (i.e. in a definite direction), the pair is known as kinematic pair. 

1.5.1 Classification of Kinematic Pairs

The kinematic pairs may be classified according to the following considerations :

 Rigid links do not exist. However, as the deformation of a connecting rod, crank etc. of a reciprocating steam engine is not appreciable; they can be considered as rigid links.



b. Flexible link : A flexible link is one which is partly deformed in a manner not to affect the transmission of motion. Example : The belts, ropes, chains and wires are flexible links and transmit tensile forces only. c. Fluid link : A fluid link is one which is formed by having a fluid in a receptacle and the motion is transmitted through the fluid by pressure or compression only. Example : In the case of hydraulic presses, jacks and brakes. 1.4.2 Structure 

Fundamentals and Type of Mechanisms

According to the type of relative motion between the elements. The kinematic pair’s according to type of relative motion between the elements may be classified as discussed below : (a) Sliding pair : When the two elements of a pair are connected in such a way that one can only slide relative to the other, the pair is known as a sliding pair. Example : The piston and cylinder, cross-head and guides of a reciprocating steam engine, ram and its guides in shaper, tail stock on the lathe bed etc.

It is an assemblage of a number of resistant bodies (members) having no relative motion between them and meant for carrying loads having straining action. Example : A railway bridge, a roof truss, machine frames etc.,

Difference between a Machine and a Structure 

The following differences between a machine and a structure : 1. The parts of a machine move relative to one another, whereas the members of a structure do not move relative to one another. 2. The links of a machine may transmit both power and motion, while the members of a structure transmit forces only.

Fig. 1.5.1 : Sliding pair

(b) Turning pair : When the two elements of a pair are connected in such a way that one can only turn or revolve about a fixed axis of another link, the pair is known as turning pair. Example : A shaft with collars at both ends fitted into a circular hole, the crankshaft in a journal bearing in an engine, lathe spindle supported in head stock, cycle wheels turning over their axles etc. are the examples of turning pair.

3. A machine transforms the available energy into some useful work, whereas in a structure no energy is transformed into useful work. TM

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- An up thrust for knowledge

Theory of Machines



1-3

It is a completely constrained motion.

Fundamentals and Type of Mechanisms

(e) Spherical pair : When the two elements of a pair are connected in such a way that one element (with spherical shape) turns or swivels about the other fixed element, the pair formed is called a spherical pair. Example : The ball and socket joint (i.e., Fig. 1.5.5), attachment of a car mirror, pen stand etc., are the examples of a spherical pair.

Fig. 1.5.2 : Turning pair

(c) Rolling pair : When the two elements of a pair are connected in such a way that one rolls over another fixed link, the pair is known as rolling pair. Example : Ball and roller bearings are examples of rolling pair.

Fig. 1.5.5 : Spherical pair 

According to the type of contact between the elements. The kinematic pairs according to the type of contact between the elements may be classified as discussed below :

Fig. 1.5.3 : Rolling pair

(d) Screw pair : When the two elements of a pair are connected in such a way that one element can turn about the other by screw threads, the pair is known as screw pair.

(a) Lower pair : When the two elements of a pair have a surface contact, when relative motion takes place and the surface of one element slides over the surface of the other, the pair formed is known as lower pair.

Example : The lead screw of a lathe with nut, and bolt with a nut are examples of a screw pair.

Examples : It will be seen that sliding pairs, turning pairs and screw pairs form lower pairs. (b) Higher pair : When the two elements of a pair have a line or point contact when relative motion takes place and the motion between the two elements is partly turning and partly sliding then the pair is known as higher pair. Examples : A pair of friction discs, toothed gearing, belt and rope drives, ball and roller bearings, cam and follower. 

According to the type of closure The kinematic pairs according to the type of closure between the elements may be classified as discussed below :

Fig. 1.5.4 : Screw pair

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(a) Self closed pair : When the two elements of a pair are connected together mechanically in such a way that only required kind of relative motion occurs, it is then known as self-closed pair. The lower pairs are self-closed pair. (b) Force - closed pair : When the two elements of a pair are not connected mechanically but are kept in contact by the action of external forces, the pair is said to be a force-closed pair. The cam and follower is an example of force closed pair, as it is kept in contact by the forces exerted by spring and gravity.

Fundamentals and Type of Mechanisms

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The motion of a square bar in a square hole, as shown in Fig. 1.6.1, and the motion of a shaft with collars at each end in a circular hole, as shown in Fig. 1.6.2, are also examples of completely constrained motion.

2. Incompletely constrained motion : When the motion between a pair can take place in more than one direction, then the motion is called an incompletely constrained motion. The change in the direction of impressed force may alter the direction of relative motion between the pair. 

Example : A circular bar or shaft in a circular hole, as shown in Fig. 1.6.3, is an example of an incompletely constrained motions it may either rotate or slide in a hole. These both motions have no relationship with the other.

Fig. 1.5.6 : Spherical pair

1.6 Types of Constrained Motions

Following are the three types of constrained motions : 1. Completely constrained motion : When the motion between a pair is limited to a definite direction irrespective of the direction of force applied, then the motion is said to be a completely constrained motion. 

Examples : The piston and cylinder (in a steam engine) form a pair and the motion of the piston is limited to a definite direction (i.e. it will only reciprocate) relative to the cylinder irrespective of the direction of motion of the crank, as shown in Fig. 1.6.1.

Fig. 1.6.3 : Shaft in a circular hole

3. Successfully constrained motion : When the motion between the elements, forming a pair, is such that the constrained motion is not completed by itself, but by some other means, then the motion is said to be successfully constrained motion. Consider a shaft in a foot-step bearing as shown in Fig. 1.6.4.

Fig. 1.6.1 : Square bar in a square hole

Fig. 1.6.4 : Shaft in a foot step bearing Fig. 1.6.2 : Shaft with collars in a circular hole

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The shaft may rotate in a bearing or it may move upwards. This is a case of incompletely constrained motion. But if the load is placed on the shaft to prevent axial upward movement of the shaft, then the motion of the pair is said to be successfully constrained motion.

Fundamentals and Type of Mechanisms

pair may be taken as equivalent to two lower pairs with an additional element or link. 

Let us, apply the above equations to the following cases to determine whether each of them is a kinematic chain or not. 1. Consider the arrangement,

The motion of an I.C. engine valve (these are kept on their seat by a spring) and the piston reciprocating inside an engine cylinder are also the examples of successfully constrained motion. 1.7 Kinematic Chain and its Types

Fig. 1.7.1 : Three link arrangement

1.7.1 Kinematic Chain Definition : 



When the kinematic pairs are (i.e. completely or successfully constrained motion), it is called a kinematic chain. In other words, a kinematic chain may be defined as a combination of kinematic pairs, joined in such a way that each link forms a part of two pairs and the relative motion between the links or elements is completely or successfully constrained. Example : The crankshaft of an engine forms a kinematic pair with the bearings which are fixed in a pair, the connecting rod with the crank forms a second kinematic pair, the piston with the connecting rod forms a third pair and the piston with the cylinder forms a fourth pair. The total combination of these links is a kinematic chain.

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If each link is assumed to form two pairs with two adjacent links, then the relation between the number of pairs (p) forming a kinematic chain and the number of links ( l ) may be expressed in the form of an equation : l = 2p – 4

… (1.7.1)

j = (3/2) * l – 2

… (1.7.2)

The equations (1.7.1) and (1.7.2) are applicable only to kinematic chains, in which lower pairs are used. These equations may also be applied to kinematic chains, in which higher pairs are used. In that case each higher TM

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Number of links,

l = 3

Number of pairs,

p = 3

And, number of joints, j = 3 From equation (1.7.1), l = 2p – 4 3 = 2×3–4=2 i.e.

L.H.S. > R.H.S.

Now from equation (1.7.2), j  l – 2 3 = ( 

  

i.e. 

L.H.S. > R.H.S.

Since the arrangement of three links, as shown in Fig. 1.7.1, does not satisfy the equations (1.7.1) and (1.7.2) and the left hand side is greater than the right hand side, therefore it is not a kinematic chain and hence no relative motion is possible. Such type of chain is called locked chain and forms a rigid frame or structure which is used in bridges and trusses. 2. Consider the arrangement of four links AB, BC, CD and DA as shown in Fig. 1.7.2.

Fig. 1.7.2 : Four link arrangement

l = 4, p = 4, and j = 4 - An up thrust for knowledge