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Kinematics Of Machine

Find out the mechanism in which higher pairs can be replaced

by lower pair

By: Lovejyot Singh Gill

Section: D4911

Reg. No. : 10900141

Roll no: RD4911a007

Submitted to: Ms. ManishaYadav


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Acknowledgment

I would like to acknowledge the contributions of the following groups and

individuals to the development of my term paper.

Our Librarian, directed me to a wide range of resources on the web and in the

library stacks. He answered all of my questions as well as asked me questions

that helped me to narrow my search.

Our Teacher, Miss Manisha Yadav, helped me to refine my thesis and pointed

out weaknesses in organization.

They directed me to two resources that she had used so that I could find more

information to elaborate on a point that I had insufficiently developed.

Last but not least, my friends who were doing this project with me and sharing

our ideas. They were helpful that when we combined and discussed together, we

had this task done.


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Contents

y Introduction

y Lower pair and Higher pair

y Equivalent linkage

y First example

y Second example

y Reference


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Introduction

If a Number of bodies are assembled in such a way that a motion of one causes

constrained and predictable motion to other, it is known as a mechanism and

combination of such mechanisms is known as machine.

A Kinematic pair or simply a pair is a joint of two links having relative motion

between them.

Types of kinematics pair:

y Nature of contact

y Nature of mechanical constrain

y Nature of relative motion

According to nature of contact we characterised pairs into two:

Lower Pair-

A pair of links having surface or area contact between the members is known

as a lower pair. The contact surface of the two links is similar.

Example: Nut turning on a screw, shaft rotating in a bearing, all pairs of

slider crank mechanism, universal joints, etc.


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Higher Pair-

When a pair has a point or line contact between the links, it is known as

higher pair. The contact surfaces of the two links are dissimilar.

Example: Wheel rolling on a surface, cam and follower pair, tooth gears, ball

and roller bearing, etc.


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Degrees of Freedom of Planar Mechanisms

The definition of the degrees of freedom of a mechanism is the number of independent

relative motions among the rigid bodies. For example, fig. below shows several cases of a

rigid body constrained by different kinds of pairs.

We write degree of freedom as equation:

Where

F = total degrees of freedom in the mechanismn = number of links (including the frame)

l = number of lower pairs (one degree of freedom)h = number of higher pairs (two degrees of freedom)

This equation is also known as Gruebler's equation.


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Equivalent Linkage

It is possible to replace higher pairs of plane mechanisms by other type of pairs

having one or two degree of freedom, su ch as turning pair at place of cam. This

can be done according to some set rules so that the new mechanisms also have

the same degree of freedom and are kinematically similar.

There are many examples in which we replace higher pairs with lower pairs.

These have many industrial uses and purposes which make our life simple

and easy. Very often a mechanism with higher pair can be replaced by an

equivalent mechanism with lower pairs. This equivalent lower -pair

mechanism facilitates analysis as a certain amount of sliding takes place

between connected link higher-pair mechanism.


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Here i an example in whi h we replace hi her pair with l wer pair. Referring

t fig bel w, link 2 and 3 are connected to the fixed link 1 by revol te

pairs(t rning pair) at A and D respectively. These links are connected to each

other at, thus forming a higher pair. The relative motion between links 2 and 3

consists of rolling, coupled with a certain amount of sliding. B and C are centres

of curvature of surface s 2 and 3, respectively, atthe point P.

orthe instant shown in figure, the kinematic behaviour oflink 2 and link 3

will be the same as ofthe links 2 and 3 shown in figure, is an equivalent

linkage ofthe higher pair mechanism left side in figure.


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Another example ofthis type of equivalent pairis given below.

The sliding block 4 is the additionallink and higher pair between link 2 and

link 3, is replaced by the two lower pairs, one revolute (turning) the other

prismatic (sliding), B is the centre of curvature ofthe cam surface atthe

point of contact between the cam and the follower. ince the centre of

curvature ofthe follower surface atthe point of contactis atinfinity, hence

the one additional pair becomes sliding, ig above is an equivalentlinkage

of higher pair mechanism.


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ome industrial examples of higher and lower pair mechanisms.


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Pistons are the other examples of kinematic pairs used in industries....


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Reference

y Theory of mechanisms and machine- AMITABHA GHOSH

y www.google.com

y www.altavista.com

y Theory of machine- S.S.RATTAN

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