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A Few Basic Concepts and Definitions Related to

Mechanisms

Sandipan Bandyopadhyay

Department of Engineering Design

Indian Institute of Technology Madras

Chennai 600 036

Machines and mechanisms: The terms machine and mechanism are both used in the

same context, to refer to a device constituted of (rigid) links and joints, which transforms and

transfers force and motion from one member of the device (input) to the other (output). When

the transmission of force is the primary objective, the device is referred to as a machine, e.g.,

the toggle press, the dumper-loader etc. On the other hand, if the transformation of motion

is the primary objective, the device is called a mechanism, e.g., the wind-shield wiper of an

automobile, the drive-train of a sewing machine etc.

Link: A link is a rigid member that connects to one or more links to form a linkage. A

link classified as binary, ternary or quaternary if it connects to two, three or four other links

respectively.

Kinematic pairs: Kinematic pairs refer to a pair of links with a mechanical joint between

them. The joints impose certain restrictions (more formally, kinematic constraints) on the

types motions the members in a pair can have relative to each other. Kinematic pairs can

be classified based on multiple criteria. For example, depending on the nature of the contact

between the members of a pair:

Lower pair: The members contact each other along a surface.

Higher pair: The members contact each other along a line or a point.

The lower pairs can be classified further, as shown in Table 1. Another basis for the classifi-

cation of the kinematic pairs is the cause of the contact between the members:

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Table 1: Classification of lower pairs

Type of pair Symbol Degree-of-freedom Equivalent representation

Revolute R 1 -

Prismatic P 1 -

Screw (Helic) H 1 -

Cylindric C 2 RP (or PR)

Planar E 3 PPR (or RPP, PRP)

Spheric S 3 RRR

Form-closed pair: The contact is ensured by the geometry or form of the members,

e.g., a cylindric pair.

Force-closed pair: The contact is ensured by an external force, such as the self-weightor the spring load on a cam-follower pair.

Linkages and mechanisms: Linkages are composed of links and lower pairs. A linkage gen-

erates a mechanism when one or more of its links are fixed or grounded. Different mechanisms

can be obtained from the same linkage by grounding a (different set of) link(s). For example,

different fourbar mechanisms can be generated by fixing a different link of the same fourbar

linkage at a time.

Depending upon the nature of the motion of the links, mechanisms can be classified in the

following manner:

Planar mechanism: If all the points of a mechanism move in planes parallelto a certain

plane (called the reference plane), then it is called a planar mechanism. Note, however,

that the reference plane can be aligned arbitrarily in space.

Spatial mechanism: If all the points of a mechanism do not move in parallel planes,

then it is defined as a spatial mechanism.

Mechanisms can also to classified according to the types on links in them:

Simple mechanism: This is the case when all the links are binary.

Complex mechanism: This is the case when there are one or more ternary or higher

links.

For further reading and more detailed discussions on these topics, please refer to the textbooks [1, 2].

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References

[1] A. Mallik and A. Ghosh, Theory of Mechanisms and Machines. New Delhi: Affiliated East-West

Press Private Limited, 2007.

[2] J. J. Uicker, G. R. Pennock, and J. E. Shighley, Theory of Machines and Mechanisms. New

Delhi: Oxford University Press, 2004.

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