In a mechanism, the number of Instantaneous centres (I-centres) N is

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ESE Mechanical 2020 Official Paper
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ST 1: UPSC ESE (IES) Civil - Building Materials
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Concept:

The instantaneous centre method of analysing the motion in a mechanism is based upon the concept that any displacement of a body having motion in one plane, can be considered as a pure rotational motion of a rigid link as a whole about some centre, and known as an instantaneous centre.

The number of instantaneous centres in a considered kinematic chain is equal to the number of combinations of two links.

If N is the number of instantaneous centres and n is the number of links, then the relation is given by

 

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