Question

The total number of instantaneous centres for a mechanism consisting of n links are

(a) n/2

(b) n

(c) n – 1/2

(d) n(n – 1)/2

I had been asked this question in an interview.

The question is from Velocity of a point Link on a Link By Instanteneous Centre Method in section Velocity in Mechanisms of Machine Kinematics

Answer 1

Correct choice is (d) n(n – 1)/2

Easy explanation: The number of instantaneous centres in a constrained kinematic chain is equal to the number of possible combinations of two links. The number of pairs of links or the number of instantaneous centres is the number of combinations of n links taken two at a time. Mathematically, number of instantaneous centres, N = n(n – 1)/2                          where n = Number of links.