Discussion
The total number of instantaneous centre for a mechanism consisting of 'n' links is :
Answer: A
The total number of instantaneous centres is \(\frac{n(n-1)}{2}\).
Every pair of links in a mechanism has one instantaneous centre, so the number of centres is the number of ways of choosing two links from n:
\[ N = \binom{n}{2} = \frac{n(n-1)}{2} \]
A four-bar chain, for example, has \(\frac{4 \times 3}{2} = 6\) instantaneous centres. The options n, \(\frac{n}{2}\) and \(\frac{n-1}{2}\) do not count the pairs; for four links they give 4, 2 and 1.5, and a count of centres cannot be fractional.
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