I’m reading “Theory of Machines and Mechanisms” by Joseph Shigley.
Page No. 118 - The author states that A mechanism has as many instant centres as there are ways of pairing the link numbers. Thus, for an n-link Mechanism there are N = n(n-1)/2 instantaneous centres.
Now consider the following image having 3 links (one of them being the fixed reference frame), two of them being connected by a revolute joint.
The way I see it, there should be 2 instantaneous centres. One, point A itself about which each link can rotate. Second, some instantaneous centre in the plane about which this linkage system, as a whole, describes rotational motion at any given instant. But by the formula the no. Should be 3.
So, where am I going wrong ?