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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.

enter image description here

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 ?

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  • $\begingroup$ Could you upload a somewhat clearer picture of the mechanism you consider? What part exactly is the third link, what does the dashed circle do? What is the point I? $\endgroup$ – OpticalResonator Mar 4 '18 at 21:54
  • $\begingroup$ A 3link mechanism with 2 revolute joints is a double pendulum? $\endgroup$ – joojaa Mar 4 '18 at 23:43
  • $\begingroup$ I is the other instantaneous centre. The dashed circle envelopes the 2 links together and shows how this system as a whole can itself exhibit mixed motions (rotational + translational) in the fixed reference frame which is the 3rd link. So, I should turn out to be the instantaneous centre for this motion as a whole of the linkage system. $\endgroup$ – RedHelmet Mar 5 '18 at 1:02
  • $\begingroup$ Ah, I get it now. How are the links 1 and 2 connected to the reference frame? $\endgroup$ – OpticalResonator Mar 5 '18 at 9:32
  • $\begingroup$ @OpticalResonator they’re not. It’s customary to consider the fixed reference frame as a link anyhow. For example, a 4 bar linkage system with 1 of the links fixed has 4 links including the fixed link. Now consider this very same 4 bar linkage system, except now its able to move freely about in the plane. So, now there are 4 links + 1 fixed reference frame (acting as a link)....giving a total of 5 links. $\endgroup$ – RedHelmet Mar 5 '18 at 10:50

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