Linkage: Velocity Analysis and Kennedy's Theorem

In the preceding post, the Instant Centers had been explained. Let us bring back the Fig. 3, of the last post, to recapitulate the method of determination of instant centers: 

Kennedy's Theorem: Also known as law of three centers, states that:

"If any three bodies 1, 2, and 3 have plane motion, their instant centers Q12, O13 and O23 must lie on a straight line" 

(The above Fig. shows how the method of applying notation works) 

In order to understand the theorem you will make use of Fig. 4, posted below:

The statement itself provides a ready basis for locating all the instant centers in any mechanism. 

Making use of the theorem to locate the Instant Centers:

You will appreciate that every link in a mechanism has an instant center with respect to every other link. Since, each instant center involves two links (in the previous post it has been seen that the order of positioning of the links is not important), we may say that the number of Instant Centers 'n' will be the number of possible combinations of 'N' links, taken two at a time. Therefore, we can express it in equation form as under:

n = N(N-1)/2

Once the number of instant centers is determined you may use some system to list all the centers. Thereafter, the easily recognized centers are identified and the Kennedy's theorem is applied for locating the remaining instant centers. 

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