A body 'm' having relative plane motion with a reference body 'n' is shown in figure. A and B are two points on body 'm'. Absolute velocity vectors of points A and B relative to body 'n' are known.
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In summary, the basic properties of instant centre are: 1. Instant centre is the point at which the two bodies having relative plane motion are relatively at rest. 2. Instant centre is the point about which the bodies are rotating relative to one another at the instant.
The Aronhold-Kennedy Theorem instant centre. At the instant, the two bodies may be regarded as having relative rotation about the instant centre.
The Aronhold-Kennedy Theorem also known as Kennedy Theorem or Kennedy Rule, states:
If three bodies have relative plane motion, they have three instant centers which lie on the same straight line.
The three bodies having relative plane motion have three instant centers: N = 3(3-1)/2 = 3. It remains to prove that they lie on the same straight line.