Theory of Instantaneous Centre

Instantaneous centre of rotation or virtual centre.

Let a plane body ‘P’ having non-linear motion relative to another plane body Q. At any instant, the linear velocities of the point ‘A’ and ‘B ’ on the body ‘P ’ are ‘Va’ and ‘Vb’ respectively.

If a line is drawn perpendicular to the direction of Va at ‘A’, the body can be imagined to rotate about some point on this line. Similarly it is for point B.

If the intersection of the two lines is at ‘I ’, the body ‘P ’ will be rotating about I at the instant.

This point ‘I’ is known as instantaneous centre of velocity.

Kennedy’s Theorem

For the three bodies having the continuous relative motion, their all instantaneous centres lie on the same line.

Angular Velocity Ratio Theorem

It is used to find angular velocity of a link if angular velocity of another link is known. The angular velocity ratio of the two links relative to the third link is inversely proportional to the distances of their common I-centres from their respective centres of rotation.

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