Instant centre of rotation

The instant center of rotation, also called instantaneous velocity center, or also instantaneous center or instant center, is the point fixed to a body undergoing planar movement that has zero velocity at a particular instant of time. At this instant, the velocity vectors of the trajectories of other points in the body generate a circular field around this point which is identical to what is generated by a pure rotation.The instant center can be considered the limiting case of the pole of a planar displacement.Consider the planar movement of a circular wheel rolling without slipping on a linear road; see sketch 3. The wheel rotates around its axis M, which translates in a direction parallel to the road. The point of contact P of the wheel with road does not slip, which means the point P has zero velocity with respect to the road. Thus, at the instant the point P on the wheel comes in contact with the road it becomes an instant center.If two planar rigid bodies are in contact, and each body has its own distinct center of rotation, then the relative center of rotation between the bodies has to lie somewhere on the line connecting the two centers. As a result, since pure rolling can only exist when the center of rotation is at the point of contact (as seen above with the wheel on the road), it is only when the point of contact goes through the line connecting the two rotation centers that pure rolling can be achieved. This is known in involute gear design as the pitch point, where there is no relative sliding between the gears. In fact, the gearing ratio between the two rotating parts is found by the ratio of the two distances to the relative center. In the example in Sketch 4 the gearing ratio is γ = A D B D {displaystyle gamma ={frac {AD}{BD}}}  Sketch 1 above shows a four-bar linkage where a number of instant centers of rotation are illustrated. The rigid body noted by the letters BAC is connected with links P1-A and P2-B to a base or frame.In biomechanical research the instant center of rotation is observed for the functioning of the joints in the upper and lower extremities.For example, in analysing the knee,ankle, or shoulder joints.Such knowledge assists in developing artificial joints and prosthesis, such as elbow or finger joints.