center of rotation

The instant center of rotation (also, instantaneous velocity center, 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 other points in the body generate a circular field around this point which is identical to what is generated by a pure rotation.
Planar movement of a body is often described using a plane figure moving in a two-dimensional plane. The instant center is the point in the moving plane around which all other points are rotating at a specific instant of time.
The continuous movement of a plane has an instant center for every value of the time parameter. This generates a curve called the moving centrode. The points in the fixed plane corresponding to these instant centers form the fixed centrode.
The generalization of this concept to 3-dimensional space is that of a twist around a screw. The screw has an axis which is a line in 3D space (not necessarily through the origin), and the screw also has a finite pitch (a fixed translation along its axis corresponding to a rotation about the screw axis).

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