Estimation of the Reciprocating Point of a Rigid Body Moving Periodically in a Two-Dimensional Space-An Iterative Method Using a Correspondence between the Forward Path and the Backward Path

This paper provides a method of estimating a rotation center to analyze kinematically the movement of a rigid body moving periodically in a two-dimensional (2-D) space. The rotation center, which is derived from an axis point of the human jaw joint, is defined as a point which moves reciprocally in periodic movement. Accordingly, it is called the reciprocating point. Separating a path of the reciprocating point by its turning point, we can divide the path into two parts—the forward path and the backward path. Both paths are identical and hence it appears that any position in one path has its counterpart in the other path. We show that if we have a function corresponding to a pair of positions mentioned in the foregoing, we can estimate the reciprocating point. Then we derive an algorithm which approximates successively the function and the reciprocating point alternatively. This algorithm is proved to be effective for estimating an axis point of the jaw joint.