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A method of extracting a kinematically characteristic point from the 3-dimensional motion of a rigid body

This paper describes a problem of estimating a kinematically characteristic point of a rigid body moving in a three-dimensional (3-D) space. We call this point the 1-D characteristic point and denote it by P1. The point P1 is characterized by its motion range which forms a curved line. Hence, if the rigid body moves periodically, we can specify P1 as a point which moves reciprocally. This paper proposes a method of estimating P1. By projecting the orbit of a point onto three planes orthogonal with each other, we reduce this estimation problem to that of solving a set of quadratic equations, and we then provide one of its solutions. In addition, we clarify how measurement errors of the motion propagate to an estimation of P1.