On the concept of the center of percussion

This paper briefly reviews the concept of the center of percussion of a rigid body, with special emphasis on the requirements for its existence, the two complementary methods used to determine its location, and the system parameters on which its location depends. A consistent generalization of this concept is then proposed for the case when the rigid body is initially moving arbitrarily in three-dimensional inertial space and is restrained in such a way that no impulsive reaction torque can be applied to the body at the point of restraint. The basic requirement for the existence of a center of percussion in this generalized case is identified, and the location of the center of percussion is obtained using one of the two complementary solution methodologies. Six special cases are considered when the existence requirement is satisfied, and these cases are illustrated using examples from common sport situations.