Instantaneous Kinematics of a Plane in Spherical Motion

Abstract

In this paper, an analytical method to study the instantaneous motion of a plane subjected to a space motion is investigated. As a point traces a point-path, a plane under a one-parameter space motion generates a plane-path which envelops a developable ruled surface. A plane-envelope is characterized through its edge of regression by a set of curvature-like dimensionless numbers. For a spherical motion, the families of planes whose envelops have the common characteristic numbers are found. Some special cases which are analogous to the subjects in the infinitesimal Burmester theory are also examined.