Instantaneous Kinematics of a Plane in Space Motion

Abstract

A plane under a one-parameter motion envelops a surface called a plane-envelope which is a developable (torse). The properties of a plane-envelope are characterized through the properties of the edge of regression. The paper presents the methodology to obtain the families of planes whose envelopes have the common characteristics. Special cases including stationary plane, cylindrical developable, stationary generator, stationary-point, and helical developable are investigated. It is also shown that, in general, a plane embedded in a body executing Darboux motion envelops a helical developable.