ON DERIVING INFINITESIMAL TWISTS AND VELOCITY SCREWS FROM FINITE DISPLACEMENT SCREWS

摘要

Suppose that every spatial location B available to a body is specified by a finite displacement screw - either a sin-screw S or tan-screw T which describes displacement of the body into location B from some reference location. The paper examines the relationship between the spatial derivative of the finite displacement screw S or T and the twist, or infinitesimal displacement screw, which is available to the body at B. Since the body is mobile in location B if and only if a non-null twist exists there, its mobility can be related to the derivative of the screw S or T. In extension, the velocity screw of the body - being the temporal rate of twisting - is related to the temporal rate of change of the finite displacement screw.