On the Basis Screws and Screw Systems of Point-Line and Line Displacements

Abstract

This paper presents a method to derive and characterize the basis screws and the screw systems associated with a general point-line displacement. The transformation of a point-line between positions is depicted as a screw displacement about their common normal accompanied by a pure translation along the point-line. Such an interpretation of point-line displacement leads to a simple screw triangle used in deriving the basis screws and the screw system. The expressions of the basis screws and screw systems are simple and concise while the geometric meaning explicit. The result from basis screws of point-line displacement is also extended to line displacement and an example is given to demonstrate the simplicity of the method.