A Geometric Interpretation of Finite Screw Systems Using the Bisecting Linear Line Complex

Abstract

This paper uses the concept of bisecting linear line complex of the two position theory in kinematics to present a geometric foundation for finite displacement screw systems, with an emphasis on incompletely specified displacement of points. It is shown that the bisecting linear line complex arising from the finite displacement of points is subject to a reciprocal condition if a specific definition of pitch of finite screws is used. The screw systems of finite displacements are then characterized in terms of intersections of bisecting linear line complexes. The line varieties corresponding to the two-system and four-system associated with finite displacements of two points and a point, respectively, are illustrated. This paper demonstrates that the bisecting linear line complex provides a geometric framework for studying finite and infinitesimal kinematics.