Interrelationship between screw systems and corresponding reciprocal systems and applications

Abstract

This paper discusses the relationship between a screw system and its corresponding reciprocal system based upon set theory, proposes a theorem, makes a proposition with corollaries to specify the relationship between the two screw systems and characterises all cases in screw systems. The theory is then applied to the one-, two-, and three-systems and their corresponding reciprocal five-, four-and three-systems, and used to predict reciprocal screws and the subsequent relationship with the existing screw system. A further application is given by selecting screws to design a system such that a certain intersection is desirable between the system and its reciprocal system. As a result, a method of generating a one-system of reciprocal screw from a five-system and of generating a reciprocal system from a co-reciprocal system is given.