Interrelationship between screw systems and corresponding reciprocal systems and applications

This paper discusses the relationship between a screw system and its corres ponding 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 t hen applied to the one-, two-, and three-systems and their corresponding re ciprocal five-, four-and three-systems, and used to predict reciprocal scre ws and the subsequent relationship with the existing screw system. A furthe r application is given by selecting screws to design a system such that a c ertain intersection is desirable between the system and its reciprocal syst em. As a result, a method of generating a one-system of reciprocal screw fr om a five-system and of generating a reciprocal system from a co-reciprocal system is given. (C) 2001 Elsevier Science Ltd. All rights reserved.