An Introduction to Screw Theory

Abstract

In this chapter, screw theory is introduced as a preliminary study to give readers an overview of screw theory and its application in compliant mechanism designs. The definition of a screw, as well as the key screw operations, are given in Sect. 2.2, such as the interchange operation of a screw, the screw coordinate transformation and the reciprocal product of two screws. Then the concept of the screw system is introduced in Sect. 2.3, which is an extension of the screw in a group form. Several typical screw systems are defined according to the reciprocal relationship between screws, notably the reciprocal screw system and repelling screw system. Further, the concepts of the screw and screw system are extended to describe the twist and wrench in Sect. 2.4, which are the two fundamental concepts in the further study of compliant mechanisms.