Basics of screw theory

Abstract

Screw theory is a powerful mathematical tool for the analysis of spatial mechanisms. A screw consists of two three-dimensional vectors. A screw can be used to denote the position and orientation of a spatial vector, the linear velocity and angular velocity of a rigid body, or a force and a couple, respectively. Therefore, the concept of a screw is convenient in kinematics and dynamics, while the transformation between the screw-based method and vector and matrix methods is straightforward. When applied in mechanism analysis, screw theory has the advantages of clear geometrical concepts, explicit physical meaning, simple expression and convenient algebraic calculation. It is worth noting that the preliminary requirements for screw theory are only linear algebra and basic dynamics in undergraduate level. Thus, screw theory has been widely applied and researchers have used screw theory to make great contribution to many frontier problems in mechanism theory.