Application of Screw Theory to Rigid Body Dynamics

Abstract

This paper applies screw theory to the dynamic analysis of a rigid body in general spatial motion. Particular emphasis is placed upon the geometric interpretation of the velocity screw, the momentum screw, and the force screw which provide valuable physical insight into the dynamic behavior of the rigid body. The geometric relation between the velocity screw and the momentum screw is discussed in some detail. The paper shows that the dual angle between the two screws provides insight into the kinetics of the rigid body. The dynamic state of motion of the body is then described by a dual vector equation, referred to as the dual Euler equation. The paper shows that the geometric equivalent of the dual Euler equation is a spatial triangle which can be used as a graphical method of solution, or as a check, of the analytical formulation. The concepts introduced in this paper are illustrated by the well-known example of a thin, homogeneous, circular disk rolling without slipping on a flat horizontal surface. With the widespread use of computer graphics and computer-aided design, the geometric approach presented here will prove useful in the graphical representation of the dynamics of a rigid body.