Unifying Screw Geometry and Matrix Transformations

Abstract

Transformation matrices are widely used in robotics for kinematic analysis and trajectory planning. Screw geome try offers better geometric insight into such analyses. In this article we unify the two approaches through the use of invariant properties of orthogonal matrices under simi larity transformations. We give a complete expression for the finite screw motion in terms of the entires of a 3 x 3 dual-number transformation matrix. Our analysis suggests that the finite screw is suitable for trajectory planning, and we develop a concise expression that gives the trans formation matrix describing the displacement at each point along the path of the finite screw motion.