Identification of Canonical Basis of Screw Systems Using General-Special Decomposition

Abstract

The theory of screws plays a fundamental role in the field of mechanisms and robotics. Based on the rank-one decomposition of positive semidefinite (PSD) matrices, this paper presents a new algorithm to identify the canonical basis of high-order screw systems. Using the proposed approach, a screw system can be decomposed into the direct sum of two subsystems, which are referred to as the general and special subsystems, respectively. By a particular choice of the general subsystem, the canonical basis of the original system can be obtained by the direct combination of the subsystems' principal elements. In the proposed decomposition, not only the canonical form of the screw system but also the corresponding distribution of all those possible base elements can be determined in a straightforward manner.