Classification of Screw Systems Composed of Three Planar Pencils of Lines

Abstract

Screw systems composed of three planar pencils of lines are closely related to the singularity analysis of a number of 3-legged parallel manipulators in which the passive joints in each leg are a spherical joint and a single-DOF (degree-of-freedom) kinematic joint or generalized kinematic joint. This paper systematically classifies the screw systems composed of three planar pencils of lines. The classification is based on the intersection of two planar pencils of lines, the classification of screw systems of order 2, and the reciprocal screw system of the three planar pencils of lines. The classification in this paper is more comprehensive than those in the literature. The above results are illustrated using CAD figures. This work may help readers better understand the geometric characteristics of the singular configuration of a number of 3-legged parallel manipulators.