Geometric Constructions for Determining the Screw Reciprocal to Five Lines

Abstract

Screws reciprocal to five lines appear in the inverse Jacobian and statics equations of many serial and parallel robots. By closely examining the geometry of systems of five lines, a set of geometric procedures for computing reciprocal screws is derived. The methodology is based on the fact that one screw in a cylindroid reciprocal to four lines is reciprocal to a fifth independent line. The constructions are easy to implement and provide geometric insight into reciprocal screws and singularities.