Singularity Analysis of Limited-dof Parallel Manipulators using Grassmann-Cayley Algebra

TL;DR

This paper provides a geometric characterization of singularities in limited-DOF parallel manipulators using Grassmann-Cayley algebra, without requiring passive spherical joints, and illustrates with three example robots.

Contribution

It introduces a novel geometric approach to analyze singularities in limited-DOF manipulators using Grassmann-Cayley algebra, removing the need for passive joints.

Findings

Geometric conditions for singularities are formulated using Grassmann-Cayley algebra.

The method applies to manipulators without passive spherical joints.

Three example robots demonstrate the approach.

Abstract

This paper characterizes geometrically the singularities of limited DOF parallel manipulators. The geometric conditions associated with the dependency of six Pl\"ucker vector of lines (finite and infinite) constituting the rows of the inverse Jacobian matrix are formulated using Grassmann-Cayley algebra. Manipulators under consideration do not need to have a passive spherical joint somewhere in each leg. This study is illustrated with three example robots