Singularity Surfaces and Maximal Singularity-Free Boxes in the Joint Space of Planar 3-RPR Parallel Manipulators

TL;DR

This paper introduces a method to identify singularity surfaces and maximal singularity-free regions in the joint space of 3-RPR planar parallel manipulators, aiding in trajectory planning and manipulator design.

Contribution

It presents a novel approach to compute joint space singularity surfaces and determine maximal singularity-free boxes, enhancing manipulator planning and design tools.

Findings

Effective computation of singularity surfaces demonstrated

Maximal singularity-free boxes identified for trajectory planning

Potential for improved manipulator design and joint limit selection

Abstract

In this paper, a method to compute joint space singularity surfaces of 3-RPR planar parallel manipulators is first presented. Then, a procedure to determine maximal joint space singularity-free boxes is introduced. Numerical examples are given in order to illustrate graphically the results. This study is of high interest for planning trajectories in the joint space of 3-RPR parallel manipulators and for manipulators design as it may constitute a tool for choosing appropriate joint limits and thus for sizing the link lengths of the manipulator.