Cusp Points in the Parameter Space of Degenerate 3-RPR Planar Parallel Manipulators

TL;DR

This paper develops an accurate algorithm to identify cusp points in the parameter space of degenerate 3-RPR planar parallel manipulators, enabling classification and increasing the singularity-free workspace.

Contribution

It introduces a refined algorithm combining algebraic methods to precisely determine cusp points and partition parameter space for degenerate 3-RPR manipulators.

Findings

Algorithm accurately determines cusp points

Parameter space partitioned into regions with constant cusp points

Enhanced classification of degenerate manipulators

Abstract

This paper investigates the conditions in the design parameter space for the existence and distribution of the cusp locus for planar parallel manipulators. Cusp points make possible non-singular assembly-mode changing motion, which increases the maximum singularity-free workspace. An accurate algorithm for the determination is proposed amending some imprecisions done by previous existing algorithms. This is combined with methods of Cylindric Algebraic Decomposition, Gr\"obner bases and Discriminant Varieties in order to partition the parameter space into cells with constant number of cusp points. These algorithms will allow us to classify a family of degenerate 3-RPR manipulators.