Singular Curves in the Joint Space and Cusp Points of 3-RPR parallel manipulators

TL;DR

This paper explores the singular curves and cusp points in the joint space of 3-RPR planar parallel manipulators, providing methods to compute these features and detect cusp points crucial for kinematic analysis.

Contribution

It introduces a novel method to compute joint space singular curves and an algorithm to detect all cusp points in 3-RPR manipulators.

Findings

Computed singular curves in the joint space.

Developed an algorithm for cusp point detection.

Enhanced understanding of kinematic behavior around cusp points.

Abstract

This paper investigates the singular curves in the joint space of a family of planar parallel manipulators. It focuses on special points, referred to as cusp points, which may appear on these curves. Cusp points play an important role in the kinematic behavior of parallel manipulators since they make possible a nonsingular change of assembly mode. The purpose of this study is twofold. First, it exposes a method to compute joint space singular curves of 3-RPR planar parallel manipulators. Second, it presents an algorithm for detecting and computing all cusp points in the joint space of these same manipulators.