Singular curves and cusp points in the joint space of 3-RPR parallel manipulators

TL;DR

This paper analyzes the singular and cusp points in the joint space of 3-RPR parallel manipulators, revealing how cusp points enable nonsingular assembly mode changes and aiding in design and trajectory planning.

Contribution

It introduces a method to identify cusp points in any 2D slice of the joint space, expanding understanding of manipulator kinematics.

Findings

Number of cusp points varies from zero to eight.

Cusp points facilitate nonsingular assembly mode changes.

Applications in design and trajectory planning.

Abstract

This paper investigates the singular curves in two-dimensional slices of 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 reviews an important previous work, which, to the authors' knowledge, has never been exploited yet. Second, it determines the cusp points in any two-dimensional slice of the joint space. First results show that the number of cusp points may vary from zero to eight. This work finds applications in both design and trajectory planning.