Joint space and workspace analysis of a two-DOF closed-chain manipulator

TL;DR

This paper introduces an interval analysis-based method combined with quadtree modeling to accurately compute maximal singularity-free domains in joint space and workspace of a 2-DOF planar parallel mechanism, improving detection and efficiency.

Contribution

It presents a novel approach integrating interval analysis with quadtree models for precise and efficient singularity domain computation in parallel mechanisms.

Findings

Interval analysis ensures no singularities are missed.

Method reduces computation time compared to pure discretization.

Successfully applied to a 2-DOF planar mechanism.

Abstract

The aim of this paper is to compute of the generalized aspects, i.e. the maximal singularity-free domains in the Cartesian product of the joint space and workspace, for a planar parallel mechanism in using quadtree model and interval analysis based method. The parallel mechanisms can admit several solutions to the inverses and the direct kinematic models. These singular configurations divide the joint space and the workspace in several not connected domains. To compute this domains, the quadtree model can be made by using a discretization of the space. Unfortunately, with this method, some singular configurations cannot be detected as a single point in the joint space. The interval analysis based method allow us to assure that no singularities are not found and to reduce the computing times. This approach is tested on a simple planar parallel mechanism with two degrees of freedom.