The Isoconditioning Loci of Planar Three-DOF Parallel Manipulators

TL;DR

This paper analyzes the singularities and isotropic configurations of a specific class of planar three-DOF parallel manipulators, introducing isoconditioning loci to evaluate and compare their performance across different modes.

Contribution

It introduces the concept of isoconditioning loci for Jacobian matrices in a special class of manipulators, providing a new way to assess their performance and singularities.

Findings

Identified singular configurations of the Jacobian matrices.

Computed isoconditioning loci for performance evaluation.

Compared different working modes based on the loci.

Abstract

The subject of this paper is a special class of parallel manipulators. First, we analyze a family of three-degree-of-freedom manipulators. Two Jacobian matrices appear in the kinematic relations between the joint-rate and the Cartesian-velocity vectors, which are called the "inverse kinematics" and the "direct kinematics" matrices. The singular configurations of these matrices are studied. The isotropic configurations are then studied based on the characteristic length of this manipulator. The isoconditioning loci of all Jacobian matrices are computed to define a global performance index to compare the different working modes.