The Isoconditioning Loci of A Class of Closed-Chain Manipulators

TL;DR

This paper investigates the isoconditioning loci of a special class of closed-chain manipulators, revealing their geometric properties and extending the analysis to a three-degree-of-freedom hybrid manipulator.

Contribution

It introduces the concept of isoconditioning loci for a class of closed-chain manipulators and characterizes their geometric nature, including the extension to a 3-DOF hybrid manipulator.

Findings

Isoconditioning loci are the coupler points of a four-bar linkage.

Loci are surfaces of revolution generated by 2-DOF isoconditioning curves.

The analysis provides insights into manipulator workspace conditioning.

Abstract

The subject of this paper is a special class of closed-chain manipulators. First, we analyze a family of two-degree-of-freedom (dof) five-bar planar linkages. 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. It is shown that the loci of points of the workspace where the condition number of the direct-kinematics matrix remains constant, i.e., the isoconditioning loci, are the coupler points of the four-bar linkage obtained upon locking the middle joint of the linkage. Furthermore, if the line of centers of the two actuated revolutes is used as the axis of a third actuated revolute, then a three-dof hybrid manipulator is obtained. The isoconditioning loci of this manipulator are surfaces of revolution generated by the isoconditioning curves of the two-dof manipulator, whose axis of symmetry is that of the third actuated revolute.