Title

Joint Workspace of Parallel Kinematic Machines

Document Type

Article

Publication Date

2-2009

Publication Source

Robotics and Computer Integrated Manufacturing

Volume

25

Issue

1

Inclusive pages

57-63

DOI

http://dx.doi.org/10.1016/j.rcim.2007.07.015

Publisher

Pergamon Press

Place of Publication

United Kingdom

ISBN/ISSN

07365845

Peer Reviewed

yes

Abstract

Robot workspace is the set of positions a robot can reach. Workspace is one of the most useful measures for the evaluation of a robot. Workspace is usually defined as the reachable space of the end-effector in Cartesian coordinate system. However, it can be defined in joint coordinate system in terms of joint motions. In this paper, workspace of the end-effector is called task workspace, and workspace of the joint motions is called joint workspace. Joint workspace of a parallel kinematic machine (PKM) is focused, and a tripod machine tool with three degrees of freedom (DOF) is taken as an example. To study the joint workspace of this tripod machine tool, the forward kinematic model is established, and an interpolating approach is proposed to solve this model. The forward kinematic model is used to determine the joint workspace, which occupies a portion of the domain of joint motions. The following contributions have been made in this paper include: (i) a new concept so-called joint workspace has been proposed for design optimization and control of a PKM; (ii) an approach is developed to determine joint workspace based on the structural constraints of a PKM; (iii) it is observed that the trajectory planning in the joint coordinate system is not reliable without taking into considerations of cavities or holes in the joint workspace.

Keywords

Parallel kinematic machine (PKM); Joint workspace; Forward kinematics; Polynomial equations; Trajectory planning; Tripod machine tool; Optimization

Disciplines

Engineering

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