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A planar quaternionapproach to the kinematic synthesis of a parallel manipulator

Published online by Cambridge University Press:  01 July 1997

Andrew P. Murray ,
François Pierrot ,
Pierre Dauchez  and
J. Michael McCarthy
Andrew P. Murray
Affiliation:
Department of Mechanical and Aerospace Engineering, University of Dayton, 300 College Park, Dayton, Ohio 45469-0210, USA
François Pierrot
Affiliation:
LIRMM UMR 9928 CNRS/Université Montpellier II 161 rue Ada, 34392 Montpellier Cedex 5, France
Pierre Dauchez
Affiliation:
LIRMM UMR 9928 CNRS/Université Montpellier II 161 rue Ada, 34392 Montpellier Cedex 5, France
J. Michael McCarthy
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California, Irvine, Irvine, California 92697, USA
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Abstract

In this paper we present a technique for designing planar parallel manipulators with platforms capable of reaching any number of desired poses. The manipulator consists of a platform connected to ground by RPR chains. The set of positions and orientations available to the end-effector of a general RPR chain is mapped into the space of planar quaternions to obtain a quadratic manifold. The coefficients of this constraint manifold are functions of the locations of the base and platform R joints and the distance between them. Evaluating the constraint manifold at each desired pose and defining the limits on the extension of the P joint yields a set of equations. Solutions of these equations determine chains that contain the desired poses as part of their workspaces. Parallel manipulators that can reach the prescribed workspace are assembled from these chains. An example shows the determination of three RPR chains that form a manipulator able to reach a prescribed workspace.

Keywords

Kinematic synthesisParallel manipulatorsRPR chainsQuaternion approach
Type
Research Article
Information
Robotica , Volume 15 , Issue 4 , July 1997 , pp. 361 - 365
Copyright
© 1997 Cambridge University Press

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