Technical Briefs

Forward Displacement Analysis of a Quadratic Planar Parallel Manipulator: 3-RP̱R Parallel Manipulator With Similar Triangular Platforms

[+] Author and Article Information
Xianwen Kong

Department of Mechanical Engineering, School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, UKx.kong@hw.ac.uk

Clément M. Gosselin

Département de Génie Mécanique, Université Laval, Pavillon Adrien-Pouliot, 1065 Avenue de la Medicine, Québec, QC, G1V 0A6, Canadagosselin@gmc.ulaval.ca

For more details on the singularity-free regions of the 3-RP̱R parallel manipulator, see Refs. 3-4.

J. Mechanisms Robotics 1(2), 024501 (Jan 12, 2009) (3 pages) doi:10.1115/1.3046180 History: Received April 07, 2008; Revised October 26, 2008; Published January 12, 2009

A quadratic parallel manipulator refers to a parallel manipulator with a quadratic characteristic polynomial. This paper revisits the forward displacement analysis (FDA) of a quadratic parallel manipulator: 3-RP̱R planar parallel manipulator with similar triangular platforms. Although it has been revealed numerically elsewhere that for this parallel manipulator, the four solutions to the FDA fall, respectively, into its four singularity-free regions (in its workspace), it is unclear if there exists a one-to-one correspondence between the four formulas, each producing one solution to the FDA, and the four singularity-free regions. Using an algebraic approach, this paper will prove that such a one-to-one correspondence exists. Therefore, a unique solution to the FDA can be obtained in a straightforward way for such a parallel manipulator if the singularity-free region in which it works is specified.

Copyright © 2009 by American Society of Mechanical Engineers
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Grahic Jump Location
Figure 1

3-RP̱R planar parallel manipulator with similar triangular platforms

Grahic Jump Location
Figure 2

Singular surface of 3-RP̱R parallel manipulator with similar triangular platforms (singularity planes, ϕ=−π, ϕ=0, and ϕ=π are omitted)



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