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TECHNICAL PAPERS

Unified Kinematic Analysis of General Planar Parallel Manipulators

[+] Author and Article Information
M. J. D. Hayes

Carleton University, Department of Mechanical & Aerospace Engineering, Ottawa, Ontario, K1S 5B6, Canada

P. J. Zsombor-Murray, C. Chen

McGill University, Dep’t. of Mech. Eng. & Center for Intelligent Machines, Montréal, Québec, H3A 2A7, Canada

J. Mech. Des 126(5), 866-874 (Oct 28, 2004) (9 pages) doi:10.1115/1.1767186 History: Received July 01, 2003; Revised January 01, 2004; Online October 28, 2004
Copyright © 2004 by ASME
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References

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Study, E., 1903, Geometrie der Dynamen., Teubner Verlag, Leipzig, Germany.
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Gosselin, C., 1988, “Kinematic Analysis, Optimization and Programming of Parallel Robotic Manipulators,” PhD thesis, Dept. of Mech. Eng., McGill University, Montréal, Qc., Canada.
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Zsombor-Murrary, P. J., Chen, C., and Hayes, M. J. D., 2002, “Direct Kinematic Mapping for General Planar Parallel Manipulators,” Proc. CSME Forum 2002, Kingston, On., Canada.
Hayes,  M. J. D., Husty,  M. L., and Zsombor-Murray,  P. J., 1999, “Solving the Forward Kinematics of a Planar 3-Legged Platform With Holonomic Higher Pairs,” ASME J. Mech. Des., 121(2), pp. 212–219.
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Hayes, M. J. D., and Zsombor-Murray, P. J., 1996, “A Planar Parallel Manipulator With Holonomic Higher Pairs: Inverse Kinematics,” Proc. CSME Forum 1996, Symposium on the Theory of Machines and Mechanisms, Hamilton, On., Canada, pp. 109–116.
Hayes, M. J. D., and Zsombor-Murray, P. J., 1998, “Inverse Kinematics of a Planar Manipulator With Holonomic Higher Pairs,” Recent Advances in Robotic Kinematics, Lenarčič, J., and Husty, M. L., eds., Kluwer Academic Publishers, Dordrecht, The Netherlands, pp. 59–68.

Figures

Grahic Jump Location
The moving frame E and fixed frame Σ for any combination of legs from Table 1
Grahic Jump Location
The seven possible leg topologies
Grahic Jump Location
A platform with three RPR legs
Grahic Jump Location
The three constraint hyperboloids projected into the hyperplane X4=1
Grahic Jump Location
The four real FK solutions for the symmetric RP_R platform
Grahic Jump Location
The image of the two real FK solutions for the asymmetric RPR platform
Grahic Jump Location
The two real FK solutions for the asymmetric RPR platform
Grahic Jump Location
The three constraint surfaces for the one PP-type leg platform
Grahic Jump Location
Intersection of hyperbolic paraboloid and hyperboloid in the image plane of the PP-type leg
Grahic Jump Location
The two real FK solutions for the one PP-type leg platform

Tables

Errata

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