Solving the Forward Kinematics of a Planar Three-Legged Platform With Holonomic Higher Pairs-Reference-Cited by-同舟云学术

Solving the Forward Kinematics of a Planar Three-Legged Platform With Holonomic Higher Pairs

Published:1999-06-01 Issue:2 Volume:121 Page:212-219
ISSN:1050-0472
Container-title:Journal of Mechanical Design
language:en
Short-container-title:

Author:

Hayes M. J. D.¹,Husty M. L.²,Zsombor-Murray P. J.³

Affiliation:

1. McGill University, Dept. of Mech. Eng. & Centre for Intelligent Machines, 817 r. Sherbrooke O., Montre´al, Que´bec, Canada

2. Universita¨tsdozent fu¨r Geometrie an der Montanuniversita¨t Leoben, Franz-Josef-Straße 18, A-8700 Leoben, O¨sterreich and McGill University, Centre for Intelligent Machines, 817 r. Sherbrooke O., Montre´al, Que´bec, Canada

3. McGill University, Dept. of Mech. Eng. & Centre for Intelligent Machines, 817 r. Sherbrooke O., Montre´al, Que´bec, Canada and Institut fu¨r Geometrie, TU Graz, Kopernikusgasse 24, A-8010 Graz, O¨sterreich

Abstract

A practical solution procedure for the forward kinematics problem of a fully-parallel planar three-legged platform with holonomic higher pairs is presented. Kinematic mapping is used to represent distinct planar displacements of the end-effector as discrete points in a three dimensional image space. Separate motions of each leg trace skew hyperboloids of one sheet in this space. Therefore, points of intersection of the three hyperboloids represent solutions to the forward kinematics problem. This reduces the problem to solving three simultaneous quadratics. Applications of the platform are discussed and an illustrative numerical example is given.

Publisher

ASME International

Subject

Computer Graphics and Computer-Aided Design,Computer Science Applications,Mechanical Engineering,Mechanics of Materials

Link

http://asmedigitalcollection.asme.org/mechanicaldesign/article-pdf/121/2/212/5575146/212_1.pdf

Reference39 articles.

1. Agrawal S. K. , and PandravadaR., 1992, “Inverse Kinematic Solutions of a Rolling Disk Between Two Planar Manipulators,” Robotic, Spatial Mechanisms, and Mechanical Systems, ASME, DE-Vol. 45, pp. 473–478.

2. Agrawal, S. K., and Pandravada, R., 1993, “Kinematics and Workspace of a Rolling Disk Between Planar Manipulators,” Proc. Am. Control Conf., San Francisco, CA, pp. 741–745.

3. Angeles, J., 1997, Fundamentals of Robotic Mechanical Systems: Theory, Methods, and Algorithms, Springer-Verlag, New York, N.Y., p. 318.

4. Blaschke W. , 1911, “Euklidische Kinematik und nichteuklidische Geometrie,” Zeitschr. Math. Phys., Vol. 60, pp. 61–91.

5. Bottema, O., and Roth, B., 1990, Theoretical Kinematics, (originally published in 1979 by North-Holland Publishing Co., Amsterdam, as Vol. 24 of North-Holland Series in Applied Mathematics and Mechanics) Dover Publications, Inc., New York, N.Y.

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