Analytic manipulators are manipulators for which a characteristic polynomial of fourth degree or lower can be obtained symbolically. Six types of analytic planar parallel manipulators (APPMs) are first generated using the component approach and the method based on the structure of the univariate equation. Of the six types, four are composed of Assur II kinematic chains while the other two are composed of Assur III kinematic chains. The forward displacement analysis (FDA) of two types of APPMs composed of Assur III kinematic chains is then performed. The FDA of each of the two types of APPMs composed of Assur III kinematic chains is reduced to the solution of a univariate cubic equation and a quadratic equation in sequence. It is also proven that the maximum number of real solutions to the FDA is 4 for the planar parallel manipulator with one aligned platform and one orthogonal platform. Examples with 4 real solutions for the planar parallel manipulator with one aligned platform and one orthogonal platform or 6 real solutions for the planar parallel manipulator with two aligned platforms are given at the end of this paper.
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June 2002
Technical Papers
Generation and Forward Displacement Analysis of Analytic Planar Parallel Manipulators
Xianwen Kong,
e-mail: xwkong@gmc.ulaval.ca
Xianwen Kong
De´partement de Ge´nie Me´canique, Universite´ Laval, Que´bec, Que´bec G1K 7P4, Canada
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Cle´ment M. Gosselin, ASME member
Cle´ment M. Gosselin, ASME member
De´partement de Ge´nie Me´canique, Universite´ Laval, Que´bec, Que´bec G1K 7P4, Canada
Search for other works by this author on:
Xianwen Kong
De´partement de Ge´nie Me´canique, Universite´ Laval, Que´bec, Que´bec G1K 7P4, Canada
e-mail: xwkong@gmc.ulaval.ca
Cle´ment M. Gosselin, ASME member
De´partement de Ge´nie Me´canique, Universite´ Laval, Que´bec, Que´bec G1K 7P4, Canada
Contributed by the Mechanisms and Robotics Committee for publication in the Journal of Mechanical Design. Manuscript received Aug. 2000. Associate Editor: G. S. Chirikjian.
J. Mech. Des. Jun 2002, 124(2): 294-300 (7 pages)
Published Online: May 16, 2002
Article history
Online:
May 16, 2002
Citation
Kong, X., and Gosselin, C. M. (May 16, 2002). "Generation and Forward Displacement Analysis of Analytic Planar Parallel Manipulators ." ASME. J. Mech. Des. June 2002; 124(2): 294–300. https://doi.org/10.1115/1.1468224
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