In this paper, we present a general and systematic analysis of cable-driven planar parallel mechanisms. The equations for the velocities are derived, and the forces in the cables are obtained by the principle of virtual work. Then, a detailed analysis of the workspace is performed and an analytical method for the determination of the boundaries of an two-dimensional subset is proposed. The new notion of dynamic workspace is defined, as its shape depends on the accelerations of the end-effector. We demonstrate that any subset of the workspace can be considered as a combination of three-cable subworkspaces, with boundaries being of two kinds: two-cable equilibrium loci and three-cable singularity loci. By using a parametric representation, we see that for the workspace of a simple no-spring mechanism, the two-cable equilibrium loci represent a hyperbolic section, degenerating, in some particular cases, to one or two linear segments. Examples of such loci are presented. We use quadratic programming to choose which sections of the curves constitute the boundaries of the workspace for any particular dynamic state. A detailed example of workspace determination is included for a six-cable mechanism.
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e-mail: gosselin@gmc.ulaval.ca
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March 2005
Article
Determination of the Dynamic Workspace of Cable-Driven Planar Parallel Mechanisms
Guillaume Barrette,
Guillaume Barrette
De´partement de Ge´nie Me´canique, Universite´ Laval, Que´bec, PQ G1K 7P4, Canada
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Cle´ment M. Gosselin
e-mail: gosselin@gmc.ulaval.ca
Cle´ment M. Gosselin
De´partement de Ge´nie Me´canique, Universite´ Laval, Que´bec, PQ G1K 7P4, Canada
Search for other works by this author on:
Guillaume Barrette
De´partement de Ge´nie Me´canique, Universite´ Laval, Que´bec, PQ G1K 7P4, Canada
Cle´ment M. Gosselin
De´partement de Ge´nie Me´canique, Universite´ Laval, Que´bec, PQ G1K 7P4, Canada
e-mail: gosselin@gmc.ulaval.ca
Contributed by the Mechanisms and Robotics Committee for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received May 14, 2004, revised June 3, 2004. Associate Editor: D. C. H. Yang.
J. Mech. Des. Mar 2005, 127(2): 242-248 (7 pages)
Published Online: March 25, 2005
Article history
Received:
May 14, 2004
Revised:
June 3, 2004
Online:
March 25, 2005
Citation
Barrette , G., and Gosselin, C. M. (March 25, 2005). "Determination of the Dynamic Workspace of Cable-Driven Planar Parallel Mechanisms ." ASME. J. Mech. Des. March 2005; 127(2): 242–248. https://doi.org/10.1115/1.1830045
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