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Research Papers

Static of Parallel Manipulators and Closeness to Singularity

[+] Author and Article Information
J. Hubert

 Institut National de Recherche en Informatique et en Automatique, BP 93, 06902 Sophia-Antipolis, Francejulien.hubert@inria.fr

J.-P. Merlet

 Institut National de Recherche en Informatique et en Automatique, BP 93, 06902 Sophia-Antipolis, Francejean-pierre.merlet@inria.fr

J. Mechanisms Robotics 1(1), 011011 (Aug 05, 2008) (6 pages) doi:10.1115/1.2961335 History: Received June 02, 2008; Revised June 20, 2008; Published August 05, 2008

Singularity is a major problem for parallel robots as in these configurations the robot cannot be controlled, and there may be infinite forces/torques in its joints, possibly leading to a robot breakdown. In the recent years classification and detection of singularities have made large progress. However, the issue of closeness to a singularity is still open and we propose in this paper an approach that is based on a static analysis. Our measure of closeness to a singularity is based on the very practical issue of having the joint forces/torques lower than a given threshold. We consider a planar parallel robot whose end-effector has a constant orientation and is submitted to a known wrench and we show that it is possible to compute the border of the region that describes all possible end-effector location for which the joint forces are lower than the fixed threshold.

FIGURES IN THIS ARTICLE
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Copyright © 2008 by American Society of Mechanical Engineers
Topics: Force , Robots , Algorithms
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References

Figures

Grahic Jump Location
Figure 3

The curves involved and the force workspace border for θ=−0.1rad and F=(4,0,0) (the force workspace is constituted of the region with a + sign)

Grahic Jump Location
Figure 4

The force workspace for θ=2.91rad and F=(0,0,5). The regions of the force workspace are denoted by a +.

Grahic Jump Location
Figure 5

The constraints induced by the minimal leg lengths impose that the platform center must lie outside the region defined by the union of the three dashed circles. Without taking these constraints into account the force workspace is constituted of two components while the real force workspace has four components (the region delimited by the border in thick line).

Grahic Jump Location
Figure 2

The curves involved and the force workspace border for θ=0.1rad and F=(4,0,0) (the force workspace is constituted of the region with a + sign)

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