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Research Papers

A Simple Proof That Generic 3-RPR Manipulators Have Two Aspects

[+] Author and Article Information
Michel Coste

 Institut de Recherche Mathématique de Rennes (IRMAR), CNRS: UMR 6625 – Université de Rennes I,35042 Rennes cedex, Francemichel.coste@univ-rennes1.fr

J. Mechanisms Robotics 4(1), 011008 (Feb 03, 2012) (6 pages) doi:10.1115/1.4005333 History: Received June 03, 2010; Revised September 20, 2011; Published February 03, 2012; Online February 03, 2012

Avoiding singularities in the workspace of a parallel robot is an important issue. The case of 3-RPR planar robots is an important subject of theoretical studies. We study the singularities of planar 3-RPR robots by using a new parameterization of the singular locus in a modified workspace. This approach enables us to give a simple alternative proof of a result recently proved by Husty: the complement of the singular locus in the workspace of a generic 3-RPR manipulator has two connected components (called aspects); we also give a procedure to design a singularity-free path connecting any two points in the same aspect. The parameterization introduced in this paper, due to its simple geometric properties, proves to be useful for the study of the singularities of 3-RPR robots.

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Copyright © 2012 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Parameters and coordinates

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Figure 2

Curves of poles and zeros for the Innocenti-Merlet manipulator

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Figure 3

Crossing the curve of poles

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Figure 4

Example of a “similar” manipulator

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Figure 5

Example of a “symmetric” manipulator

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Figure 6

Non generic manipulator with bA  = bB  = 5, hA  = hB  = 3, dA  = −dB  = 2

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