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Singularity Analysis of a Six-Dof Parallel Manipulator Using Grassmann-Cayley Algebra and Gröbner Bases

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Brain, Body and Machine

Part of the book series: Advances in Intelligent and Soft Computing ((AINSC,volume 83))

Abstract

The subject of this paper deals with the singularity analysis of a sixdof three-legged parallel manipulator for force-feedback interface. To this end, a geometric condition for the manipulator singularities is obtained by means of Grassmann-Cayley algebra; the parallel singularities of the manipulator are computed using Jacobian and Gröbner basis. As a result, the algebraic relations of the singularities satisfied by the orientation variables are reported. Finally, the parallel singularities of the manipulator are plotted in its orientation workspace.

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Author information

Authors and Affiliations

  1. Institut de Recherche en Communications et Cybernétique de Nantes, France

    Stéphane Caro, Guillaume Moroz, Thibault Gayral & Damien Chablat

  2. Department of Mechanical and Aerospace Engineering, Monash University, Australia

    Thibault Gayral & Chao Chen

Authors
  1. Stéphane Caro
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  2. Guillaume Moroz
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  3. Thibault Gayral
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  4. Damien Chablat
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  5. Chao Chen
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Editor information

Editors and Affiliations

  1. Department of Mechanical Engineering & Centre for Intelligent Machines, McGill University, 817 Sherbrooke St. W., H3A 2K6, Montreal, Quebec, Canada

    Jorge Angeles

  2. Department of Electrical and Computer Engineering & Centre for Intelligent Machines, McGill University, 3480 University Street, H3A 2A7, Montreal, Quebec, Canada

    Benoit Boulet  & James J. Clark  & 

  3. Department of Mechanical Engineering & Centre for Intelligent Machines, McGill University, 817 Sherbrooke St.West, H3A 2K6, Montreal, Quebec, Canada

    József Kövecses

  4. School of Computer Science & Centre for Intelligent Machines, McGill University, 3480 University Street, H3A 2A7, Montreal, QC, Canada

    Kaleem Siddiqi

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Caro, S., Moroz, G., Gayral, T., Chablat, D., Chen, C. (2010). Singularity Analysis of a Six-Dof Parallel Manipulator Using Grassmann-Cayley Algebra and Gröbner Bases. In: Angeles, J., Boulet, B., Clark, J.J., Kövecses, J., Siddiqi, K. (eds) Brain, Body and Machine. Advances in Intelligent and Soft Computing, vol 83. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16259-6_26

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  • DOI: https://doi.org/10.1007/978-3-642-16259-6_26

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-16258-9

  • Online ISBN: 978-3-642-16259-6

  • eBook Packages: EngineeringEngineering (R0)

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