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A Short Note on Point Singularities for Robot Manipulators

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Abstract

We consider a specific type of singularities for kinematic chains, so-called point singularities. These were characterized in 2005 by Borcea and Streinu. We give a new proof for this result in the framework of the Exterior Algebra. As an illustration we give an exhaustive list of the point singularities of a specific robot manipulator.

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References

  1. Ball, R.S.: A Treatise on the Theory of Screws. Cambridge University Press, Cambridge (1900)

    Google Scholar 

  2. Barnabei, M., Bini, A., Rota, G.-C.: On the exterior calculus of invariant theory. J. Algebra 96, 120–160 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  3. Borcea, C., Streinu, I.: Singularities of hinge structures. In: Efficient Methods in Algebraic Geometry. MEGA ’05 (2005)

  4. Crapo, H.H., Whiteley, W.: Statics of frameworks and motions of panel structures: a projective geometric introduction. Struct. Topol. 6, 43–82 (1982)

    MathSciNet  Google Scholar 

  5. Dandurand, A.: The rigidity of compound spatial grids. Struct. Topol. 10, 41–56 (1984)

    MATH  MathSciNet  Google Scholar 

  6. Hao, F., McCarthy, J.M.: Conditions for line-based singularities in spatial platform manipulators. J. Robot. Syst. 15(1), 43–55 (1998)

    Article  MATH  Google Scholar 

  7. Murray, R., Li, Z., Sastry, S.: A Mathematical Introduction to Robot Manipulation. Taylor & Francis, Bristol (1994)

    Google Scholar 

  8. Pottmann, H., Wallner, J.: Computational Line Geometry. Springer, Berlin (2001)

    MATH  Google Scholar 

  9. White, N.: Grassmann-Cayley algebra and robotics. J. Intell. Robot. Syst. 11(1–2), 91–107 (1994)

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Industrial Sciences and Technology, Karel de Grote-Hogeschool, Antwerp, Belgium

    Rudi Penne & Erwin Smet

  2. Department of Mathematics and Computer Science, University of Antwerp, Antwerp, Belgium

    Przemyslaw Klosiewicz

Authors
  1. Rudi Penne
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  2. Erwin Smet
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  3. Przemyslaw Klosiewicz
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Correspondence to Rudi Penne.

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Penne, R., Smet, E. & Klosiewicz, P. A Short Note on Point Singularities for Robot Manipulators. J Intell Robot Syst 62, 205–216 (2011). https://doi.org/10.1007/s10846-010-9444-5

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  • DOI: https://doi.org/10.1007/s10846-010-9444-5

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