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Curvature properties of 6-parametric robot manipulators

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Abstract

The Lie group C6 of all orientation preserving congruences of the Euclidean space E3 has a natural invariant pseudo-Riemannian structure determined by the Klein quadratical form of its Lie algebra.In the paper we connect the acceleration properties of a 6-parametric robot manipulator with the properties of the Levi-Civita connection and its curvature tensor of the pseudo-Riemannian structure of C6.The paper is a continuation of [3].

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References

  1. Helgasson,S.: Differential Geometry and Symmetric Spaces,Acad.Press, N.Y.,London,1962

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  2. O'Neill,B.: Semi-Riemannian geometry with applications to relativity, Acad.Press,N.Y.,London,1983

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  3. Karger,A.: Geometry of the motion of robot manipulators,manuscr. math.62,115–162,1988

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Authors and Affiliations

  1. Matematicko-fyzikální fakulta, Universita Karlova, Sokolovská 83, 186 00, Praha 8, Czechoslovakia

    Adolf Karger

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  1. Adolf Karger
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Karger, A. Curvature properties of 6-parametric robot manipulators. Manuscripta Math 65, 311–328 (1989). https://doi.org/10.1007/BF01303040

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  • DOI: https://doi.org/10.1007/BF01303040

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