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A New Approach to the Direct Geometrico-Static Problem of Cable Suspended Robots Using Kinematic Mapping

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Cable-Driven Parallel Robots

Part of the book series: Mechanisms and Machine Science ((Mechan. Machine Science,volume 53))

Abstract

The direct kinematic problem of \(n-n\ (n=2,3,4,5)\) underconstrained cable manipulators has been solved previously by exploiting the line geometric equilibrium condition and using optimization techniques, heavy algebraic or numeric algebraic computation. In this paper another solution method is proposed. It uses kinematic mapping, distance constraint equations and a local plane constraint. This method can be used for all cases of underconstrained cable manipulators and it is also applicable to the case of \(n-i\) equilibria of \(n-\)cable manipulators. Univariate polynomials are computed in examples for the \(3-3\) and \(5-5\) cases as well as for \(n-1\) equilibria of the \(5-5\) case.

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Notes

  1. 1.

    The kinematic images of planar and spherical displacements subordinate completely to this description because both cases are obtained by three dimensional sub-spaces of \(\mathbb {P}^7\). The corresponding geometry of their image spaces and the algorithms to derive these geometries can be found in [3] p.393ff. resp. [11] p.60ff.

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Acknowledgements

The authors acknowledge the support of the FWF project I 1750-N26 “Kinematic Analysis of Lower-Mobility Parallel Manipulators Using Efficient Algebraic Tools”.

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Authors and Affiliations

  1. Unit Geometry and CAD, University Innsbruck, Innsbruck, Austria

    Manfred Husty & Josef Schadlbauer

  2. CIM, McGill University, Montreal, Canada

    Paul Zsombor-Murray

Authors
  1. Manfred Husty
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  2. Josef Schadlbauer
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  3. Paul Zsombor-Murray
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Corresponding author

Correspondence to Manfred Husty .

Editor information

Editors and Affiliations

  1. Fac. Sciences et de Génie, Université Laval, Quebec City, Québec, Canada

    Clément Gosselin

  2. Mechanical Engineering, Université Laval, Quebec City, Québec, Canada

    Philippe Cardou

  3. Chair for Mechatronics, Universität Duisburg-Essen, Duisburg, Nordrhein-Westfalen, Germany

    Tobias Bruckmann

  4. Fraunhofer-Institut für Produktionstechnik und Automatisierung IPA, Stuttgart, Baden-Württemberg, Germany

    Andreas Pott

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Husty, M., Schadlbauer, J., Zsombor-Murray, P. (2018). A New Approach to the Direct Geometrico-Static Problem of Cable Suspended Robots Using Kinematic Mapping. In: Gosselin, C., Cardou, P., Bruckmann, T., Pott, A. (eds) Cable-Driven Parallel Robots. Mechanisms and Machine Science, vol 53. Springer, Cham. https://doi.org/10.1007/978-3-319-61431-1_9

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  • DOI: https://doi.org/10.1007/978-3-319-61431-1_9

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-61430-4

  • Online ISBN: 978-3-319-61431-1

  • eBook Packages: EngineeringEngineering (R0)

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