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Stiffness Analysis of a Planar 2-DoF Cable-Suspended Mechanism While Considering Cable Mass

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Cable-Driven Parallel Robots

Part of the book series: Mechanisms and Machine Science ((Mechan. Machine Science,volume 12))

Abstract

The mass of the cables is not considered in most existing research on cable-driven mechanisms (CDM). Moreover, of those papers where cable mass is considered, few have examined its effects on mechanism stiffness. The research presented herein seeks to better understand these effects with regards to a planar two-degree-of-freedom suspended CDM. The mechanism’s stiffness matrix is first developed and then used to generate mappings of intuitive stiffness indices over the workspace. The sagging of the cables under their own weight is found to heavily influence mechanism stiffness. The importance of maintaining a minimum level of cable tension to minimize the effect of cable sagging on the mechanism’s stiffness and workspace is also demonstrated.

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Notes

  1. 1.

    The task of computing the cable rest lengths corresponding to a given pose of the EE is referred to here as the inverse kinematic problem though its solution also requires the consideration of the mechanism’s static equilibrium equations.

  2. 2.

    In the interest of brevity, the details regarding the development of the model for the elastic catenary are not included in this paper.

  3. 3.

    It is recognized that other algorithms may be more efficient in solving this problem. However, it is not an aim of this work to attempt to identify them.

  4. 4.

    This condition is optional.

  5. 5.

    While this holds for the planar 2-DoF suspended CDM, it does not for all suspended CDMs [21].

  6. 6.

    Though the minimum tension constraint (i.e., \(t_{\text{ min}_c}\)) does not constrain the workspace in the cases discussed here, it has the potential to do so depending on the mechanism geometry and mechanical properties.

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Acknowledgments

The author wishes to thank the NSERC (Natural Science and Engineering Research Council of Canada) for its financial support.

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Authors and Affiliations

  1. Department of Mechanical and Aerospace Engineering, Royal Military College of Canada, Kingston, K7K 7B4, Ontario, Canada

    Marc Arsenault

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  1. Marc Arsenault
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Correspondence to Marc Arsenault .

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Editors and Affiliations

  1. Universität Duisburg-Essen, Lotharstraße 1, Duisburg, 47057, Germany

    Tobias Bruckmann

  2. technik und Automatisierung IPA, Fraunhofer-Institut für Produktions-, Nobelstr 12, Stuttgart, 70569, Germany

    Andreas Pott

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Arsenault, M. (2013). Stiffness Analysis of a Planar 2-DoF Cable-Suspended Mechanism While Considering Cable Mass. In: Bruckmann, T., Pott, A. (eds) Cable-Driven Parallel Robots. Mechanisms and Machine Science, vol 12. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31988-4_25

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  • DOI: https://doi.org/10.1007/978-3-642-31988-4_25

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  • Print ISBN: 978-3-642-31987-7

  • Online ISBN: 978-3-642-31988-4

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