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Modelling of Flexible Cable-Driven Parallel Robots Using a Rayleigh-Ritz Approach

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Cable-Driven Parallel Robots

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

Abstract

This paper investigates the use of the Rayleigh-Ritz method to model single degree-of-freedom flexible cable-driven parallel robots (CDPRs) using a set of time-dependent basis functions to discretize cables of varying length. An energy-based model simplification is proposed to further facilitate reduction in the computational load when performing numerical simulations involving the proposed model. Open-loop system responses are used to compare the effect of the energy-based model simplification. Frequency responses are used to compare the influence of the number of basis functions used and to provide a comparison to a lumped-mass model.

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References

  1. Arsenault, M.: Stiffness analysis of a planar 2-DoF cable-suspended mechanism while considering cable mass. In: Cable-Driven Parallel Robots, pp. 405–421. Springer, Berlin (2013)

    Google Scholar 

  2. Caverly, R.J., Forbes, J.R.: Dynamic modeling and noncollocated control of a flexible planar cable-driven manipulator. IEEE Trans. Robot. 30(6), 1386–1397 (2014)

    Article  Google Scholar 

  3. Caverly, R.J., Forbes, J.R., Mohammadshahi, D.: Dynamic modeling and passivity-based control of a single degree of freedom cable-actuated system. IEEE Trans. Control Syst. Technol. 23(3), 898–909 (2015)

    Article  Google Scholar 

  4. Damaren, C.J.: Approximate inverse dynamics and passive feedback for flexible manipulators with large payloads. IEEE Trans. Robot. Autom. 12(1), 131–138 (1996)

    Article  Google Scholar 

  5. Damaren, C.J.: Modal properties and control system design for two-link flexible manipulators. Int. J. Robot. Res. 17(6), 667–678 (1998)

    Article  Google Scholar 

  6. Damaren, C.J.: An adaptive controller for two cooperating flexible manipulators. J. Robot. Syst. 20(1), 15–21 (2003)

    Article  MATH  Google Scholar 

  7. Du, J., Ding, W., Bao, H.: Cable vibration analysis for large workspace cable-driven parallel manipulators. In: Cable-Driven Parallel Robots, pp. 437–449. Springer, Berlin (2013)

    Google Scholar 

  8. Lambert, C., Nahon, M., Chalmers, D.: Implementation of an aerostat positioning system with cable control. IEEE-ASME Trans. Mechatron. 12(1), 32–40 (2007)

    Article  Google Scholar 

  9. Laulusa, A., Bauchau, O.A.: Review of classical approaches for constraint enforcement in multibody systems. J. Comput. Nonlin. Dyn. 3(1), 011004 (2008)

    Article  Google Scholar 

  10. Li, H.: On the static stiffness of incompletely restrained cable-driven robot. In: Cable-Driven Parallel Robots, pp. 55–69. Springer International Publishing (2015)

    Google Scholar 

  11. Miermeister, P., Lächele, M., Boss, R., Masone, C., Schenk, C., Tesch, J., Kerger, M., Teufel, H., Pott, A., Bülthoff, H.H.: The CableRobot simulator large scale motion platform based on cable robot technology. In: IEEE International Conference on Intelligent Robots, pp. 3024–3029 (2016)

    Google Scholar 

  12. Sanderson, C., Curtin, R.: Armadillo: a template-based C++ library for linear algebra. J. Open Source Softw. 1(2), 26–32 (2016)

    Article  Google Scholar 

  13. Walsh, A., Forbes, J.R.: Modeling and control of a wind energy harvesting kite with flexible cables. In: Proceedings of the American Control Conference, pp. 2383–2388 (2015)

    Google Scholar 

  14. Wang, D., Vidyasagar, M.: Passive control of a stiff flexible link. Int. J. Robot. Res. 11(6), 572–578 (1992)

    Article  Google Scholar 

  15. Zhang, Y., Agrawal, S.K., Hagedorn, P.: Longitudinal vibration modeling and control of a flexible transporter system with arbitrarily varying cable lengths. J. Vib. Control 11(3), 431–456 (2005)

    MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, McGill University, 817 Sherbrooke Street West, Montreal, QC, H3A 0C3, Canada

    Harsh Atul Godbole & James Richard Forbes

  2. Department of Aerospace Engineering, University of Michigan, 1320 Beal Avenue, Ann Arbor, MI, 48109, USA

    Ryan James Caverly

Authors
  1. Harsh Atul Godbole
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  2. Ryan James Caverly
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  3. James Richard Forbes
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Corresponding author

Correspondence to Harsh Atul Godbole .

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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Godbole, H.A., Caverly, R.J., Forbes, J.R. (2018). Modelling of Flexible Cable-Driven Parallel Robots Using a Rayleigh-Ritz Approach. 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_1

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  • DOI: https://doi.org/10.1007/978-3-319-61431-1_1

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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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