A Unified Approach to Forward Kinematics for Cable-Driven Parallel Robots Based on Energy

  • Andreas PottEmail author
  • Philipp Tempel
Conference paper
Part of the Springer Proceedings in Advanced Robotics book series (SPAR, volume 8)


This paper deals with a unified approach to forward kinematics for both over-constrained and under-constrained cable robots. Moreover, little assumptions on the cable model are required. This makes the proposed method applicable to a variety of currently discussed cable models including the standard model, an elastic cable model, static cable sagging, or even finite elements model. Solutions to the forward kinematics problem are computed by minimizing potential energy in the cable robot. As shown in this paper, the method unifies forward kinematics of both over-constrained and under-constrained cable robots.


Cable-driven parallel robots Forward kinematics Cable model 



The authors would like to thank the German Research Foundation (DFG) for financial support of the project within the Cluster of Excellence in Simulation Technology (EXC 310/1) at the University of Stuttgart.


  1. 1.
    Afshari, A., Meghdari, A.: New Jacobian matrix and equations of motion for a 6 d.o.f cable-driven robot. Int. J. Adv. Robot. Syst. 4(1), 63–68 (2007)CrossRefGoogle Scholar
  2. 2.
    Behzadipour, S., Khajepour, A.: Stiffness of cable-based parallel manipulators with application to stability analysis. J. Mech. Des. 128(1), 303–310 (2006)CrossRefGoogle Scholar
  3. 3.
    Carricato, M., Merlet, J.-P.: Stability analysis of underconstrained cable-driven parallel robots. IEEE Trans. Robot. 29(1), 289–296 (2013)CrossRefGoogle Scholar
  4. 4.
    Nguyen, D.Q., Gouttefarde, M., Company, O., Pierrot, F.: On the simplifications of cable model in static analysis of large-dimension cable-driven parallel robots. In: IEEE International Conference on Intelligent Robots and Systems (IROS) (2013)Google Scholar
  5. 5.
    Dietmaier, P.: The Stewart-Gough platform of general geometry can have 40 real postures. In: Lenarčič, J., Husty, M.L. (eds.) Advances in Robot Kinematics, pp. 7–16. Kluwer Academic Publishers, Salzburg, Austria (1998)Google Scholar
  6. 6.
    Hansen, E., Walster, G.W.: Global Optimization Using Interval Analysis. Marcel Dekker, NEw York (2004)zbMATHGoogle Scholar
  7. 7.
    Husty, M.L.: An algorithm for solving the direct kinematic of Stewart-Gough-type platforms. Mech. Mach. Theor. 31(4), 365–380 (1996)CrossRefGoogle Scholar
  8. 8.
    Khosravi, M.A., Taghirad, H.D.: Dynamic modeling and control of parallel robots with elastic cables: singular perturbation approach. IEEE Trans. Robot. 30(3), 694–704 (2014)CrossRefGoogle Scholar
  9. 9.
    Kraus, W.: Force control of cable-driven parallel robots. Ph.D. thesis. Universität Stuttgart, Germany (2015)Google Scholar
  10. 10.
    Merlet, J.-P.: Solving the forward kinematics of a gough-type parallel manipulator with interval analysis. Int. J. Robot. Res. 23(3), 221–235 (2004)CrossRefGoogle Scholar
  11. 11.
    Merlet, J.-P.: A generic numerical continuation scheme for solving the direct kinematics of cable-driven parallel robot with deformable cables. In: IEEE International Conference on Intelligent Robots and Systems, pp. 4337–4343 (2016)Google Scholar
  12. 12.
    Merlet, J.-P., Alexandre dit Sandretto, J.: The forward kinematics of cable-driven parallel robots with sagging cables. In: Pott A., Bruckmann T. (eds) Cable-Driven Parallel Robots, pp. 3–15. Springer, Cham (2014)Google Scholar
  13. 13.
    Ming, A., Higuchi, T.: Study on multiple degree-of-freedom positioning mechanism using wires (part 2) - development of a planar completely restrained positioning Mechanism. Int. J. Japan Soc. Precis. Eng. 28(3), 235–242 (1994)Google Scholar
  14. 14.
    Pott, A.: An algorithm for real-time forward kinematics of cable-driven parallel robots. In: Advances in Robot Kinematics, pp. 529–538. Springer, Dordrecht (2010)CrossRefGoogle Scholar
  15. 15.
    Pott, A., Schmidt, V.: On the forward kinematics of cable-driven parallel robots. In: IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 3182–3187 (2015)Google Scholar
  16. 16.
    Schmidt, V., Pott, A.: Implementing extended kinematics of a cable-driven parallel robot in real-time. In: Cable-Driven Parallel Robots. Mechanisms and Machine Science, pp. 287–298. Springer, Heidelberg (2013)Google Scholar

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© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Institute for Control Engineering of Machine Tools and Manufacturing Units, Fraunhofer IPAUniversity of StuttgartStuttgartGermany
  2. 2.Institute for Control Engineering of Machine Tools and Manufacturing UnitsUniversity of StuttgartStuttgartGermany

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