The Forward Kinematics of Cable-Driven Parallel Robots with Sagging Cables

  • Jean-Pierre Merlet
  • Julien Alexandre-dit-Sandretto
Conference paper
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 32)


Solving the forward kinematics (FK) of parallel robots is known to be a difficult task and the problem is even more complex for cable driven parallel robot (CDPR): the system of equations that has to be solved is larger than with rigid legs as first the static equations have to be taken into account and, second because the deformation of the cables because of their elasticity and their mass may play a role, while being described by a relatively non algebraic complex model. We consider in this paper any arbitrary CDPR whose cables may present a significant deformation due to their elasticity and own mass and we present for the first time an interval analysis based generic algorithm that allows to calculate in a guaranteed manner all the FK solutions and illustrate its use for a CDPR with 8 cables.


Reference Frame Interval Analysis Parallel Robot Minimal Representation Cable Length 



This research has received partial funding from the European Community’s Seventh Framework Program under grant agreement NMP2-SL-2011-285404 (CABLEBOT).


  1. 1.
    Merlet J-P (2012) The kinematics of the redundant N-1 wire driven parallel robot. In: IEEE international conference on robotics and automation, Saint Paul, 14–18 May 2012, pp 2313–2318Google Scholar
  2. 2.
    Carricato M, Merlet J-P (2013) Stability analysis of underconstrained cable-driven parallel robots. IEEE Trans Robot 29(1):288–296CrossRefGoogle Scholar
  3. 3.
    Carricato M, Abbasnejad G (2012) Direct geometrico-static analysis of under-constrained cable-driven parallel robots with 4 cables. In: 1st international conference on cable-driven parallel robots, Stuttgart, 3–4 Septembre 2012, pp 269–286Google Scholar
  4. 4.
    Jiang Q, Kumar V (2010) The inverse kinematics of 3-d towing. In: ARK, Piran, June 28– July 1, 2010, pp 321–328Google Scholar
  5. 5.
    Merlet J-P (2012) Managing the redundancy of N-1 wire-driven parallel robots. In: ARK, Innsbruck, 25–28 June 2012, pp 405–412Google Scholar
  6. 6.
    Such M et al (2009) An approach based on the catenary equation to deal with static analysis of three dimensional cable structures. Eng Struct 31(9):2162–2170CrossRefGoogle Scholar
  7. 7.
    Gouttefarde M et al (2012) Simplified static analysis of large-dimension parallel cable-driven robots. In IEEE international conference on robotics and automation, Saint Paul, 14–18 May 2012, pp 2299–2305Google Scholar
  8. 8.
    Kozak K et al (2006) Static analysis of cable-driven manipulators with non-negligible cable mass. IEEE Trans Robot 22(3):425–433Google Scholar
  9. 9.
    Riehl N et al (2009) Effects of non-negligible cable mass on the static behavior of large workspace cable-driven parallel mechanisms. In: IEEE international conference on robotics and automation, Kobe, 14–16 May 2009, pp 2193–2198Google Scholar
  10. 10.
    Irvine HM (1981) Cable structures. MIT Press, CambridgeGoogle Scholar
  11. 11.
    Merlet J-P (2004) Solving the forward kinematics of a Gough-type parallel manipulator with interval analysis. Int J Robot Res 23(3):221–236CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Jean-Pierre Merlet
    • 1
  • Julien Alexandre-dit-Sandretto
    • 1
  1. 1.INRIACedexFrance

Personalised recommendations