Practical Stability of Under-Constrained Cable-Suspended Parallel Robots

  • Dragoljub SurdilovicEmail author
  • Jelena Radojicic
Conference paper
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 74)


This paper, motivated by the development of a novel gait rehabilitation system, presents a mechanical approach for the dynamic modelling and analysis of equilibrium stability of under-constrained cable suspended parallel robots. These types of cable robots exhibit interesting characteristics of self-motion in the Jacobian null-space. Modelling and understanding of this motion is essential for their applications. It is demonstrated that both a wrench consistency test and proof of stability conditions, derived for real robots with a pulley mechanism, play a crucial role for practical equilibrium stability assessment. Thereby dynamic simulation of the null-space motion help to analyse robustness of the equilibrium against perturbations. Several examples with a 4-4 type robots illustrate the theoretical analysis.


cable-driven parallel robots under-constrained cable suspended structures equilibrium stability analysis gait rehabilitation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    B. Zi and S. Qian, Design, Analysis and Control of Cable-Suspended Parallel Ro-bots and Its Application, Springer-Verlag, 2017.Google Scholar
  2. [2]
    J-P. Merlet, On the robustness of cable configurations of suspended cable-driven parallel robots, Proc. 14th IFTOMM World-Congress, Taipei, October 2015.Google Scholar
  3. [3]
    J. Albus, R. Bostelman and N. Dagalakis, The NIST Robocrane, Journal of Robotic Systems, Vol. 10, No. 5, 1993, pp.709-724.CrossRefGoogle Scholar
  4. [4]
    N. Michael, S. Kim, J. Fink and V. Kumar, Kinematics and Statics of Cooperative Multi-Robot Aerial Manipulation with Cables, Proceedings of ASME 2009 IDETC/CIE Conference, San Diego, pp. 83-91.Google Scholar
  5. [5]
    J. Fink, N. Michael, S. Kim and V. Kumar, Planning and control for cooperative manipulation and transportation with aerial robots, The Int. Journal of Robotic Research, 30(3), 2015, pp. 324-334.Google Scholar
  6. [6]
    M. Carricato and J-P. Merlet, Stability Analysis of Underconstrained Cable-Driven Parallel Robots, IEEE Transaction on Robotics, Vol. 29, No. 1, February 2013, pp. 288-296.CrossRefGoogle Scholar
  7. [7]
    Karger, A. and Husty, M.L. (1998). Classification of all self-motions of the original Stewart-Gough platform. Computer-Aided Design 30(3), 1998, pp. 205–215.CrossRefGoogle Scholar
  8. [8]
    G. Abbasnejad and M. Carricato, Direct Geometrico-Static Problem of Undercon-strained Cable-Driven Parallel Robots with n-Cables, IEEE Transaction on Robotics, Vol. 31, No. 2, April 2015, pp. 468-478.Google Scholar
  9. [9]
    A. Berti, J-P. Merlet and M. Carricato, Solving the direct geometrico-static problem of underconstrained cable-driven parallel robots by interval-analysis, The Int. Journal of Robotic Research, Vol. 36, 2017, pp. 723-729.Google Scholar
  10. [10]
    J-F. Collard and P. Cordou, Computing the lowest Equilibrium Pose of a Cable-Suspended Rigid Body, Optim. Eng. 14, 2013, pp. 457–476.MathSciNetCrossRefGoogle Scholar
  11. [11]
    G. Liwen, X. Huayang and L. Zhihua, Kinematic analysis of cable-driven parallel mechanisms based on minimum potential energy principle, Advances in Mechanical Engineering, Vol. 7(12), 2015, pp. 1-11.CrossRefGoogle Scholar
  12. [12]
    A. Pott, Influence of pulley kinematics on cable-driven parallel robots, In Latest Advances in Computation Kinematics (Ed. J. Lenarcic), Springer, 2012, pp. 197-204.Google Scholar
  13. [13]
    J. LaSalle and S. Lefshetz, Stability by Lyapunov’s Direct Method, Academic Press, New York, 1961.Google Scholar
  14. [14]
    D. Surdilovic. R. Bernhardt, T. Schmidt and J. Zhang, STRING-MAN: A Novel Wire Robot for Gait Rehabilitation, in Advances in Rehabilitation Robotics, Lecture Notes in Control and Information Sciences, Vol. 306, 2004, pp. 413-424.Google Scholar
  15. [15]
    M. Carricato and G. Abasnejad, Direct Geometrico-Static Analysis of Under-Constrained Cable-Driven Parallel Robots with 4 Cables, Cable-Driven Parallel Robots (Eds. T. Bruckmann and A. Pott), Springer, 2013, pp. 269-285.Google Scholar
  16. [16]
    G. Stepan, A. Toth, L. Kovacs, G. Bolmsjo, G. Nikoleris, D. Surdilovic, A. Conrad, A. Gasteratos,, N. Kyriakoulis R, J. Canou, T. Smith, W. Harwin, R. Loureiro, R. Lopez and R. Moreno, ACROBOTER: a ceiling based crawling, hoisting and swinging service ro-bot platform, Proceedings of beyond gray droids: domestic robot design for the 21st century workshop at HCI 2009.Google Scholar
  17. [17]
    O.A. Bauchau and A. Laulusa, Review of Contemporary Approaches for Constraint Enforcement in Multibody Systems, Journal of Computational and Nonlinear Dynamics, 3(1), 2008, pp. 1-8.CrossRefGoogle Scholar
  18. [18]
    X-S. Yang, Practical stability in dynamical systems, Chaos, Solitons and Fractals, Pergamon, 11 (2000), pp. 1087-1092.Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Fraunhofer Institute for Production Systems and Design Technology IPK-Berlin, Department Robotics and AutomationBerlinGermany

Personalised recommendations