Direct Geometrico-Static Problem of Underconstrained Cable-Driven Parallel Robots with Five Cables

  • Ghasem Abbasnejad
  • Marco CarricatoEmail author
Conference paper
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 15)


The direct geometrico-static problem of cable-driven parallel robots with five cables is presented. The study provides procedures for the identification of all equilibrium poses of the end-effector when cable lengths are assigned. A least-degree univariate polynomial in the ideal governing the problem is obtained, thus showing that the latter has \(140\) solutions in the complex field. By a continuation technique, an upper bound on the number of real solutions is estimated. An algorithm based on parameter homotopy continuation is developed for the efficient computation of the whole solution set, including equilibrium poses with slack cables.


Cable-driven robots Underconstrained robots Kinematics Statics. 


  1. 1.
    Abbasnejad, G., Carricato, M.: Real solutions of the direct geometrico-static problem of under-constrained cable-driven parallel robots with 3 cables: a numerical investigation. Meccanica 47(7), 1761–1773 (2012)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Bates, D.J., Hauenstein, J.D., Sommese, A.J., Wampler, C.W.: Bertini: software for numerical algebraic geometry.
  3. 3.
    Carricato, M.: Direct geometrico-static problem of underconstrained cable-driven parallel robots with three cables. ASME J. Mech. Rob. 5(3), 031008 (2013)Google Scholar
  4. 4.
    Carricato, M., Abbasnejad, G.: Direct geometrico-static analysis of under-constrained cable-driven parallel robots with 4 cables. In: Bruckmann, T., Pott, A. (eds.) Cable-Driven Parallel Robots, pp. 269–285. Springer-Verlag, Berlin Heidelberg (2013)CrossRefGoogle Scholar
  5. 5.
    Carricato, M., Merlet, J.P.: Stability analysis of underconstrained cable-driven parallel robots. IEEE Trans. Rob. 29(1), 288–296 (2013)CrossRefGoogle Scholar
  6. 6.
    Cox, D., Little, J., O’Shea, D.: Ideals, Varieties, and Algorithms. Springer, New York (2007)CrossRefzbMATHGoogle Scholar
  7. 7.
    Dhingra, A.K., Almadi, A.N., Kohli, D.: A Gröbner–Sylvester hybrid method for closed-form displacement analysis of mechanisms. ASME J. Mech. Des. 122(4), 431–438 (2000)CrossRefGoogle Scholar
  8. 8.
    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: Analysis and Control, pp. 7–16. Kluwer Academic Publishers, Dordrecht (1998)CrossRefGoogle Scholar
  9. 9.
    Faugère, J.C., Gianni, P., Lazard, D., Mora, T.: Efficient computation of zero-dimensional Gröbner bases by change of ordering. J. Symb. Comput. 16(4), 329–344 (1993)CrossRefzbMATHGoogle Scholar
  10. 10.
    McCarthy, J.M.: 21st century kinematics: synthesis, compliance, and tensegrity. ASME J. Mech. Rob. 3(2), 020201/1–3 (2011)Google Scholar
  11. 11.
    Merlet, J.P.: Parallel Robots. Springer, Dordrecht (2006)zbMATHGoogle Scholar
  12. 12.
    Merlet, J.P.: Wire-driven parallel robot: open issues. In: Padois, V., Bidaud, P., Khatib, O. (eds.) Romansy 19—Robot Design, Dynamics and Control, pp. 3–10. Springer, Vienna (2013)CrossRefGoogle Scholar
  13. 13.
    Ming, A., Higuchi, T.: Study on multiple degree-of-freedom positioning mechanism using wires—part 1: concept, design and control. Int. J. Tpn. Soc. Precis. Eng. 28(2), 131–138 (1994)Google Scholar
  14. 14.
    Sommese, A.J., Wampler, C.W.: The Numerical Solution of Systems of Polynomials Arising in Engineering and Science. World Scientific Publishing, Singapore (2005)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Department of Industrial Engineering and Interdepartment Center for Health Sciences and TechnologiesUniversity of BolognaBolognaItaly

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