On the Minimum 2-Norm Positive Tension for Wire-Actuated Parallel Manipulators

  • Leila NotashEmail author
Conference paper
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 15)


Utilizing the Moore-Penrose generalized inverse of the Jacobian matrix of wire-actuated parallel robot manipulators, one or more wire tensions could be negative. In this paper, a methodology for calculating positive wire tensions, with minimum 2-norm for tension vector, is presented. A planar parallel manipulator is simulated to illustrate the proposed methodology.


Cable-driven robots Positive wire tension Minimum 2-norm solution 


  1. 1.
    Notash, L., Huang, L.: On the design of fault tolerant parallel manipulators. Manipulators Mech. Mach. Theor. 38(1), 85–101 (2003)CrossRefzbMATHGoogle Scholar
  2. 2.
    Roberts, R.G., Graham, T., Lippitt, T.: On the inverse kinematics, statics, and fault tolerance of cable-suspended robots. J. Robot. Syst. 15(10), 581–597 (1998)CrossRefzbMATHGoogle Scholar
  3. 3.
    Notash, L.: Failure recovery for wrench capability of wire-actuated parallel manipulators. Robotica 30(6), 941–950 (2012)CrossRefGoogle Scholar
  4. 4.
    Notash, L.: Designing positive tension for wire-actuated parallel manipulators. In: Proceedings of the 19th CISM-IFToMM Symposium on Robot Design, Dynamics, and Control (RoManSy) (2012)Google Scholar
  5. 5.
    Notash, L.: Designing positive tension for wire-actuated parallel manipulators. Adv. Mech. Robot. Des. Edu. Res. 14, 251–263 (2013)Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Institute of Complex SystemsQueen’s UniversityKingstonCanada

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