Measuring How Well a Structure Supports Varying External Wrenches

  • François Guay
  • Philippe Cardou
  • Ana Lucia Cruz-Ruiz
  • Stéphane Caro
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 17)


An index is introduced, the minimum degree of constraint satisfaction, which quantifies the robustness of the equilibrium of an object with a single scalar. This index is defined under the assumptions that the object is supported by forces of known lines of action and bounded amplitudes, and that the external perturbation forces and moments vary within a known set of possibilities. A method is proposed to compute the minimum degree of constraint satisfaction by resorting to the quick hull algorithm. The method is then applied to two examples chosen for their simplicity and diversity, as evidence of the broad spectrum of applications that can benefit from the index. The first example tackles the issue of fastening a workpiece, and the second, the workspace of a cable-driven parallel robot. From these numerical experiments, the minimum degree of constraint satisfaction proves useful in grasping, cable-driven parallel robots, Gough-Stewart platforms and other applications.


Kinematic index dexterity manipulability kinematic sensitivity grasping stability cable-driven robot wire-driven robot Gough-Stewart platform 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Angeles, J.: The design of isotropic manipulator architectures in the presence of redundancies. The International Journal of Robotics Research 11(3), 196–201 (1992)CrossRefGoogle Scholar
  2. 2.
    Bouchard, S., Gosselin, C., Moore, B.: On the ability of a cable-driven robot to generate a prescribed set of wrenches. ASME Journal of Mechanisms and Robotics 2(1), 011,010 (2010)Google Scholar
  3. 3.
    Gouttefarde, M., Daney, D., Merlet, J.P.: Interval-analysis-based determination of the wrench-feasible workspace of parallel cable-driven robots. IEEE Transactions on Robotics 27(1), 1–13 (2011)CrossRefGoogle Scholar
  4. 4.
    Khan, W.A., Angeles, J.: The kinetostatic optimization of robotic manipulators: The inverse and the direct problems. ASME Journal of Mechanical Design 128(1), 168–178 (2006)CrossRefGoogle Scholar
  5. 5.
    Merlet, J.P.: Jacobian, manipulability, condition number, and accuracy of parallel robots. ASME Journal of Mechanical Design 128(1), 199–206 (2006)CrossRefGoogle Scholar
  6. 6.
    Park, M.K., Kim, J.W.: Kinematic manipulability of closed chains. In: Advances in Robot Kinematics, pp. 99–108. Portoroz-Bernadin (1996)Google Scholar
  7. 7.
    Salisbury, J.K., Craig, J.J.: Articulated hands: Force control and kinematic issues. The International Journal of Robotics Research 1(4), 4–17 (1982)CrossRefGoogle Scholar
  8. 8.
    Tandirci, M., Angeles, J., Farzam, R.: Characteristic point and the characteristic length of robotic manipulators. In: ASME Design Engineering Conferences, 22nd Biennial Mechanisms Conference (1992)Google Scholar
  9. 9.
    Yoshikawa, T.: Analysis and control of robot manipulators with redundancy. In: Proceedings of the First International Symposium on Robotics Research, Bretton Woods, NH, USA, pp. 735–747 (1983)Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • François Guay
    • 1
  • Philippe Cardou
    • 1
  • Ana Lucia Cruz-Ruiz
    • 2
  • Stéphane Caro
    • 3
  1. 1.Laboratoire de robotique, Département de génie mécaniqueUniversité LavalQuebec CityCanada
  2. 2.IRCCyNÉcole Centrale de NantesNantesFrance
  3. 3.CNRS/IRCCyNNantesFrance

Personalised recommendations