Analysis Methods for the 3-RRR with Uncertainties in the Design Parameters

  • Joshua K. Pickard
  • Juan A. Carretero
  • Jean-Pierre Merlet
Part of the Springer Proceedings in Advanced Robotics book series (SPAR, volume 4)


Accounting for uncertainties in the design variables of a parallel manipulator is important for a reliable analysis of a mechanism. The design of the 3-RRR planar parallel manipulator is modelled with uncertainties. Interval analysis techniques are utilised to solve for the reachable workspace and the collision-free workspace. It is necessary to ensure that a fabricated design can achieve some desired criteria. Here, we consider generating a desired set of wrenches at the end-effector. The wrench capabilities under uncertainties are verified throughout the collision-free workspace. The results describe the set of poses which are guaranteed to be collision free and satisfy the desired wrench capabilities given the uncertainties in the specified design.


Interval analysis Self-collisions Wrench workspace 



The authors would like to thank the Natural Sciences and Engineering Research Council of Canada (NSERC), Mitacs, and Inria for their funding of this research.


  1. 1.
    Bouchard, S., Gosselin, C.M.: Workspace optimization of a very large cable-driven parallel mechanism for a radiotelescope application. In: Proceedings of the 2007 ASME DETC, Las Vegas, Nevada, USA, 4–7 Sept 2007Google Scholar
  2. 2.
    Caro, S., Chablat, D., Goldsztejn, A., Ishii, D., Jermann, C.: A branch and prune algorithm for the computation of generalized aspects of parallel robots. Artif. Intell. 211, 34–50 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Gouttefarde, M., Daney, D., Merlet, J.: Interval-analysis-based determination of the wrench-feasible workspace of parallel cable-driven robots. IEEE Trans. Robot. 27(1), 1–13 (2011)CrossRefzbMATHGoogle Scholar
  4. 4.
    Jaulin, L., Kieffer, M., Didrit, O., Walter, E.: Applied Interval Analysis. Springer, Berlin (2001)Google Scholar
  5. 5.
    Ketchel, J.S., Larochelle, P.M.: Self-collision detection in spatial closed chains. J. Mech. Design 130(9), 92305-1–92305-9 (2008)Google Scholar
  6. 6.
    Merlet, J.P., Daney, D.: Legs interference checking of parallel robots over a given workspace or trajectory. In: Proceedings 2006 IEEE ICRA, pp. 757–762, Orlando, FL, 15–19 May (2006)Google Scholar
  7. 7.
    Moore, R., Kearfott, R., Cloud, M.: Introduction to Interval Analysis. Society for Industrial and Applied Mathematics, Philadelphia (2009)Google Scholar
  8. 8.
    Oetomo, D., Daney, D., Shirinsadeh, B., Merlet, J.: An interval-based method for workspace analysis of planar flexure-jointed mechanism. J. Mech. Design 131(1), 011014-1–011014-11 (2008)Google Scholar
  9. 9.
    Pickard, J., Carretero, J.: Design optimisation of the 3-\({\underline{\rm R}}\)RR planar parallel manipulator via wrench capability analysis. In: Proceedings of 14th World Congress, Taipei, Taiwan, 25–30 Oct (2015)Google Scholar
  10. 10.
    Pickard, J., Carretero, J.: An interval method for wrench workspace determination of parallel manipulator architectures. In: Proceedings of 2015 CCToMM M\(^3\), Ottawa, Ontario, Canada, 28–29 May 2015Google Scholar
  11. 11.
    Rohn, J.: Solvability of systems of interval linear equations and inequalities. Linear Optimization Problems with Inexact Data, pp. 35–77. Springer, Berlin (2006)Google Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Joshua K. Pickard
    • 1
  • Juan A. Carretero
    • 1
  • Jean-Pierre Merlet
    • 2
  1. 1.University of New BrunswickFrederictonCanada
  2. 2.INRIA Sophia-AntipolisSophia-AntipolisFrance

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