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Computation of the interference-free wrench feasible workspace of a 3-DoF translational tensegrity robot

  • Marc ArsenaultEmail author
Conference paper
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 74)

Abstract

This paper proposes a method to compute the workspace of a three-degree-of-freedom translational tensegrity robot. Equivalent compression spring legs incorporating variable radius drums are used to emulate linear compression springs that replace the struts of the tensegrity system from which the robot is inspired. The workspace is computed based on the interval analysis evaluation of constraints related to the kinematics of the equivalent spring legs, the avoidance of interferences between the robot’s components and the need to generate required wrenches on the robot’s mobile platform while ensuring acceptable cable tensions. Sufficient conditions for the satisfaction of these constraints that may be suitably evaluated using interval analysis are developed. Results suggest that the size of the workspace may be increased by introducing pre-load in the robot’s components.

Keywords

tensegrity workspace computation interval analysis wrench feasible workspace cable interference 

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References

  1. 1.
    Arsenault, M.: Design of convex variable radius drum mechanisms. Mechanism and Machine Theory 129, 175–190 (2018)CrossRefGoogle Scholar
  2. 2.
    Arsenault, M., Gosselin, C.M.: Kinematic and static analysis of a planar modular 2-DoF tensegrity mechanism. In: Proceedings - IEEE International Conference on Robotics and Automation, vol. 2006, pp. 4193–4198 (2006)Google Scholar
  3. 3.
    Arsenault, M., Gosselin, C.M.: Kinematic and static analysis of a three-degree-of-freedom spatial modular tensegrity mechanism. International Journal of Robotics Research 27(8), 951–966 (2008)Google Scholar
  4. 4.
    Arsenault, M., Mohr, C.: Design and fabrication of a functional prototype for a 3-DoF translational tensegrity robot. In: Proceedings of the 2016 CSME International Congress (2016)Google Scholar
  5. 5.
    Berti, A., Merlet, J.P., Carricato, M.: Solving the direct geometrico-static problem of underconstrained cable-driven parallel robots by interval analysis. International Journal of Robotics Research 35(6), 723–739 (2016)CrossRefGoogle Scholar
  6. 6.
    Calladine, C., Pellegrino, S.: First-order infinitesimal mechanisms. International Journal of Solids and Structures 27(4), 505–515 (1991)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Fuller, B.: Tensile-integrity structures. United States Patent No. 3,063,521 (1962)Google Scholar
  8. 8.
    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
  9. 9.
    Hansen, E., Walster, G.W.: Global Optimization Using Interval Analysis, second edn. Marcel Dekker Inc., New York (2004)Google Scholar
  10. 10.
    Mohr, C.A., Arsenault, M.: Kinematic analysis of a translational 3-DoF tensegrity mechanism. Transactions of the CSME 35(4), 573–584 (2011)CrossRefGoogle Scholar
  11. 11.
    Moore, R.E., Kearfott, R.B., Cloud, M.J.: Introduction to Interval Analysis. Society for Industrial and Applied Mathematics, Philadelphia (2009)Google Scholar
  12. 12.
    Paul, C., Lipson, H., Valero-Cuevas, F.: Design and control of tensegrity robots for locomotion. IEEE Transactions on Robotics 22(5), 944–957 (2006)CrossRefGoogle Scholar
  13. 13.
    Pellegrino, S.: Analysis of prestressed mechanisms. International Journal of Solids and Structures 26(12), 1329–1350 (1990)CrossRefGoogle Scholar
  14. 14.
    Pugh, A.: An introduction to tensegrity. University of California Press (1976)Google Scholar
  15. 15.
    Rohn, J.: An algorithm for computing the hull of the solution set of interval linear equations. Linear Algebra and Its Applications 435(2), 193–201 (2011)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Rovira, A.G., Tur, J.M.: Control and simulation of a tensegrity-based mobile robot. Robotics and Autonomous Systems 57, 526–535 (2009)CrossRefGoogle Scholar
  17. 17.
    Rump, S.: INTLAB – INTerval LABoratory. In: T. Csendes (ed.) Developments in Reliable Computing, pp. 77–104. Kluwer Academic Publishers, Dordrecht (1999)CrossRefGoogle Scholar
  18. 18.
    Schmidt, V., Muller, B., Pott, A.: Solving the forward kinematics of cable-driven parallel robots with neural networks and interval arithmetic. pp. 103–110. Kluwer Academic Publishers (2014)Google Scholar
  19. 19.
    Snelson, K.: Continuous tension, discontinuous compression structures. United States Patent No. 3,169,611 (1965)Google Scholar
  20. 20.
    Sultan, C., Corless, M., Skelton, R.: Tensegrity flight simulator. Journal of Guidance, Control and Dynamics 23(6), 1055–1064 (2000)CrossRefGoogle Scholar
  21. 21.
    Wenger, P., Chablat, D.: Kinetostatic analysis and solution classification of a class of planar tensegrity mechanisms. Robotica (2018)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Laurentian UniversitySudburyCanada

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