Geometric Based Approach for Workspace Analysis of Translational Parallel Robots

  • I. Ben HamidaEmail author
  • M. A. Laribi
  • A. Mlika
  • L. Romdhane
  • S. Zeghloul
Conference paper
Part of the CISM International Centre for Mechanical Sciences book series (CISM, volume 584)


The aim of this paper is to propose a geometric based approach for workspace analysis of Translational Parallel Manipulators (TPMs), which will be useful for the dimensional synthesis problem. For this purpose, a non-exhaustive list of TPMs in the bibliography is presented and grouped according to the structure of their legs as well as the shape of their workspaces. The approach is easy to implement and it is illustrated through three TMPs examples, having each a different workspace shape.


Workspace Dimensional synthesis Translational parallel manipulators 



This research is supported by ROBOTEX, the French national network of robotics platforms (N° ANR-10-EQPX-44-01) and by the French National Research Agency (ANR-14-CE27-0016).


  1. 1.
    Gough, V.E., Whitehall, S.G.: Universal tyre test machine. FISITA Proc. 117, 117–137 (1962)Google Scholar
  2. 2.
    Stewart, D.: A platform with six degrees of freedom. Proc. Inst. Mech. Eng. 180(428), 371–386 (1965)CrossRefGoogle Scholar
  3. 3.
    Vischer, P., Clavel, R.: Delta_kinematic calibration.pdf. Robotica 16, 207–218 (1997)CrossRefGoogle Scholar
  4. 4.
    Kim, D., Chung, W.K.: Kinematic condition analysis of three-DOF pure translational parallel manipulators. J. Mech. Des. Trans. ASME 125(2), 323–331 (2003)CrossRefGoogle Scholar
  5. 5.
    Romdhane, L., Affi, Z., Fayet, M.: Design and singularity analysis of a 3-translational-DOF in-parallel manipulator. J. Mech. Des. 124(3), 419–426 (2002)CrossRefGoogle Scholar
  6. 6.
    Callegari, M., Palpacelli, M.C.: Prototype design of a translating parallel robot. Meccanica 43(2), 133–151 (2008)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Essomba, T., Laribi, M.A., Zeghloul, S., Poisson, G.: Optimal synthesis of a spherical parallel mechanism for medical application. Robotica 34(3), 671–686 (2016)CrossRefGoogle Scholar
  8. 8.
    Pierrot, F., Reynaud, C., Fournier, A.: DELTA: a simple and efficient parallel robot. Robotica 8(pt 2), 105–109 (1990)CrossRefGoogle Scholar
  9. 9.
    Laribi, M.A., Romdhane, L., Zeghloul, S.: Analysis and dimensional synthesis of the DELTA robot for a prescribed workspace. Mech. Mach. Theory 42(7), 859–870 (2007)CrossRefGoogle Scholar
  10. 10.
    Stan, S., Manic, M., Maties, V., Vistrian, M., Radu, B.: Evolutionary approach to optimal design of 3 DOF translation exoskeleton and medical parallel robots (good literature on workspace analysis). In: Conference on Human System Interactions, pp. 720–725 (2008)Google Scholar
  11. 11.
    Tsai, L., Walsh, G.C., Stamper, R.E.: Kinematics of a novel three DOF translational platform. In: Proceedings of the 1996 IEEE International Conference on Robotics and Automation, Minneapolis, Minnesota, pp. 3446–3451 (1996)Google Scholar
  12. 12.
    Chebbi, A.H., Parenti-Castelli, V.: Geometric and manufacturing issues of the 3-UPU pure translational manipulator. In: Pisla, D., Ceccarelli, M., Husty, M., Corves, B. (eds.) New Trends in Mechanism Science. Mechanisms and Machine Science, vol. 5, pp. 595–596 (2010)Google Scholar
  13. 13.
    Chebbi, A.H.: The potential of the 3-UPU translational parallel manipulator and a procedure to select the best architecture. Università di Bologna (2011)Google Scholar
  14. 14.
    Walter, D.R.: Analysis of Planar and Spatial Mechanisms Using Algebraic Methods. Innsbruck University (2011)Google Scholar
  15. 15.
    Walter, M.L.H.D.R.: Kinematic analysis of the TSAI 3-UPU parallel manipulator using algebraic methods. In: 13th IFToMM World Congress (2007)Google Scholar
  16. 16.
    Tsai, L.-W., Joshi, S.: Kinematic analysis of 3-DOF position mechanisms for use in hybrid kinematic machines. J. Mech. Des. 124(2), 245 (2002)CrossRefGoogle Scholar
  17. 17.
    Siciliano, B.: The tricept robot: inverse kinematics, manipulability analysis and closed-loop direct kinematics algorithm. Robotica 17(4), 437–445 (1999)CrossRefGoogle Scholar
  18. 18.
    Ruggiu, M.: Kinematics analysis of the CUR translational manipulator. Mech. Mach. Theory 43(9), 1087–1098 (2008)CrossRefGoogle Scholar
  19. 19.
    Gosselin, I.A., Kong, C.M., Foucault, X., Bonev, S.: A fully-decoupled 3-DOF translational parallel mechanism. In: Proceedings of the Fourth Chemnitz Parallel Kinematics Seminar, Parallel Kinematic Machines International Conference, pp. 595–610 (2004)Google Scholar
  20. 20.
    Hervé, J.M.: Design of parallel manipulators via the displacement group. In: Proceedings of Ninth World Congress on the Theory of Machines and Mechanisms, vol. 3, pp. 2079–2082, April 1995Google Scholar
  21. 21.
    Kong, X., Gosselin, C.M.: Generation of parallel manipulators with three translational degrees of freedom based on screw theory. In: Symposium on sur les mécanismes, les machines et la mécatronique de CCToMM, pp. 3–5, September 2001Google Scholar
  22. 22.
    Carricato, M., Parenti-Castelli, V.: Singularity-free fully-isotropic translational parallel mechanisms. Int. J. Rob. Res. 21(2), 161–174 (2002)CrossRefGoogle Scholar
  23. 23.
    Zeng, Q., Ehmann, K.F., Cao, J.: Tri-pyramid robot: design and kinematic analysis of a 3-DOF translational parallel manipulator. Robot. Comput. Integr. Manuf. 30(6), 648–657 (2014)CrossRefGoogle Scholar

Copyright information

© CISM International Centre for Mechanical Sciences 2019

Authors and Affiliations

  • I. Ben Hamida
    • 1
    • 2
    Email author
  • M. A. Laribi
    • 2
  • A. Mlika
    • 1
  • L. Romdhane
    • 1
    • 3
  • S. Zeghloul
    • 2
  1. 1.Laboratoire de Mécanique (LR11ES36)Université de Sousse - Ecole Nationale d’Ingénieurs de SousseSousse-ErriadhTunisia
  2. 2.Institut PPRIME, UPR 3346, CNRS – Université de Poitiers – ENSMA, Bd Pierre et Marie CurieFuturoscope ChasseneuilFrance
  3. 3.Department of Mechanical EngineeringAmerican University of SharjahSharjahUAE

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