Exact Workspace Synthesis for RCCR Linkages

  • Batchimeg Batbold
  • Yimesker Yihun
  • James S. Wolper
  • Alba Pérez-GraciaEmail author
Conference paper
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 15)


A tool for the exact kinematic synthesis of a given workspace may be of interest when designing closed linkages. In these cases, finite-position synthesis cannot ensure smoothness of motion between task positions. In order to keep the simplicity of the finite-position synthesis approach, the workspace of relative displacements is described as a set of finite screws forming a screw surface. The screw surface is characterized by a number of screws which are used to generate the whole surface, and in turn to perform the dimensional synthesis. The methodology is here applied to the overconstrained RCCR closed linkage, for which the workspace of finite displacements yields a point-path synthesis problem.


Workspace synthesis RCCR linkage 


  1. 1.
    Affi, Z., Romdhane, L., Maalej, A.: Dimensional synthesis of a 3-translational-dof in-parallel manipulator for a desired workspace. Eur. J. Mech. A. Solids 23, 311–324 (2004)CrossRefzbMATHGoogle Scholar
  2. 2.
    Brunnthaler, K.: Synthesis of 4r linkages using kinematic mapping. Ph.D. Thesis, Institute for basic sciences and engineering, University of Innsbruck, Innsbruck (2006)Google Scholar
  3. 3.
    Chablat, D., Wenger, P.: Architecture optimization of a 3-dof parallel mechanism for machining applications, the orthoglide. IEEE Trans. Robot. Autom. 19(3), 403–410 (2003)CrossRefGoogle Scholar
  4. 4.
    Gracia, P.A., McCarthy, J.M.: The kinematic synthesis of spatial serial chains using Clifford algebra exponentials. In: Proceedings of the Institution of Mechanical Engineers, Part C. J. Mech. Eng. Sci. 220(7), 953–968 (2006)Google Scholar
  5. 5.
    Gracia, A.P.: Synthesis of spatial RPRP closed linkages for a given screw system. ASME J. Mech. Robot. 3(2), 1–8 (2011)Google Scholar
  6. 6.
    Hayes, M.J.D., Luu, T., Chang, X.W.: Kinematic mapping application to approximate type and dimension synthesis of planar mechanisms. In: Lenarcic, J., Galletti, C. (eds.) On Advances in Robot Kinematics, Kluwer Academic Publisher, Dordrecht, The Netherlands (2004)Google Scholar
  7. 7.
    Huang, C.: The cylindroid associated with finite motions of the Bennett mechanism. In: Proceedings of the ASME Design Engineering Technical Conferences, USA (1996)Google Scholar
  8. 8.
    Huang, T., Li, M., Zhao, X.M., Mei, J., Chetwynd, D.G., Hu, S.J.: Conceptual design and dimensional synthesis for a 3-dof module of the trivariant - a novel 5-dof reconfigurable hybrid robot. IEEE Trans. Robot. 21(3), 449–456 (2005)CrossRefGoogle Scholar
  9. 9.
    Huang, C.: Linear property of the screw surface of the spatial RPRP linkage. ASME J. Mech. Des. 128, 581–586 (2006)CrossRefGoogle Scholar
  10. 10.
    Husty, M.L., Pfurner, M., Schrocker, H.P., Brunnthaler, K.: Algebraic methods in mechanism analysis and synthesis. Robotica 25, 661–675 (2007)CrossRefGoogle Scholar
  11. 11.
    Kim, H.S., Tsai, L.W.: Kinematic synthesis of a spatial 3-RPS parallel manipulator. ASME J. Mech. Des. 125, 92–97 (2003)CrossRefGoogle Scholar
  12. 12.
    Kim, H.S., Tsai, L.W.: Design optimization of a cartesian parallel manipulator. ASME J. Mech. Des. 125, 43–51 (2003)CrossRefGoogle Scholar
  13. 13.
    Kosinska, A., Galicki, M., Kedzior, K.: Design and optimization of parameters of delta-4 parallel manipulator for a given workspace. J. Rob. Syst. 20(9), 539–548 (2003)CrossRefzbMATHGoogle Scholar
  14. 14.
    Merlet, J.P.: Optimal design of robots. In: Proceedings of Robotics: Science and Systems, USA, June 2005Google Scholar
  15. 15.
    Parkin, I.A.: A third conformation with the screw systems: finite twist displacements of a directed line and point. Mech. Mach. Theory 27, 177–188 (1992)CrossRefGoogle Scholar
  16. 16.
    Rao, N.M., Rao, K.M.: Dimensional synthesis of a 3-RPS parallel manipulator for a prescribed range of motion of spherical joints. Mech. Mach. Theory 44, 477–486 (2009)CrossRefzbMATHGoogle Scholar
  17. 17.
    Ravani, B., Roth, B.: Motion synthesis using kinematic mappings. ASME J. Mech. Trans. Autom. Des. 105(3), 460–467 (1983)CrossRefGoogle Scholar
  18. 18.
    Schrocker, H.P., Husty, M.L., McCarthy, J.M.: Kinematic mapping based assembly mode evaluation of planar four-bar mechanisms. AMSE J. Mech. Des. 129, 924–929 (2007)CrossRefGoogle Scholar
  19. 19.
    Waldron, K.J.: A study of overconstrained linkage geometry by solution of closure equations - part II- four-bar linkages with lower pair joints other than screw joints. Mech. Mach. Theory 8, 233–247 (1972)CrossRefGoogle Scholar
  20. 20.
    Wolbrecht, E., Su, H.J., Perez, A., McCarthy, J.M.: Geometric design of symmetric 3-RRS constrained parallel platforms. In: ASME (ed.) Proceedings of the 2004 ASME International Mechanical Engineering Congress and Exposition, Anaheim, 13–19 November, 2004Google Scholar
  21. 21.
    Wu, J., Purwar, A., Ge, Q.J.: nteractive dimensional synthesis and motion design of planar 6r single-loop closed chains via constraint manifold modification. ASME J. Mecha. Robot. 2(3), 1–8 (2010)Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Batchimeg Batbold
    • 1
  • Yimesker Yihun
    • 1
  • James S. Wolper
    • 2
  • Alba Pérez-Gracia
    • 2
    Email author
  1. 1.Institut de Robòtica i Informàtica IndustrialCSIC-UPCBarcelonaSpain
  2. 2.Idaho State UniversityPocatelloUSA

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