Self Dual Topology of Parallel Mechanisms with Configurable Platforms

  • Patrice LambertEmail author
  • Just L. Herder
Conference paper
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 15)


This paper presents first an analysis of the topology of mechanisms via Graph Theory and Screw Theory and next the principle of dual mechanisms in terms of their mobility and overconstraints. Using dual graphs, the graph representations of the mechanisms that are dual to hybrid and Delta mechanisms are revealed. The concept of parallel mechanisms with configurable platforms (PMCPs) is introduced and it is shown that the graph reduction of PMCPs always results in a wheel graph, which has the interesting property of being self-dual. In case of self dual topology, it is then possible to directly convert any method developed for their mobilty analysis into an overconstraint analysis method and vice versa. This self dual topology property can also be exploited to create new PMCPs and is an important aspect in the future development of a type synthesis method that includes PMCPs.


Parallel mechanisms Configurable platform Topology Mobility Overconstraints Duality 



This research is supported by the Dutch Technology Foundation STW (project number 12158).


  1. 1.
    Davies, T.H.: Simple examples of dual coupling network. In: 12th IFToMM World Congress, Loughborough University, UK (2007)Google Scholar
  2. 2.
    Gogu, G.: Structural Synthesis of Parallel Robots: Part 1: Methodology, Solid Mechanics and its Applications. Springer, Dordrecht (2007)Google Scholar
  3. 3.
    Kong, X., Gosselin, C.M.: Type synthesis of parallel mechanisms. Springer tracts in. Advanced Robotics, vol. 33, Heidelberg (2007)Google Scholar
  4. 4.
    Lambert, P., Herder, J.L.: Mobility analysis of non series-parallel mechanisms. New Trends in Mechanism and Machine Science, Mechanisms and Machine Science, vol. 7, pp. 63–71. Springer (2012)Google Scholar
  5. 5.
    Lambert, P., Langen, H., Munnig Schmidt, R.: A novel 5 DOF fully parallel robot combining 3T1R motion and grasping. In: 34th Annual IDETC, Parts A and B, vol. 2, pp. 1123–1130. ASME (2010)Google Scholar
  6. 6.
    Mohamed, M., Gosselin, C.: Design and analysis of kinematically redundant parallel manipulators with configurable platforms. IEEE Trans. Rob. 21(3), 277–287 (2005)CrossRefGoogle Scholar
  7. 7.
    Nabat, V., de la O Rodriguez, M., Company, O., Krut, S., Pierrot, F.: Par4: very high speed parallel robot for pick-and-place In: 2005 IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 553–558 (2005)Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Delft University of TechnologyDelftThe Netherlands

Personalised recommendations