Enumeration of Driving Mechanisms in Robotics by Combinatorial Analysis Method

  • P. MitrouchevEmail author
  • J. Chen
  • F. Mafray
  • Y. Zheng
Conference paper
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 37)


This research deals with the development of a new method for restricted morphological number enumeration for planar pin-jointed driving mechanisms of mobility 1 and 2. It is based on combinatorial analysis by using the symmetries of kinematic chains. Since the restricting criterion is the position of the robot’s frame, different cases of symmetries are addressed. New expressions for calculating the number of positions of the actuators in a mechanism are presented. These help to reduce the number of chains by avoiding those that are isomorphic with regard to the position of the robot frame. The expressions offer a corrected formulation for counting the number of actuators for planar mechanisms in robotics. Different examples of applications for various planar pin-jointed driving mechanisms of mobility 1 and 2 are presented.


Kinematics chains Driving mechanisms Combinatorial analysis Actuators Symmetry Conceptual design 


  1. 1.
    Lee, K., Tortorelli, D.A.: CAD system for designing robotic manipulators, In: Proceedings of IEEE International Conference on Robotics and automation, Saint-Louis, pp. 376–380. doi:  10.1109/ROBOT.1985.1087336 (1985)
  2. 2.
    Gonzales-Palacois, M., Angeles, J.: USyCaMs, a software package for the interactive synthesises of cam mechanisms. In: Proceedings of 1-st Integrated Design and Manufacturing in Mechanical Engineering I.D.M.M.E.’96, vol. 1, pp. 85–94. Nantes France (1996)Google Scholar
  3. 3.
    Gogu, G.: Mobility of mechanisms: a critical review, Elsevier, IFToMM. J. Mech. Mach. Theory 40, 1068–1097 (2005)zbMATHMathSciNetCrossRefGoogle Scholar
  4. 4.
    Crossley, F.R.E.: A contribution to Grubler’s theory in the number synthesis of plane mechanisms. Trans ASME J. Eng. Ind. 86, 1–8 (1964)Google Scholar
  5. 5.
    Woo, L.S.: Type synthesis of plane linkages. ASME J. Eng. Ind. Ser. B 89, 159–172 (1967)CrossRefGoogle Scholar
  6. 6.
    Freudenstein, F., Dobrjanskyj, L.: On a theory for the type synthesis of mechanisms. In: Proceedings of the 11-th International Congress of Applied Mechanics, pp. 420–428. Springer, Berlin (1964)Google Scholar
  7. 7.
    Mruthyunjaya, T.S.: A computerized methodology for structural synthesis of kinematic chains: part 1-formulation. Mech. Mach. Theory 19(6), 487–495 (1984)CrossRefGoogle Scholar
  8. 8.
    Manolescu, N., Tudosie, I.: Structural and kinematic synthesis of planar kinematic chain (PKC) and mechanisms (PM) with variable chain during the work. In: Proceedings of the 7-th World Congress, The Theory of Machines and Mechanisms, 1, Sevilla, pp. 45–48 Spain (1987)Google Scholar
  9. 9.
    Li, S., Wang, H., Dai, J.S.: Assur-Group inferred structural synthesis for planar mechanisms. Mech. Robot. 7, 041001 (2015). doi: 10.1115/1.4029116 CrossRefGoogle Scholar
  10. 10.
    Davies, T., Crossley, F.R.E.: Structural analysis of plan linkages by Frankes condensed notation. Pergamon Press, J. Mech. 1, 171–183 (1966)Google Scholar
  11. 11.
    Mitrouchev, P.: Sub-chain symmetry approach for morphological choice of planar mechanisms in robotics. Eur. J. Mech. (A Solids) 25(1), 166–188 (2006)zbMATHMathSciNetCrossRefGoogle Scholar
  12. 12.
    Mitrouchev, P.: Formulation for actuators’ number enumeration for main planar chains in robotics. Eur. J. Mech. (A Solids) 27(4), 622–646 (2008)zbMATHMathSciNetCrossRefGoogle Scholar
  13. 13.
    Mitrouchev, P.: Symbolic structural synthesis and a description method for planar kinematic chains in robotics. Eur. J. Mech. (A Solids), ISSN: 0997-7538, Ed. Elsevier, N°20(2001), 777–794Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Université Grenoble Alpes, G-SCOPGrenobleFrance
  2. 2.College of Mechanical Engineering and AutomationHuaqiao UniversityQuanzhouPR China

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