Advertisement

Maximally Regular Planar Non Fully Parallel Manipulators

Conference paper
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 3)

Abstract

This paper presents a new family of maximally regular planar non fully parallel manipulators (PPMs). The moving platform has three planar degrees of freedom, which are two planar translations and one rotation around an axis perpendicular to the plane of translations. A one-to-one correspondence exists between the actuated joint velocity space and the external velocity space of the moving platform. The Jacobian matrix mapping the two vector spaces of the maximally regular PPMs is a 3×3 identity matrix throughout the entire workspace. The condition number and the determinant of the Jacobian matrix being equal to one, the maximally regular parallel robots perform very well with regard to force and motion transmission capabilities. The new kinematic criteria, used for structural synthesis, are based on the recent formulae proposed by the author for mobility, connectivity, redundancy and overconstraint of parallel robots. These kinematic criteria allow us to get new families of over constrained and non overconstrained maximally regular parallel robots with planar motion of the moving platform. The non fully-parallel solutions are presented for the first time in the literature.

Keywords

Planar parallel manipulators Mobility Redundancy Overconstraint 

References

  1. 1.
    Angeles, J: Fundamentals of Robotic Mechanical Systems: Theory, Methods, and Algorithms, 1st ed. Springer, 1997.Google Scholar
  2. 2.
    Angeles, J: The qualitative synthesis of parallel manipulators. ASME Journal of Mechanical Design 126 (2004) 617-624.CrossRefGoogle Scholar
  3. 3.
    Ceccarelli, M: Fundamentals of Mechanics of Robotic Manipulation. Springer, 2004.Google Scholar
  4. 4.
    Di Gregorio, R. and Parenti-Castelli, V: A translational 3-dof parallel manipulator. In Advances in Robot Kinematics: analysis and control, J. Lenarčič, M. Husty (eds), Kluwer Academic Publishers (1998), 49-58.Google Scholar
  5. 5.
    Fatah, A., Hasan Ghasemi, A.M.: Isotropic design of spatial parallel manipulators. International Journal of Robotics Research 21, 9 (2002), 811-824.CrossRefGoogle Scholar
  6. 6.
    Frisoli, A., Checcacci, D., Salsedo, F. and Bergamasco, M.: Synthesis by screw algebra of translating in-parallel actuated mechanisms. In: Lenarčič J, Stanišić MM (eds) Advances in robot kinematics, Kluwer Academic Publishers (2000) 433-440.Google Scholar
  7. 7.
    Gogu, G.: Fully-isotropic over-constrained planar parallel manipulators. In Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems, Sendai (2004) 3519-3524.Google Scholar
  8. 8.
    Gogu, G.: Mobility of mechanisms: a critical review. Mechanism and Machine Theory 40 (2005) 1068-1097.MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Gogu, G.: Chebychev-Grubler-Kutzbach’s criterion for mobility calculation of multi-loop mechanisms revisited via theory of linear transformations. European Journal of Mechanics-A/Solids 24 (2005), 427-441.MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Gogu, G.: Mobility and spatiality of parallel robots revisited via theory of linear transformations. European Journal of Mechanics-A/Solids 24 (2005), 690-711.MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Gogu, G.: Structural synthesis of parallel robots. Part 1: Methodology. Springer, 2008.Google Scholar
  12. 12.
    Gogu, G.: Structural synthesis of parallel robots. Part 3: Topologies with planar motion of the moving platform. Springer, 2010.Google Scholar
  13. 13.
    Gogu, G.: Kinematic criteria for structural synthesis of maximally regular parallel robots with planar motion of the moving platform. In Interdisciplinary Applications of Kinematics, A. Kecskeméthy (Ed.), Lima (2008) 61-79.Google Scholar
  14. 14.
    Hayes, M.J.D., Zsombor-Murray, P.J. and Chen, C.: Unified kinematic analysis of general planar parallel manipulators. ASME Journal of Mechanical Design 126 (2004) 866-874.CrossRefGoogle Scholar
  15. 15.
    Herve, J.M.: Design of parallel manipulators via the displacement group. In Proceedings of the 9th IFToMM World Congress, Milan (1995) 2079-2082.Google Scholar
  16. 16.
    Herve, J.M.: The Lie group of rigid body displacements, a fundamental tool for mechanism design. Mechanism and Machine Theory 34 (1999) 719-730.MathSciNetzbMATHCrossRefGoogle Scholar
  17. 17.
    Huang, Z., Li, Q.C.: Type synthesis of symmetrical lower-mobility parallel mechanisms using the constraint-synthesis method. International Journal of Robotics Research 22(1) (2003) 59-79.Google Scholar
  18. 18.
    Ionescu, T.G.: Terminology for mechanisms and machine science. Mechanism and Machine Theory 38 (2003) 597-901.zbMATHCrossRefGoogle Scholar
  19. 19.
    Kong, X., Gosselin, C.M.:Type Synthesis of Parallel Mechanisms, Springer, 2007.Google Scholar
  20. 20.
    Merlet, J.P.: Parallel robots, 2nd ed. Springer, 2006.Google Scholar
  21. 21.
    Rico Martinez, J.M. and Ravani, B.: On mobility analysis of linkages using group theory. ASME Journal of Mechanical Design 125 (2003) 70-80.CrossRefGoogle Scholar
  22. 22.
    Rico Martinez, J.M., Gallardo, J. and Ravani, B.: Lie algebra and the mobility of kinematic chains. Journal of Robotic Systems 20(8) (2003) 477-499.CrossRefGoogle Scholar
  23. 23.
    Salsbury, J.K. and Craig, J.J.: Articulated hands: force and kinematic issues. International Journal of Robotics Research 1(1) (1982) 1-17.Google Scholar
  24. 24.
    Tsai, K.Y. and Huang, D.: The design of isotropic 6-DOF parallel manipulators using isotropy generators. Mechanism and Machine Theory 38 (2003) 1199-1214.zbMATHCrossRefGoogle Scholar
  25. 25.
    Tsai, L.-W. Robot analysis: the mechanics of serial and parallel manipulators. Willey, 1999.Google Scholar
  26. 26.
    Zanganeh, K.E. and Angeles, J.: Kinematic isotropy and the optimum design of parallel manipulators. International Journal of Robotics Research 16(2) (1997) 185-197.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.LaMIIFMA, Clermont UniversityClermontFrance

Personalised recommendations