A Geometrical Characterization of Workspace Singularities in 3R Manipulators

  • M. Husty
  • E. Ottaviano
  • M. Ceccarelli


In this paper we present an algorithm, based on a level set representation of a crosssection of the Cartesian workspace of 3R regional manipulators, which is useful to show clearly the nature of the cusps and double points on the boundary. Furthermore it is shown that singularities of the level set surface (graph of the level set) characterize non-generic manipulators and we demonstrate the non-singular posture change ability of cuspidal manipulators with help of the level set surface.

Key words

serial manipulators workspace singularities level set posture change 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Burdick, J.W., A classification of 3R regional manipulator singularities and geometries, Mechanism and Machine Theory 30(1), 71-89, (1995).CrossRefGoogle Scholar
  2. 2.
    Ceccarelli, M., On the workspace of 3R robot arms, in Proc. 5th IFToMM Int. Symp. on Theory and Practice of Mechanism, Bucharest, Vol. II-1, pp. 37-46 (1989).Google Scholar
  3. 3.
    Ottaviano, E., Ceccarelli, M., Lanni, C., A characterization of ring void in workspace of three-revolute manipulators, in Proc. 10th World Congress on the Theory of Machines and Mechanisms, Oulu, Finland, Vol. 3, pp. 1039-1044 (1999).Google Scholar
  4. 4.
    Ottaviano E., Husty M., Ceccarelli M. (2004), A Cartesian representation for the boundary workspace of 3R manipulators, in On Advances in Robot Kinematics, J. Lenar či č and C. Galletti (Eds.), Kluwer, Dordrecht, pp. 247-254 (2004).Google Scholar
  5. 5.
    Ottaviano, E., Husty, M., Ceccarelli, M., Identification of the workspace boundary of a general 3-R manipulator, ASME Journal of Mechanical Design 128(1), 236-242 (2006).CrossRefGoogle Scholar
  6. 6.
    Ottaviano, E., Husty, M., Ceccarelli, M., Level-set method for workspace analysis of serial manipulator, in Advances in Robot Kinematics: Mechanisms and Motion, J. Lenar či č and B. Roth (Eds.), Springer, Dordrecht, pp. 307-314 (2006).Google Scholar
  7. 7.
    Ottaviano, E., Husty, M., Ceccarelli, M., Workspace topologies of industrial 3R manipulators, International Journal of Advanced Robotic Systems 4(3), 355-364 (2007).Google Scholar
  8. 8.
    Parenti-Castelli, V., Innocenti, C., Position analysis of robot manipulators: Regions and sub-regions, in Advances in Robot Kinematics, Ljubljana, pp. 150-158 (1988).Google Scholar
  9. 9.
    Sethian, J.A., Level-Set Methods and Fast Marching Methods, Cambridge University Press, Cambridge (1996).Google Scholar
  10. 10.
    Zein, M., Wenger, P., Chablat, D., An exhaustive study of the workspaces topologies of all 3R orthogonal manipulators with geometrical simplifications, Mechanism and Machine Theory 41(8),971-986 (2006).MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Wenger, P., Some guidelines for the kinematic design of new manipulators, Mechanism and Machine Theory 35(3), 437-449 (2000).MATHCrossRefGoogle Scholar
  12. 12.
    Wenger, P., Uniqueness domains and regions of feasable paths for cuspidal manipulators, IEEE Transactions on Robotics 20(4), 745-750 (2004).CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media B.V 2008

Authors and Affiliations

  • M. Husty
    • 1
  • E. Ottaviano
    • 2
  • M. Ceccarelli
    • 2
  1. 1.Institute for Basic Sciences in EngineeringUniversity of InnsbruckInnsbruckAustria
  2. 2.LARM: Laboratory of Robotics and Mechatronics – DiMSATUniversity of CassinoCassino (Fr)

Personalised recommendations