Skip to main content
SpringerLink
Log in

A survey of instantaneous poles for a class of two-degree-of-freedom spherical mechanisms

  • Research Article
  • Published:
Frontiers of Mechanical Engineering Aims and scope Submit manuscript

Abstract

This paper is a detailed exploration of instantaneous poles for a class of two-degree-of-freedom (two-DOF) spherical mechanisms (SMs) with seven links or bars. For two-DOF SMs, the secondary instantaneous poles (the ones which cannot be found by direct inspection) must lie on the specified great circles. For many of these mechanisms, however, some of these great circles cannot be obtained by a direct application of Aronhold-Kennedy theorem. This paper presents geometrical and analytical techniques to locate these unknown great circles for three topologies of seven-bar two-DOF SMs.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Hain K. Applied Kinematics. 2nd ed. New York: McGraw-Hill Book Co., 1967

    Google Scholar 

  2. Beyer R. The Kinematic Synthesis of Mechanisms. New York: McGraw-Hill Book Co., 1963

    Google Scholar 

  3. Uicker J J, Pennock G R, Shigley J E. Theory of Machines and Mechanisms. 3rd ed. New York: Oxford University Press, 2003

    Google Scholar 

  4. Hunt K H. Kinematic Geometry of Mechanisms. Oxford: Oxford University Press, 1978

    MATH  Google Scholar 

  5. Yan H S, Wu L I. The stationary configurations of planar six-bar kinematic chains. Mechanism and Machine Theory, 1988, 23(4): 287–293

    Article  MathSciNet  Google Scholar 

  6. Yan H S, Wu L I. On the dead-center positions of planar linkage mechanisms. Journal of Mechanical Design, 1989, 111(1): 40–46

    MathSciNet  Google Scholar 

  7. Di Gregorio R. A novel geometric and analytic technique for the singularity analysis of one-dof planar mechanisms. Mechanism and Machine Theory, 2007, 42(11): 1462–1483

    Article  MATH  MathSciNet  Google Scholar 

  8. Pennock G R, Kamthe G M. Study of dead-center positions of single-degree-of-freedom planar linkages using Assur kinematic chains. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2006, 220: 1057–1074

    Google Scholar 

  9. Di Gregorio R. An algorithm for analytically calculating the positions of the secondary instant centers of indeterminate linkages. Journal of Mechanical Design, 2008, 130(4): 042303

    Article  Google Scholar 

  10. Sen D, Mruthyunjaya T S. A centro-based characterization of singularities in the workspace of planar closed-loop manipulators. Mechanism and Machine Theory, 1998, 33(8): 1091–1104

    Article  MATH  Google Scholar 

  11. Di Gregorio R. A novel method for the singularity analysis of planar mechanisms with more than one degree of freedom. Mechanism and Machine Theory, 2009, 44(1): 83–102

    Article  MATH  Google Scholar 

  12. Foster D E, Pennock G R. A study of the instantaneous centers of velocity for two-degree-of-freedom planar linkages. Mechanism and Machine Theory, 2010, 45(4): 641–657

    Article  MATH  Google Scholar 

  13. Foster D E, Pennock G R. A graphical method to find the secondary instantaneous centers of zero velocity for the double butterfly linkage. Journal of Mechanical Design, 2003, 125(2): 268–274

    Article  Google Scholar 

  14. Foster D E, Pennock G R. Graphical methods to locate the secondary instant centers of single-degree-of-freedom indeterminate linkages. Journal of Mechanical Design, 2005, 127(2): 249–256

    Article  Google Scholar 

  15. Di Gregorio R. A general algorithm for analytically determining all the instantaneous pole axis locations in single-DOF spherical mechanisms. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2011, 225(9): 2062–2075

    Google Scholar 

  16. Zarkandi S. A new geometric method for singularity analysis of spherical mechanisms. Robotica, 2011, 29(7): 1083–1092

    Google Scholar 

  17. Zarkandi S. On singularities of multi-degree-of-freedom spherical mechanisms. Journal of Mechanical Science and Technology, 2012, 26(3): 839–846

    Article  MathSciNet  Google Scholar 

  18. Zarkandi S. On the location of the secondary instantaneous poles in two-degree-of-freedom spherical mechanisms. Frontiers of Mechanical Engineering, 2014, 9(1): 34–40

    Article  Google Scholar 

  19. Chiang C H. Kinematics of Spherical Mechanisms. New York: Cambridge University Press, 1988

    Google Scholar 

  20. Craig J J. Introduction to Robotics: Mechanics and Control. Wokingham: Addison-Wesley, 1989

    MATH  Google Scholar 

  21. Angeles J. Fundamentals of Robotic Mechanical Systems: Theory, Methods and Algorithms. 2nd ed. New York: Springer, 2003

    Book  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Babol Noshirvani University of Technology, Babol, Iran

    Soheil Zarkandi

Authors
  1. Soheil Zarkandi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Soheil Zarkandi.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zarkandi, S. A survey of instantaneous poles for a class of two-degree-of-freedom spherical mechanisms. Front. Mech. Eng. 9, 344–353 (2014). https://doi.org/10.1007/s11465-014-0320-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11465-014-0320-z

Keywords

Search

Navigation