Skip to main content
SpringerLink
Log in

Singularity Analysis of Lower-Mobility Parallel Robots with an Articulated Nacelle

  • Conference paper
  • First Online:
Advances in Robot Kinematics: Motion in Man and Machine

Abstract

This paper presents a generic approach to analyze the singularity of robots with an articulated nacelle like the H4 robot. Using screw theory, the concept of equivalent twist graph is introduced in order to characterize the constraint wrenches and the actuation wrenches applied to the moving platform. Using Grassmann–Cayley Algebra, the geometric conditions associated with the dependency of six Plücker vectors of finite and infinite lines in the projective space P3 are reformulated in the superbracket decomposition in order to characterize geometrically the parallel singularities of the robot.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J.P. Merlet. Singular configurations of parallel manipulators and Grassmann geometry. The International Journal of Robotics Research, 8, 45–56 (1989).

    Article  Google Scholar 

  2. P. Ben-Horin and P. Shoham. Singularity condition of six-degree-of-freedom three-legged parallel robots based on Grassmann–Cayley Algebra. IEEE Transactions on Robotics, 22, 577–590 (2006).

    Article  Google Scholar 

  3. P. Ben-Horin and P. Shoham. Application of Grassmann–Cayley Algebra to geometrical interpretation of parallel robot singularities. International Journal of Robotics Research, 1, 127–141 (2009).

    Google Scholar 

  4. S.A. Joshi and L.W. Tsai. Jacobian analysis of limited-DOF parallel manipulators. Transactions of the ASME, 124 (2002).

    Article  Google Scholar 

  5. D. Kanaan, P. Wenger, S. Caro, and D. Chablat. Singularity analysis of lower-mobility parallel manipulators using Grassmann–Cayley Algebra. IEEE Transactions on Robotics, 25, 995–1004 (2009).

    Article  Google Scholar 

  6. H.B. Choi, A. Konno, and M. Uchiyama. Singularity analysis of a novel 4-DOFs parallel robot H4 by using screw theory. In Proceedings of DETC’03 ASME 2003 Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Chicago, Illinois, USA, September 2–6 (2003).

    Google Scholar 

  7. J. Wu, Z. Yin, and Y. Xiong. Singularity analysis of a novel 4-DOF parallel manipulator H4. The International Journal of Advanced Manufacturing Technology, 29, 794–802 (2006).

    Article  Google Scholar 

  8. N.L. White. Grassmann–Cayley Algebra and robotics applications. In Handbook of Geometric Computing, Part VIII, pp. 629–656 (2005).

    Google Scholar 

  9. R.S. Ball. A Treatise on the Theory of Screws. Cambridge University Press, Cambridge (1900).

    Google Scholar 

  10. K.J. Waldron. The constraint analysis of mechanisms. Journal of Mechanisms, 1, 101–114 (1966).

    Article  Google Scholar 

  11. K.H. Hunt. Kinematic Geometry of Mechanisms. Clarendon Press, Oxford (1978).

    MATH  Google Scholar 

  12. K.H. Hunt. Structural kinematics of in. parallel actuated robot arms. ASME J. of Mech. Transm. and Automn. in Design, 105, 705–712 (1983).

    Google Scholar 

  13. M. Mohamed and J. Duffy. A direct determination of the instantaneous kinematics of fully parallel robot manipulators. ASME J. of Mechanisms, Transmissions and Automation in Design, 107(2), 226–229 (1985).

    Article  Google Scholar 

  14. D. Zlatanov, I. Bonev, and C. Gosselin. Constraint singularities of parallel mechanisms. In IEEE ICRA’02, Washington DC, Vol. 1, pp. 496–502 (2002).

    Google Scholar 

  15. W. Kong and C.M. Gosselin. Type Synthesis of Parallel Mechanisms. Springer (2007).

    MATH  Google Scholar 

  16. T.S. Zhao, J.S. Dai, and Z. Huang. Geometric analysis of overconstrainted parallel manipulators with three and four degrees of freedom. JSME International Journal, 4(3), 730–740 (2002).

    Article  Google Scholar 

  17. F. Pierrot and O. Company. H4: A new family of 4-DOF parallel robots. In Proc. of the IEEE / ASME Int. Conf. on Advanced Intelligent Mechatronics, Atlanta, Georgia, USA, September, pp. 508–513 (1999).

    Google Scholar 

  18. F. Pierrot, F. Marquet, O Company, and T. Gil. H4 parallel robot: Modeling, design and preliminary experiments. In Proceedings of the IEEE International Conference on Robotics and Automation, pp. 3256–3261 (2001).

    Google Scholar 

  19. G. Gogu. Structural Synthesis of Parallel Robots, Part 1: methodology edition, Solid Mechanics and Its Applications, Vol. 149, Springer (2008).

    Google Scholar 

  20. T. McMillan and N.L. White. The dotted straightening algorithm. Journal of Symbolic Computation, 11, 471–482 (1991).

    Article  MATH  MathSciNet  Google Scholar 

  21. S. Amine, D. Kanaan, S. Caro, and P. Wenger. Singularity analysis of the H4 robot using Grassmann–Cayley Algebra. Internal Report IRCCyN 2010, http://www.irccyn.ecnantes.fr/∼caro/Publications/ARK2010/IntReport.pdf.

  22. V. Nabat, M. de la Rodriguez, O. Company, S. Krut, and F. Pierrot. Par4: Very high speed parallel robot for pick-and-place. In Proceedings Intelligent Robots and Systems, IEEE/RSJ International Conference, August, pp. 553–558 (2005).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut de Recherche en Communications et Cybernétique de Nantes, Nantes, France

    Semaan Amine, Daniel Kanaan, Stéphane Caro & Philippe Wenger

Authors
  1. Semaan Amine
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Daniel Kanaan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Stéphane Caro
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Philippe Wenger
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Semaan Amine .

Editor information

Editors and Affiliations

  1. Inst. J. Stefan, University Ljubljana, Ljubljana, Slovenia

    Jadran Lenarcic

  2. , Aerospace and Mechanical Engineering, University of Notre Dame, Fitzpatrick Hall 365, Notre Dame, 46556-5637, USA

    Michael M. Stanisic

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer Science+Business Media B.V.

About this paper

Cite this paper

Amine, S., Kanaan, D., Caro, S., Wenger, P. (2010). Singularity Analysis of Lower-Mobility Parallel Robots with an Articulated Nacelle. In: Lenarcic, J., Stanisic, M. (eds) Advances in Robot Kinematics: Motion in Man and Machine. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-9262-5_29

Download citation

  • DOI: https://doi.org/10.1007/978-90-481-9262-5_29

  • Published:

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-9261-8

  • Online ISBN: 978-90-481-9262-5

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation