Skip to main content
SpringerLink
Log in

Obtaining the Maximal Singularity-Free Workspace of 6-UPS Parallel Mechanisms via Convex Optimization

  • Conference paper
  • First Online:
Computational Kinematics

Part of the book series: Mechanisms and Machine Science ((Mechan. Machine Science,volume 15))

  • 2076 Accesses

Abstract

This paper explores the maximal volume inscribed ellipsoid in the singularity free constant-orientation workspace of two classes of 6-UPS parallel mechanisms, namely, quadratic and quasi-quadratic Gough-Stewart platforms. It is of paramount importance to obtain the optimum singularity-free ellipsoid by taking into account the stroke of actuators. Convex optimization is applied as the fundamental optimization tool of this paper. For this purpose, a matrix modeling for the kinematic properties of Gough-Stewart platform is proposed. The main contribution of this paper consists in improving an existing method in a such a way that it leads to a global optimum rather than a suboptimal solution. The proposed algorithm could be regarded as one of the most reliable, in terms of obtaining the global extremum, and propitious approaches, in terms of computational time in comparison with other approaches proposed in the literature for obtaining the singularity-free workspace which make it suitable for real-time applications.

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 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 219.99
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

References

  1. Kong, X., Gosselin, C.: Type Synthesis of Parallel Mechanisms, vol. 33. Springer, Heidelberg (2007)

    MATH  Google Scholar 

  2. Gosselin, C.: Determination of the workspace of 6-DOF parallel manipulators. ASME J. Mech. Des. 112(3), 331–336 (1990)

    Article  Google Scholar 

  3. Gosselin, C., Angeles, J.: Singularity analysis of closed-loop kinematic chains. IEEE Trans. Robotics Autom. 6(3), 281–290 (1990)

    Article  Google Scholar 

  4. Li, H., Gosselin, C.M., Richard, M.J.: Determination of the maximal singularity-free zones in the six-dimensional workspace of the general Gough-Stewart platform. Mech. Mach. Theory 42(4), 497–511 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  5. Jiang, Q.: Singularity-free workspace analysis and geometric optimization of parallel mechanisms. Ph.D. thesis, Laval University, Quebec, Oct 2008

    Google Scholar 

  6. Merlet, J.P.: Parallel Robots. Springer, Dordrecht (2006)

    Google Scholar 

  7. Rao, S.S.: Engineering Optimization: Theory and Practice. Wiley, Hoboken (2009)

    Book  Google Scholar 

  8. Boyd, S., Vandenberghe, L.: Convex Optimization. Cambridge University Press, Cambridge (2004)

    Google Scholar 

  9. Vandenberghe, L., Boyd, S., Comanor, K.: Generalized chebyshev bounds via semidefinite programming. SIAM Rev. 49(1), 52–64 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  10. Grant, M., Boyd. S.: CVX Users Guide for CVX Version 1.21. April 2011

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. The Faculty of New Sciences and Technologies, University of Tehran, Tehran, Iran

    Amirhossein Karimi & Mehdi Tale Masouleh

  2. Department of Mechanical Engineering, Laval University, Quebec City, QC, Canada

    Philippe Cardou

Authors
  1. Amirhossein Karimi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mehdi Tale Masouleh
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Philippe Cardou
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Philippe Cardou .

Editor information

Editors and Affiliations

  1. Llorens Artigas, Inst Robótica e Informática Industrial, Barcelona, Spain

    Federico Thomas

  2. Mechanical Engineering, Idaho State University, Pocatello, Idaho, USA

    Alba Perez Gracia

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer Science+Business Media Dordrecht

About this paper

Cite this paper

Karimi, A., Masouleh, M.T., Cardou, P. (2014). Obtaining the Maximal Singularity-Free Workspace of 6-UPS Parallel Mechanisms via Convex Optimization. In: Thomas, F., Perez Gracia, A. (eds) Computational Kinematics. Mechanisms and Machine Science, vol 15. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-7214-4_27

Download citation

  • DOI: https://doi.org/10.1007/978-94-007-7214-4_27

  • Published:

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-007-7213-7

  • Online ISBN: 978-94-007-7214-4

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation