Skip to main content

Force Capability Polytope of a 4RRR Redundant Planar Parallel Manipulator

  • Chapter
  • First Online:

Abstract

In this chapter the characteristic force capability polytope of a 4RRR parallel manipulator is obtained from the optimization of its static equations. In order to solve the problem regarding the global optimization, an evolutionary algorithm known as Differential Evolution (DE) is used. The objective function of the optimization problem of force capability is defined by employing the Screws Theory and Davies’s method as a primary mathematical tool. Finally, some force capability polytopes are obtained for different kinematic positions of the manipulator.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD   169.99
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

Learn about institutional subscriptions

References

  1. Cazangi, H.R.: Aplicação do método de davies para análise cinemática e estática de mecanismos de múltiplos graus de liberdade. Ph.D. thesis, Universidade Federal de Santa Catarina, Brazil (2008)

    Google Scholar 

  2. Chiacchio, P., Bouffard-VercelliO, Y., Pierroto, F.: Evaluation of force capabilities for redundant manipulators. In: IEEE International Conference on Robotics and Automation, pp. 3520–3525 (1996)

    Google Scholar 

  3. Davies, T.H.: Mechanical networks: wrenches on circuit screws. Mech. Mach. Theory 18, 107–112 (1983)

    Google Scholar 

  4. Nokleby, S.B., Firmani, F., Zibil, A., Podhorodeski, R.P.: Force moment capabilities of redundantly actuated planar parallel architectures. In: 12th IFToMM 2007 World Congress, pp. 17–21 (2007)

    Google Scholar 

  5. Nokleby, S.B., Fisher, R., Podhorodeski, R.P., Firmani, F.: Force capabilities of redundantly-actuated parallel manipulators. Mech. Mach. Theory 40, 578–599 (2004)

    Article  Google Scholar 

  6. Storn, R., Price, K.: Differential evolution: a simple and efficient adaptive scheme for global optimization over continuous spaces. Technical Report TR-95-012. International Computer Science Institute (2005)

    Google Scholar 

  7. Tsai, L.W.: Robot Analysis and Design: the Mechanics of Serial and Parallel Manipulators, 1st edn. Wiley, New York (1999)

    Google Scholar 

  8. Weihmann, L., Martins, D., Coelho, L.S.: Force capabilities of kinematically redundant planar parallel manipulators. In: 13th World Congress in Mechanism and Machine Science, pp. 483–483 (2011)

    Google Scholar 

  9. Weihmann, L., Martins, D., dos Santos Coelho, L.: Modified differential evolution approach for optimization of planar parallel manipulators force capabilities. In: Expert Systems with Applications, vol. 39. http://dx.doi.org/10.1016/j.eswa.2011.11.099 (2012)

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Leonardo Mejia .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Mejia, L., Simas, H., Martins, D. (2014). Force Capability Polytope of a 4RRR Redundant Planar Parallel Manipulator. In: Lenarčič, J., Khatib, O. (eds) Advances in Robot Kinematics. Springer, Cham. https://doi.org/10.1007/978-3-319-06698-1_10

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-06698-1_10

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-06697-4

  • Online ISBN: 978-3-319-06698-1

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics