Skip to main content

On the Resolution of Forward Kinematic Problem Using CAD Graphical Techniques: Application on Planar Parallel Robotic Manipulators

  • Conference paper
  • First Online:
New Trends in Mechanism and Machine Science

Part of the book series: Mechanisms and Machine Science ((Mechan. Machine Science,volume 24))

Abstract

The existence of singularity-free trajectories joining different assembly modes of a parallel robotic manipulator is a crucial property that permits to have a large effective workspace. The investigation of such a characteristic requires considering the forward kinematics problem. In this paper, an original method for forward kinematics resolution and singularity-free trajectory planning between different assembly modes is presented. The proposed method is based on a pure geometric approach and exploits the CAD environments utilities for geometric entity manipulations such as Boolean operations. The developments presented herein are mainly performed on 3-RPR planar parallel robot (PPR) and can be extended to several 3-DOF PPRs providing some adaptations.

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

Access this chapter

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. Arrouk KA (2012) Techniques de Conception Assistées par Ordinateur (CAO) pour la caractérisation de l’espace de travail de robots manipulateurs parallèles. Ph.D. Thesis, Unversity Blaise PASCAL-Clermont II, Institut PASCAL

    Google Scholar 

  2. Arrouk KA et al (2012) CAD based geometric procedures for workspace and singularity determination of the 3-RPR parallel manipulator. In: Gogu G, Maniu I, Lovasz E-C, Fauroux J-C, Ciupe V (eds), Mechanisms, mechanical transmissions and robotics, pp 131–140, Trans Tech Publications, ISBN 978-3-03785-395-5

    Google Scholar 

  3. Gosselin C et al (1992) Polynomial solutions to the direct kinematic problem of planar 3-DOF parallel manipulators. Mech Mach Theor 27(2):107–119

    Article  Google Scholar 

  4. Hayes MJD et al (2004) Kinematic analysis of general planar parallel manipulators. ASME J Mech Des 126(5):866–874

    Article  Google Scholar 

  5. Husty ML (1995) Kinematic mapping of planar three-legged platforms. In: Proceedings of 15th Canadian congress of applied mechanics CANCAM, Victoria, Br. Columbia, Canada, vol 2, pp 876–877

    Google Scholar 

  6. Kilit O (2010) A new geometric algorithm for direct position analysis of planar 3-RRR manipulator. In: Proceedings of international symposium of mechanism and machine science IFToMM, Turkey, pp 396–402

    Google Scholar 

  7. Kinzel EC et al (2006) Kinematic synthesis for finitely separated positions using geometric constraint programming. ASME J Mech Des 128(5):1070–1079

    Article  Google Scholar 

  8. Pennock GR, Kassner DJ (1992) Kinematic analysis of a planar eight-bar linkage: application to a platform type robot. ASME J Mech Des 114(1):87–95

    Article  Google Scholar 

  9. Rojas N, Thomas F (2011) The forward kinematics of 3-RPR planar robots: a review and a distance-based formulation. IEEE Trans Rob 27(1):143–150

    Article  Google Scholar 

  10. Rojas N, Thomas F (2013) The univariate closure conditions of all fully parallel planar robots derived from a single polynomial. IEEE Trans Rob 29(3):758–765

    Article  Google Scholar 

  11. Tancredi L, Teillaud M (1999) Application de la géométrie synthétique au problème de modélisation géométrique directe des robots parallèles. Mech Mach Theor 34:255–269

    Article  MATH  MathSciNet  Google Scholar 

  12. Zein M et al (2008) Non-singular assembly mode changing motions for 3-RPR parallel manipulators. Mech Mach Theory 43(4):480–490

    Article  MATH  Google Scholar 

Download references

Acknowledgments

This work is supported financially by the Excellence Laboratory “LabEX” IMobS3 of Clermont-Ferrand, and the Research National Agency.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to K. A. Arrouk .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Arrouk, K.A., Bouzgarrou, B.C., Gogu, G. (2015). On the Resolution of Forward Kinematic Problem Using CAD Graphical Techniques: Application on Planar Parallel Robotic Manipulators. In: Flores, P., Viadero, F. (eds) New Trends in Mechanism and Machine Science. Mechanisms and Machine Science, vol 24. Springer, Cham. https://doi.org/10.1007/978-3-319-09411-3_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-09411-3_5

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-09410-6

  • Online ISBN: 978-3-319-09411-3

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics