Skip to main content
SpringerLink
Log in

Stiffness Modelling of Parallelogram-Based Parallel Manipulators

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

Part of the book series: Mechanisms and Machine Science ((Mechan. Machine Science,volume 5))

Abstract

The paper presents a methodology to enhance the stiffness analysis of parallel manipulators with parallelogram-based linkage. It directly takes into account the influence of the external loading and allows computing both the non-linear “load-deflection” relation and relevant rankdeficient stiffness matrix. An equivalent bar-type pseudo-rigid model is also proposed to describe the parallelogram stiffness by means of five mutually coupled virtual springs. The contributions of this paper are highlighted with a parallelogram-type linkage used in a manipulator from the Orthoglide family.

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 259.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 329.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 329.99
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. Ceccarelli M. and Carbone G., A stiffness analysis for CaPaMan (Cassino Parallel Manipulator), Mechanism and Machine Theory, 37(5):427–439, 2002.

    Article  MATH  Google Scholar 

  2. Company O., Krut S., and Pierrot F., Modelling and preliminary design issues of a 4-axis parallel machine for heavy parts handling, Journal of Multibody Dynamics, 216:1–11, 2002.

    Google Scholar 

  3. Gosselin C., Stiffness mapping for parallel manipulators, IEEE Transactions on Robotics and Automation, 6(3):377–382, 1990.

    Article  Google Scholar 

  4. Kovecses J. and Angeles J., The stiffness matrix in elastically articulated rigid-body systems, Multibody System Dynamics, 18(2):169–184, 2007.

    Article  MathSciNet  Google Scholar 

  5. Majou F., Gosselin C., Wenger P. and Chablat D., Parametric stiffness analysis of the Orthoglide, Mechanism and Machine Theory, 42:296–311, 2007.

    Article  MATH  Google Scholar 

  6. Merlet, J.-P., Parallel Robots, Kluwer Academic Publishers, Dordrecht, 2000.

    MATH  Google Scholar 

  7. Pashkevich A., Chablat D. and Wenger Ph., Stiffness analysis of overconstrained parallel manipulators, Mechanism and Machine Theory, 44:966–982, 2009.

    Article  MATH  Google Scholar 

  8. Pashkevich A., Klimchik A., Chablat D. and Wenger Ph., Stiffness analysis of multichain parallel robotic systems with loading, Journal of Automation, Mobile Robotics & Intelligent Systems, 3(3):75–82, 2009.

    Google Scholar 

  9. Pashkevich A., Klimchik A., Chablat D. and Wenger Ph., Accuracy improvement for stiffness modeling of parallel manipulators. In Proceedings of 42nd CIRP Conference on Manufacturing Systems, Grenoble, France, 2009.

    Google Scholar 

  10. Salisbury J., Active stiffness control of a manipulator in Cartesian coordinates, in Proceedings of 19th IEEE Conference on Decision and Control, pp. 87–97, 1980.

    Google Scholar 

  11. Timoshenko S. and Goodier J.N., Theory of Elasticity, 3rd ed., McGraw-Hill, New York, 1970.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut de Recherche en Communications et en Cybernetique de Nantes, 44321, Nantes, France

    A. Pashkevich, A. Klimchik, S. Caro & D. Chablat

  2. Ecole des Mines de Nantes, Nantes, France

    A. Pashkevich, A. Klimchik, S. Caro & D. Chablat

Authors
  1. A. Pashkevich
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. Klimchik
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. Caro
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. D. Chablat
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. Pashkevich .

Editor information

Editors and Affiliations

  1. Technical University of Cluj-Napoca, Memorandumului 28, Cluj-Napoca, 400114, Romania

    Doina Pisla

  2. Dipto. Meccanica, Strutture,, Ambiente e Territorio (DiMSAT), Università Cassino, Via G. di Biasio 43, Cassino, 03043, Italy

    Marco Ceccarelli

  3. Inst. Technische Mathematik,, Geometrie und Bauinformatik, Universität Innsbruck, Technikerstr. 13, Innsbruck, 6020, Austria

    Manfred Husty

  4. FB 4 Inst. f. Getriebetechnik u., Maschinendynamik, RWTH Aachen, Eilfschornsteinstr. 18, Aachen, 52062, Germany

    Burkhard Corves

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer Science+Business Media B.V.

About this paper

Cite this paper

Pashkevich, A., Klimchik, A., Caro, S., Chablat, D. (2010). Stiffness Modelling of Parallelogram-Based Parallel Manipulators. In: Pisla, D., Ceccarelli, M., Husty, M., Corves, B. (eds) New Trends in Mechanism Science. Mechanisms and Machine Science, vol 5. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-9689-0_77

Download citation

  • DOI: https://doi.org/10.1007/978-90-481-9689-0_77

  • Published:

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-9688-3

  • Online ISBN: 978-90-481-9689-0

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation