Skip to main content

Stiffness Analysis of Parallel Manipulators with Preloaded Passive Joints

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

Abstract

The paper presents a methodology for the enhanced stiffness analysis of parallel manipulators with internal preloading in passive joints. It also takes into account influence of the external loading and allows computing both the non-linear “load-deflection” relation and the stiffness matrices for any given location of the end-platform or actuating drives. Using this methodology, it is proposed the kinetostatic control algorithm that allows to improve accuracy of the classical kinematic control and to compensate position errors caused by elastic deformations in links/joints due to the external/internal loading. The results are illustrated by an example that deals with a parallel manipulator of the Orthoglide family where the internal preloading allows to eliminate the undesired buckling phenomena and to improve the stiffness in the neighborhood of its kinematic singularities.

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 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. Merlet, J.-P.: Parallel Robots, 2nd ed. Springer, Dordrecht (2006).

    MATH  Google Scholar 

  2. Arsenault M., Gosselin C.: Kinematic and static analysis of a 3-PUPS spatial tensegrity mechanism. Mechanism and Machine Theory 44, 162–179 (2009).

    Article  MATH  Google Scholar 

  3. Griffis M.: Preloading compliant couplings and the applicability of superposition. Mechanism and Machine Theory 41, 845–862 (2006).

    Article  MATH  Google Scholar 

  4. Ceccarelli M., Carbone G.: A stiffness analysis for CaPaMan (Cassino Parallel Manipulator). Mechanism and Machine Theory 37 (5), 427–439 (2002).

    Article  MATH  Google Scholar 

  5. Company O., Krut S., 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 

  6. Chen S., Kao I.: Conservative congruence transformation for joint and Cartesian stiffness matrices of robotic hands and fingers. The International Journal of Robotics Research 19(9), 835–847 (2000).

    Article  Google Scholar 

  7. Alici, G., Shirinzadeh, B.: The stiffness matrix in elastically articulated rigid-body systems. Multibody System Dynamics 18(2), 169–184 (2007).

    Article  MathSciNet  Google Scholar 

  8. Ciblak N., Lipkin H.: Synthesis of Cartesian stiffness for robotic applications. In: IEEE International Conference on Robotics and Automation (ICRA), Detroit, MI, pp. 2147–2152 (1999).

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  10. Quennouelle C., Gosselin C.: Stiffness matrix of compliant parallel mechanisms. In: Advances in Robot Kinematics: Analysis and Design, J. Lenarčič and P. Wenger, Springer, Dordrecht, pp. 331–341 (2008).

    Chapter  Google Scholar 

  11. Timoshenko S., Goodier J.N.: Theory of Elasticity, 3d ed. McGraw-Hill, New York (1970).

    Google Scholar 

  12. Su, H.J., McCarthy, J.M.: A polynomial homotopy formulation of the inverse static analysis of planar compliant mechanisms. Journal of Mechanical Design 128, 776–786 (2006).

    Article  Google Scholar 

  13. Carricato M., Duffy J., Parenti-Castelli V.: Catastrophe analysis of a planar system with flexural pivots. Mechanism and Machine Theory 37, 693–716 (2002).

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  Google Scholar 

  15. Crane C.D., Bayat J., Vikas V., Roberts R.: Kinematic analysis of a planar tensegrity mechanism with pre-stressed springs. In: Advances in Robot Kinematics: Analysis and Design, J. Lenarčič and P. Wenger, Springer, Dordrecht, pp. 419–427 (2008).

    Chapter  Google Scholar 

  16. Salisbury, J.: Active stiffness control of a manipulator in Cartesian coordinates. In: 19th IEEE Conference on Decision and Control, pp. 87–97 (1980).

    Google Scholar 

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

    Article  Google Scholar 

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

    Google Scholar 

  19. Chablat, D., Wenger, P.: Architecture optimization of a 3-DOF parallel mechanism for machining applications, the Orthoglide. IEEE Transactions on Robotics and Automation 19(3), 403–410 (2003).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. Pashkevich .

Editor information

Editors and Affiliations

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., Chablat, D. (2010). Stiffness Analysis of Parallel Manipulators with Preloaded Passive Joints. 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_50

Download citation

  • DOI: https://doi.org/10.1007/978-90-481-9262-5_50

  • 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