Skip to main content

Stiffness Analysis of Parallel Manipulator Using Matrix Structural Analysis

  • Conference paper
Proceedings of EUCOMES 08

Abstract

This paper describes a stiffness analysis of a 6-RSS parallel architecture by using matrix structural analysis. The stiffness analysis is based on standard concepts of static elastic deformations. The formulation has been implemented in order to obtain the stiffness matrix that can be numerically computed by defining a suitable model of the manipulator, which takes into account the stiffness properties of each element such as links, actuators and joints. In order to simplify the model, joints and actuators stiffness have been neglected. The obtained stiffness matrix was used to map the end-effector compliant displacements when external forces and torques are applied on it.

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 PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Rivin, E.I., 1999, “Stiffness and Damping in Mechanical Design”, Marcel Dekker Inc., New York.

    Google Scholar 

  2. Liu, X.-J., Jin, Z.-L. and Gao, F., 2000, “Optimum Design of 3-Dof Spherical Parallel Manipulators with Respect to the Conditioning and Stiffness Indices”, Mechanism and Machine Theory, Vol. 35, No. 9, pp. 1257–1267.

    Article  Google Scholar 

  3. Simaan, N. and Shoham, M., 2002, “Stiffness Synthesis of a Variable Geometry Planar Robot”, 8th International Symposium on Advances in Robot Kinematics ARK 2002, Lenarcic J. and Thomas F. (Editors), Kluwer Academic Publishers, Caldes de Malavella, pp. 463–472.

    Google Scholar 

  4. Carbone, G., Lim, H.O., Takanishi, A. and Ceccarelli, M., 2003, “Optimum Design of a New Humanoid Leg by Using Stiffness Analysis”, 12th International Workshop on Robotics in Alpe-Andria-Danube Region RAAD 2003, Cassino, paper 045RAAD03.

    Google Scholar 

  5. Tsai, L.W., 1999, “Robot Analysis: The Mechanics of Serial and Parallel Manipulators”, John Wiley & Sons, New York, pp. 260–297.

    Google Scholar 

  6. Yoon, W.K., Suehiro, T., Tsumaki, Y. and Uchiyama, M., 2004, “Stiffness Analysis and Design of a Compact Modified Delta Parallel Mechanism”, Robotica, Vol. 22, pp. 463–475.

    Article  Google Scholar 

  7. Deblaise, D., Hernot, X. and Maurine, P., 2006, “A Systematic Analytical Method for PKM Stiffness Matrix Calculation”.

    Google Scholar 

  8. Zhang, D., Xi, F., Mechefske, C.M. and Lang, S.Y.T., 2004, “Analysis of Parallel Kinematic Machine with Kinetostatic Modeling Method”, Robotics and Computer-Integrated Manufacturing, Vol. 20, No. 2, pp. 151–165.

    Article  Google Scholar 

  9. Majou, F., Gosselin, C.M., Wenger, P. and Chablat, D., 2004, “Parametric Stiffness Analysis of the Orthoglide”, Proc. Of the 35th International Symposium on Robotics, Paris, France.

    Google Scholar 

  10. Company, O., Pierrot, F. and Fauroux, J.C., 2005, “A Method for Modeling Analytical Stiffness of a Lower Mobility Parallel Manipulator”, Proceedings of IEEE ICRA: International Conference on Robotic and Automation, Barcelona, Spain.

    Google Scholar 

  11. Bouzgarrou, B.C., Fauroux, J.C., Gogu, G. and Heerah, Y., 2004, “Rigidity Analysis of T3R1 Parallel Robot with Uncoupled Kinematic”, Proceedings of the 35th International Symposium on Robotics, Paris, France.

    Google Scholar 

  12. Corradini, C., Fauroux, J.C., Krut, S. and Company, O., 2004, “Evaluation of a 4 Degree of Freedom Parallel Manipulator Stiffness”, Proceedings of the 11th Word Congress. In Mechanism & Machine Science, IFTOMM’2004, Tianjin, China.

    Google Scholar 

  13. Przemieniecki, J.S., 1985, “Theory of Matrix Structural Analysis”, Dover Publications, Inc., New York.

    Google Scholar 

  14. Dong, W., Du, Z. and Sun, L., 2005, “Stiffness Influence Atlases of a Novel Flexure Hinge-Based Parallel Mechanism with Large Workspace”, Proceedings of IEEE ICRA: International Conference on Robotic and Automation, Barcelona, Spain.

    Google Scholar 

  15. Shabana, A.A., 1989, “Dynamics of Multibody Systems”, John Wiley & Sons.

    Google Scholar 

  16. Alves, A.F., 2006, “Elementos Finitos A Base da Tecnologia CAE”, Editora Érica. (in Portuguese

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer Science+Business Media B.V.

About this paper

Cite this paper

Gonçalves, R.S., Carvalho, J.C.M. (2009). Stiffness Analysis of Parallel Manipulator Using Matrix Structural Analysis. In: Ceccarelli, M. (eds) Proceedings of EUCOMES 08. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-8915-2_31

Download citation

  • DOI: https://doi.org/10.1007/978-1-4020-8915-2_31

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-4020-8914-5

  • Online ISBN: 978-1-4020-8915-2

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics