Skip to main content
SpringerLink
Log in
Book cover

Advances in Robot Kinematics: Motion in Man and Machine pp 263–272Cite as

Equilibrium Analysis of Tensegrity Structures with Elastic Ties

  • Conference paper
  • First Online:

  • 3392 Accesses

Abstract

In this paper, the equilibrium analysis of a passive tensegrity structure with elastic connecting ties is addressed. The problem is modeled as a constrained optimization of the total potential energy of the system and the Lagrange multiplier method is used to deduce the equilibrium equations. The homotopy continuation method is used to completely solve the resulting nonlinear polynomial system and all the equilibrium positions are identified. Furthermore, the stability analysis of the equilibrium configurations is carried out using the second order condition and higher order condition for cases where the second order condition fails. One numerical example is provided to demonstrate the analysis

This is a preview of subscription content, 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   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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Tobie, R.S.: A report on an inquiry into the existence, formation and representation of tensile structures. Master of Industrial Design Thesis, Pratt Institute, New York (1976).

    Google Scholar 

  2. Yin, J.P.: An analysis for the design of self-deployable tensegrity and reinforced tensegrity prisms with elastic ties. Ph.D. Dissertation, University of Florida, Gainesville, FL (2000).

    Google Scholar 

  3. Edmondson, A., A Fuller Explanation: The Synergetic Geometry of R. Buckminster Fuller. Birkhäuser, Boston (1987).

    Google Scholar 

  4. Fuller, R., Synergetics: The Geometry of Thinking. MacMillan Publishing, New York (1975).

    Google Scholar 

  5. Kenner, H.: Geodesic Math and How to Use It. University of California Press, Berkeley (1976).

    Google Scholar 

  6. Stern, I.: Development of design equations for self-deployable N-strut tensegrity systems. M.S. Thesis, University of Florida, Gainesville, FL (1999).

    Google Scholar 

  7. Correa, J., Crane, C., Duffy, J.: Static analysis of tensegrity structures. ASME Journal of Mechanical Design, 127(2), 257–268 (2005).

    Article  Google Scholar 

  8. Roth, B., Whitely, W.: Tensegrity frameworks. Transactions of the American Mathemetical Society, 265, 419–446 (1981).

    MATH  Google Scholar 

  9. Connelly, R.: Rigidity and energy. Inventiones Mathematicae, 66, 11–33 (1982).

    Article  MATH  MathSciNet  Google Scholar 

  10. Pellegrino, S., Calladine, C., Two step matrix analysis of prestresssed cable nets. In: Proceedings of the Third International Conference of Space Structures (1984).

    Google Scholar 

  11. Pellegrino, S.: Matrix analysis of statically and kinematically indeterminate frameworks. International Journal of Solids and Structures, 22(4), 409–428 (1986).

    Article  MathSciNet  Google Scholar 

  12. Pellegrino, S.: Analysis of prestressed mechanisms. International Journal of Solids and Structures, 26(12), 1329–1350 (1989).

    Article  Google Scholar 

  13. Calladine, C.: First order infinitesimal mechanisms. International Journal of Solids and Structures, 27(4), 505–515 (1991).

    Article  MATH  MathSciNet  Google Scholar 

  14. Calladine, C., Pellegrino, S.: Further remarks on first order infinitesimal mechanisms. International Journal of Solids and Structures, 29, 2119–2122 (1992).

    Article  Google Scholar 

  15. Tibert, A., Pellegrino, S.: Review of form-finding methods for tensegrity structures. International Journal of Solids and Structures, 18(4), 209–223 (2003).

    Google Scholar 

  16. Arsenault, M., Gosselin, C.: Static balancing of tensegrity mechanisms. ASME Journal of Mechanical Design, 129, 295–300 (2007).

    Article  Google Scholar 

  17. Streit, D., Gilmore, B.: Perfect spring equilibrators for rotable bodies. ASME Journal of Mechanisms, Transmissions, Automation in Design, 111(4), 451–458 (1989).

    Article  Google Scholar 

  18. Herder, J., Energy-free systems: Theory, conception and design of statically balanced spring mechanisms. Ph.D. Dissertation, Delft University of Technology, Delft, FL (2001).

    Google Scholar 

  19. Connelly, R., Whiteley, W.: Second order rigidity and prestress stability for tensegrity frameworks. Discrete Mathematics, 9(3), 453–491 (1996).

    Article  MATH  MathSciNet  Google Scholar 

  20. Bayat, J., Crane, C., Closed-form equilibrium analysis of planar tensegrity structures. In: Proceedings of the ASME 2007 International Design Engineering Technical Conferences and Computers and Information Engineering Conference, Las Vegas (2007).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Florida, Gainesville, Florida, USA

    O. Anubi & C. Crane

Authors
  1. O. Anubi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. C. Crane
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to O. Anubi .

Editor information

Editors and Affiliations

  1. Inst. J. Stefan, University Ljubljana, Ljubljana, Slovenia

    Jadran Lenarcic

  2. , Aerospace and Mechanical Engineering, University of Notre Dame, Fitzpatrick Hall 365, Notre Dame, 46556-5637, USA

    Michael M. Stanisic

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer Science+Business Media B.V.

About this paper

Cite this paper

Anubi, O., Crane, C. (2010). Equilibrium Analysis of Tensegrity Structures with Elastic Ties. 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_28

Download citation

  • DOI: https://doi.org/10.1007/978-90-481-9262-5_28

  • 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

Search

Navigation