Skip to main content
Log in

A passive-biped model with multiple routes to chaos

  • Research Paper
  • Published:
Acta Mechanica Sinica Aims and scope Submit manuscript

Abstract

This paper presents a new passive-biped model consisting of a simplest walking model beneath an upper body, with no kinematic constraint. The upper body is attached to the legs with a linear torsional spring. The model is a passive dynamic walker, so it walks down a slope without energy input. The governing equations of motion are derived and simulated for the parameter analysis purposes. Simulation results reveal some different routes to chaos that have not been observed in previous models.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. McGeer, T.: Passive dynamic walking. International Journal of Robotics Research 9(5), 62–82 (1990)

    Google Scholar 

  2. McGeer, T.: Dynamics and control of bipedal locomotion. Journal of Theoretical Biology 163(3), 277–314 (1993)

    Article  Google Scholar 

  3. Garcia, M., Chatterjee, A., Ruina, A., et al.: The simplest walking model: Stability, complexity, and scaling. ASME Journal of Biomechanical Engineering 120, 281–288 (1998)

    Article  Google Scholar 

  4. Tehrani Safa, A., Ghaffari Saadat, M., Naraghi, M.: Passive dynamic of the simplest walking model: Replacing ramps with stairs. Mechanism and Machine Theory 42(10), 1314–1325 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  5. Wisse, M., Schwab, A.L., Vander Helm, F.C.T.: Passive dynamic walking model with upper body. Robotica 22, 681–688 (2004)

    Article  Google Scholar 

  6. Gomes, M.W., Ruina, A.L.: A walking model with no energy cost. Department of Theoretical and Applied Mechanics, Cornell University, 25 Aug. (2004) http://ruina.tam.cornell.edu/research/topics/locomotion and robotics/

  7. Kurz, M.J., Stergiou, N., Heidel, J., et al.: A template for the exploration of chaotic locomotive patterns. Chaos Solutions & Fractals 23(2), 485–493 (2005)

    Article  MATH  Google Scholar 

  8. Hilborn, R.C.: Chaos and Nonlinear Dynamics, An Introduction for Scientists and Engineers. 2nd edn. Oxford University Press, Oxford (2000)

    MATH  Google Scholar 

  9. Stillwell, J.: Classical Topology and Combinatorial Group Theory. 2nd edn. Springer Press, Berlin (1993)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to M. Naraghi.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Farshimi, F., Naraghi, M. A passive-biped model with multiple routes to chaos. Acta Mech Sin 27, 277–284 (2011). https://doi.org/10.1007/s10409-011-0422-3

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10409-011-0422-3

Keywords

Navigation