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A passive-biped model with multiple routes to chaos. (English) Zbl 1270.70011

Summary: 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.

MSC:

70E60 Robot dynamics and control of rigid bodies
70K55 Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics
92C10 Biomechanics
Full Text: DOI

References:

[1] McGeer, T.: Passive dynamic walking. International Journal of Robotics Research 9(5), 62–82 (1990) · doi:10.1177/027836499000900206
[2] McGeer, T.: Dynamics and control of bipedal locomotion. Journal of Theoretical Biology 163(3), 277–314 (1993) · doi:10.1006/jtbi.1993.1121
[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) · doi:10.1115/1.2798313
[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) · Zbl 1130.70005 · doi:10.1016/j.mechmachtheory.2006.11.001
[5] Wisse, M., Schwab, A.L., Vander Helm, F.C.T.: Passive dynamic walking model with upper body. Robotica 22, 681–688 (2004) · doi:10.1017/S0263574704000475
[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) · Zbl 1088.37054 · doi:10.1016/j.chaos.2004.04.034
[8] Hilborn, R.C.: Chaos and Nonlinear Dynamics, An Introduction for Scientists and Engineers. 2nd edn. Oxford University Press, Oxford (2000) · Zbl 1015.37001
[9] Stillwell, J.: Classical Topology and Combinatorial Group Theory. 2nd edn. Springer Press, Berlin (1993) · Zbl 0774.57002
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