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How well can spring-mass-like telescoping leg models fit multi-pedal sagittal-plane locomotion data? (English) Zbl 1400.92052
Summary: Idealized mathematical models of animals, with point-mass bodies and spring-like legs, have been used by researchers to study various aspects of terrestrial legged locomotion. Here, we fit a bipedal spring-mass model to the ground reaction forces of human running, a horse trotting, and a cockroach running. We find that, in all three cases, while the model captures center-of-mass motions and vertical force variations well, horizontal forces are less well reproduced, primarily due to variations in net force vector directions that the model cannot accommodate. The fits result in different apparent leg stiffnesses in the three animals. Assuming a simple fixed leg-angle touch-down strategy, we find that the gaits of these models are stable in different speed-step length regimes that overlap with those used by humans and horses, but not with that used by cockroaches.

92C10 Biomechanics
Full Text: DOI
[1] Alexander, R.M., Optimum walking techniques for quadrupeds and bipeds, J. zool. lond., 192, 97-117, (1980)
[2] Alexander, R.M., A model of bipedal locomotion on compliant legs, Philos. trans. R. soc. lond. B, 338, 189-198, (1992)
[3] Alexander, R.M.; Jayes, A.S., Fourier analysis of forces exerted in walking and running, J. biomech., 13, 383-390, (1980)
[4] Altendorfer, R.; Koditschek, D.E.; Holmes, P., Stability analysis of legged locomotion models by symmetry-factored return maps, Int. J. robotics res., 23, 10-11, 979-999, (2004)
[5] Blickhan, R., The spring-mass model for running and hopping, J. biomech., 22, 1217-1227, (1989)
[6] Blickhan, R.; Full, R.J., Similarity in multilegged locomotion: bouncing like a monopode, J. comp. physiol. A., 173, 509-517, (1993)
[7] Bullimore, S.R.; Burn, J.F., Consequences of forward translation of the point of force application for the mechanics of running, J. theor. biol., 238, 211-219, (2006)
[8] Carver, S.G., 2003. Control of a spring mass hopper. Ph.D. Thesis, Cornell University, Ithaca.
[9] Dutto, D.J.; Hoyt, D.F.; Cogger, E.A.; Wickler, S.J., Ground reaction forces in horses trotting up an incline and on the level over a range of speeds, J. exp. biol., 207, 3507-3514, (2004)
[10] Farley, C.T.; Gonzalez, O., Leg stiffness and stride frequency in human running, J. biomech., 29, 181-186, (1996)
[11] Farley, C.T.; Glasheen, J.; McMahon, T.A., Running springs: speed and animal size, J. exp. biol., 185, 71-86, (1993)
[12] Full, R.J.; Tu, M.S., Mechanics of six-legged runners, J. exp. biol., 148, 129-146, (1990)
[13] Full, R.J.; Tu, M.S., Mechanics of a rapid running insect: two-, four- and six-legged locomotion, J. exp. biol., 156, 215-231, (1991)
[14] Geyer, H.; Seyfarth, A.; Blickhan, R., Spring mass running: simple approximate solution and application to gait stability, J. theor. biol., 232, 315-328, (2005)
[15] Geyer, H.; Seyfarth, A.; Blickhan, R., Compliant leg behaviour explains basic dynamics of walking and running, Proc. R. soc. lond. ser. B, 273, 2861-2867, (2006)
[16] Ghigliazza, R.; Altendorfer, R.; Holmes, P.; Koditschek, D., A simply stabilized running model, SIAM J. appl. dyn. syst., 2, 2, 187-218, (2003), Revised and updated version in SIGEST, SIAM Rev. 47(3), 519-549, 2005 · Zbl 1088.34517
[17] Hamill, J.; Bates, B.T.; Knutzen, K.M.; Sawhill, J.A., Variations in ground reaction force parameters at different running speeds, Human mov. sci., 2, 47-56, (1983)
[18] Holmes, P.; Full, R.J.; Koditschek, D.; Guckenheimer, J., The dynamics of legged locomotion: models, analyses and challenges, SIAM rev., 48, 2, 207-304, (2006) · Zbl 1100.34002
[19] Holmes, P., Srinivasan, M., Rogale, K., Kukillaya, R., 2006b. On spring-mass models for running animals: approximate solutions, natural frequencies, stability and double stance phases. In: James H. Belfer Memorial Symposium on Nonlinear Mechanics. Technion, Israel.
[20] Höltje, M.; Hustert, R., Rapid mechano-sensory pathways code leg impact and elicit very rapid reflexes in insects, J. exp. biol., 206, 2715-2724, (2003)
[21] Hoyt, D.F.; Wickler, S.J.; Cogger, E.A., Time of contact and step length: the effect of limb length, running speed, load carrying and incline, J. exp. biol., 203, 221-227, (2000)
[22] Kram, R.; Griffin, T.M.; Donelan, J.M.; Chang, Y.H., Force treadmill for measuring vertical and horizontal ground reaction forces, J. appl. physiol., 85, 764-769, (1998)
[23] McGeer, T., Passive bipedal running, Proc. R. soc. lond. B, 240, 107-134, (1990)
[24] McMahon, T.A.; Cheng, G.C., The mechanics of running: how does stiffness couple with speed?, J. biomech., 23, Suppl. 1, 65-78, (1990)
[25] O’Connor, S.M., Kuo, A.D., 2006. Passive dynamic walking with springy legs. In: Dynamic Walking Meeting: Mechanics and Control of human and robot locomotion, Ann Arbor, MI, USA.
[26] Schmitt, J.; Holmes, P., Mechanical models for insect locomotion: dynamics and stability in the horizontal plane, Theory biol. cybern., 83, 6, 501-515, (2000) · Zbl 1033.92005
[27] Seipel, J.; Holmes, P., Three dimensional translational dynamics and stability of multi-legged runners, Int. J. robotics res., 25, 9, 889-902, (2006)
[28] Seipel, J.E.; Holmes, P., Running in three dimensions: analysis of a point-mass sprung-leg model, Int. J. robotics res., 24, 8, 657-674, (2005)
[29] Seyfarth, A.; Geyer, H.; Gunther, M.; Blickhan, R., A movement criterion for running, J. biomech., 35, 649-655, (2002)
[30] Seyfarth, A.; Geyer, H.; Herr, H., Swing-leg retraction: a simple control model for stable running, J. exp. biol., 206, 2547-2555, (2003)
[31] Srinivasan, M.; Ruina, A., Computer optimization of a minimal biped model discovers walking and running, Nature, 439, 72-75, (2006)
[32] Ting, L.H.; Blickhan, R.; Full, R.J., Dynamic and static stability in hexapedal runners, J. exp. biol., 197, 251-269, (1994)
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