Compliant leg behaviour explains basic dynamics of walking and running

Proceedings of the Royal Society B: Biological Sciences

Volumn 273, Issue 1603, 2006, Pages 2861-2867

  Geyer, Hartmut ^a,b   Seyfarth, Andre ^a   Blickhan, Reinhard ^a  

^a FRIEDRICH SCHILLER UNIVERSITY JENA   (Germany)

^b MIT MEDIA LAB   (United States)

Author keywords

Biomechanics; Human gait; Spring mass model

Indexed keywords

BIOMECHANICS; BIPEDALISM; MODEL; MOVEMENT;

ARTICLE; BIOMECHANICS; COMPLIANCE (PHYSICAL); DYNAMICS; GAIT; GRAVITY; LEG; LOCOMOTION; OSCILLATION; PRIORITY JOURNAL; RIGIDITY; RUNNING; WALKING; WALKING SPEED;

EID: 33751082090     PISSN: 09628452     EISSN: 14712970     Source Type: Journal    
DOI: 10.1098/rspb.2006.3637     Document Type: Article

References (42)

1. Alexander, R. 1976 Mechanics of bipedal locomotion. In Perspectives in experimental biology (ed. P. S. Davies), pp. 493-504. Oxford, UK: Pergamon Press.
2. Alexander, R. 1989 Optimization and gaits in the locomotion of vertebrates. Physiol. Rev. 69, 1199-1227.
3. Alexander, R. 1991 Energy-saving mechanisms in walking and running. J. Exp. Biol. 160, 55-69.
4. Blickhan, R. 1989 The spring-mass model for running and hopping. J. Biomech. 22, 1217-1227. (doi:10.1016/0021-9290(89)90224-8)
5. Borelli, G. 1685. De motu animalium, vol. 1. Leiden, The Netherlands: Lugduni.
6. Cavagna, G., Saibene, F. & Margaria, R. 1964 Mechanical work in running. J. Appl. Physiol. 19, 249-256.
7. Cavagna, G., Heglund, N. & Taylor, C. 1977 Mechanical work in terrestrial locomotion: two basic mechanisms for minimizing energy expenditure. Am. J. Physiol. 233, 243-261.
8. Cham, J., Karpick, J. K. & Cutkosky, M. R. 2004 Stride period adaptation for a biomimetic running hexapod. Int. J. Robotics Res. 23, 141-153.
9. Collins, S., Ruina, A., Tedrake, R. & Wisse, M. 2005 Efficient bipedal robots based on passive-dynamic walkers. Science 307, 1082-1085. (doi:10.1126/science.1107799)
10. Dickinson, M., Farley, C., Full, R., Koehl, M., Kram, R. & Lehman, S. 2000 How animals move: an integrative view. Science 288, 100-106. (doi:10.1126/science.288.5463.100)
11. Farley, C., Glasheen, J. & McMahon, T. 1993 Running springs: speed and animal size. J. Exp. Biol. 185, 71-86.
12. Fischer, O. 1899. Der Gang des Menschen 2. Teil: Die Bewegung des Gesamtschwerpunktes und die äußeren Kräfte. Abhandlungen der mathematisch-physischen Klasse der Königl, vol. 25. Leipzig, Germany: Sächsischen Gesellschaft der Wissenschaften.
13. Fukunaga, T., Kubo, K., Kawakami, Y., Fukashiro, S., Kanehisa, H. & Maganaris, C. 2001 In vivo behaviour of human muscle tendon during walking. Proc. R. Soc. B 268, 229-233. (doi:10.1098/rspb.2000.1361)
14. Full, R. & Koditschek, D. 1999 Templates and anchors: neuromechanical hypotheses of legged locomotion on land. J. Exp. Biol. 202, 3325-3332.
15. Garcia, M., Chatterjee, A., Ruina, A. & Coleman, M. 1998 The simplest walking model: stability, complexity, and scaling. J. Biomech. Eng. 120, 281-288.
16. Gard, S., Miff, S. & Kuo, A. 2004 Comparison of kinematic and kinetic methods for computing the vertical motion of the body center of mass during walking. Hum. Mov. Sci. 22, 597-610. (doi:10.1016/j.humov.2003.11.002)
17. Ghigliazza, R., Altendorfer, R., Holmes, P. & Koditschek, D. 2003 A simply stabilized running model. SIAM J. Appl. Dyn. Syst. 2, 187-218. (doi:10.1137/S1111111102408311)
18. Gurp, M. V., Schamhardt, H. & Crowe, A. 1987 The ground reaction force pattern from the hindlimb of the horse simulated by a spring model. Acta Anat. 129, 31-33.
19. Hreljac, A. 1993 Preferred and energetically optimal gait transition speeds in human locomotion. Med. Sci. Sports Exerc. 25, 1158-1162.
20. Keller, T., Weisberger, A., Ray, J., Hasan, S., Shiavi, R. & Spengler, D. 1996 Relationship between vertical ground reaction force and speed during walking, slow jogging, and running. Clin. Biomech. 11, 253-259. (doi:10.1016/0268-0033(95)00068-2)
21. Kram, R., Domingo, A. & Ferris, P. 1997 Effect of reduced gravity on the preferred walk-run transition speed. J. Exp. Biol. 200, 821-826.
22. Kuo, A. 1999 Stabilization of lateral motion in passive dynamic walking. Int. J. Rob. Res. 18, 917-930. (doi:10.1177/02783649922066655)
23. Lee, C. & Farley, C. 1998 Determinants of the center of mass trajectory in human walking and running. J. Exp. Biol. 201, 2935-2944.
24. Marey, E. 1894 Le mouvement. Paris, France: Masson.
25. McGeer, T. 1990 Passive dynamic walking. Int. J. Rob. Res. 9, 62-82.
26. McMahon, T. & Cheng, G. 1990 The mechanism of running: how does stiffness couple with speed? J. Biomech. 23, 65-78. (doi:10.1016/0021-9290(90) 90042-2)
27. Minetti, A. 2001 Walking on other planets. Nature 409, 467-468. (doi:10.1038/35054166)
28. Minetti, A., Ardigo, L. & Saibene, F. 1994 The transition between walking and running in humans: metabolic and mechanical aspects at different gradients. Acta Physiol. Scand. 150, 315-323.
29. Minetti, A., Ardigo, L., Reinach, E. & Saibene, F. 1999 The relationship between mechanical work and energy expenditure of locomotion in horses. J. Exp. Biol. 202, 2329-2338.
30. Mochon, S. & McMahon, T. 1980 Ballistic walking. J. Biomech. 13, 49-57. (doi:10.1016/0021-9290(80)90007-X)
31. Neptune, R., Kautz, S. & Zajac, F. 2001 Contribution of the individual ankle plantar flexors to support, forward progression and swing initiation during walking. J. Biomech. 34, 1387-1398. (doi:10.1016/S0021- 9290(01)00105-1)
32. Pandy, M. 2003 Simple and complex models for studying muscle function in walking. Phil. Trans. R. Soc. B 358, 1501-1509. (doi:10.1098/rstb.2003.1338)
33. Pandy, M. & Berme, N. 1988 Synthesis of human walking: a planar model for single support. J. Biomech. 21, 1053-1060. (doi:10.1016/0021-9290(88)90251- 5)
34. Raibert, M. 1986 Legged robots that balance. Cambridge, UK: MIT Press.
35. Saranli, U., Buehler, M. & Koditschek, D. 2001 Rhex: a simple and highly mobile hexapod robot. Int. J. Rob. Res. 20, 616-631. (doi:10.1177/ 02783640122067570)
36. Seyfarth, A., Geyer, H., Günther, M. & Blickhan, R. 2002 A movement criterion for running. J. Biomech. 35, 649-655. (doi:10.1016/S0021- 9290(01)00245-7)
37. Siegler, S., Seliktar, R. & Hyman, W. 1982 Simulation of human gait with the aid of a simple mechanical model. J. Biomech. 15, 415-425. (doi:10.1016/0021-9290(82)90078-1)
38. Srinivasan, M. & Ruina, A. 2005 Computer optimization of a minimal biped model discovers walking and running. Nature 439, 72-75. (doi:10.1038/nature04113)
39. Strogatz, S. 2001 Nonlinear dynamics and chaos. New York, NY: Perseus.
40. Thorstensson, A. & Roberthson, H. 1987 Adaptations to changing speed in human locomotion: speed of transition between walking and running. Acta Physiol. Scand. 131, 211-214.
41. Weber, W. & Weber, E. 1836 Mechanik der menschlichen Gehwerkzeuge. Göttingen, Germany: Dietrichsche Buchhandlungen.
42. Zajac, F., Neptune, R. & Kautz, S. 2003 Biomechanics and muscle coordination of human walking part II: lessons from dynamical simulations and clinical implications. Gait Posture 17, 1-17. (doi:10.1016/S0966-6362(02)00069- 3)