Spring-mass running: Simple approximate solution and application to gait stability

Journal of Theoretical Biology

Volumn 232, Issue 3, 2005, Pages 315-328

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

^a FRIEDRICH SCHILLER UNIVERSITY JENA   (Germany)

Author keywords

Approximate solution; Biomechanics; Spring mass running; Stability

Indexed keywords

BIOMECHANICS;

ACCURACY; ANALYTIC METHOD; ARTICLE; BIOMECHANICS; CORRELATION ANALYSIS; EMPIRICISM; GAIT; LOCOMOTION; MATHEMATICAL COMPUTING; MATHEMATICAL MODEL; MECHANICAL STRESS; PARAMETER; PREDICTION; PRIORITY JOURNAL; ROBOTICS; RUNNING; STANDING;

ANIMALS; BIOMECHANICS; GAIT; HUMANS; MODELS, BIOLOGICAL; RUNNING;

ANIMALIA;

EID: 9644275307     PISSN: 00225193     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jtbi.2004.08.015     Document Type: Article

References (28)

1. R.M. Alexander Optimization and gaits in the locomotion of vertebrates Physiol. Rev. 69 1989 1199 1227
2. Altendorfer, R., Koditschek, D.E., Holmes, P., 2003. Towards a factored analysis of legged locomotion models. In: Proceedings of the International Conference on Robotics and Automation. Taipei, Taiwan, pp. 37-44.
3. A. Arampatzis, G. Brüggemann, and V. Metzler The effect of speed on leg stiffness and joint kinetics in human running J. Biomech. 32 1999 1349 1353
4. R. Blickhan The spring-mass model for running and hopping J. Biomech. 22 1989 1217 1227
5. R. Blickhan, and R.J. Full Similarity in multilegged locomotion bouncing like a monopode J. Comp. Physiol. 173 1993 509 517
6. M.J. Coleman, and P. Holmes Motions and stability of a piecewise holonomic system the discrete chaplygin sleigh Regul. Chaot. Dynamics 4 2 1999 1 23
7. M.J. Coleman, A. Chatterjee, and A. Ruina Motions of a rimless spoked wheel a simple three-dimensional system with impacts Dynamics Stability Systems 12 1997 139 159
8. C.T. Farley, and O. Gonzalez Leg stiffness and stride frequency in human running J. Biomech. 29 2 1996 181 186
9. C.T. Farley, R. Blickhan, J. Saito, and C.R. Taylor Hopping frequency in humans A test of how springs set stride frequency in bouncing gaits J. Appl. Physiol. 71 6 1991 2127 2132
10. C.T. Farley, J. Glasheen, and T.A. McMahon Running springs speed and animal size J. Exp. Biol. 185 1993 71 86
11. Geyer, H., 2001. Movement criterion of fast locomotion: mathematical analysis and neuro-biomechanical interpretation with functional muscle reflexes. Diploma Thesis.
12. Geyer, H., Blickhan, R., Seyfarth, A., 2002. Natural dynamics of spring-like running - emergence of selfstability. In: Proceedings of the Fifth International Conference on Climbing and Walking Robots. Professional Engineering Publishing Limited, pp. 87-92.
13. R.M. Ghigliazza, R. Altendorfer, P. Holmes, and D.E. Koditschek A simply stabilized running model SIAM J. Appl. Dynamical Systems 2 2 2003 187 218
14. J.P. He, R. Kram, and T.A. McMahon Mechanics of running under simulated low gravity J. Appl. Physiol. 71 3 1991 863 870
15. T.A. McMahon, and G.C. Cheng The mechanism of running how does stiffness couple with speed? J Biomech. 23 1990 65 78
16. M.H. Raibert Legged Robots that Balance 1986 MIT Press Cambridge
17. A. Ruina Non-holonomic stability aspects of piecewise holonomic systems Rep. Math. Phys. 42 1/2 1998 91 100
18. Saranli, U., Koditschek, D.E., 2003. Template based control of hexapedal running. In: Proceedings of the IEEE International Conference on Robotics and Automation, Taipei, Taiwan, pp. 1374-1379.
19. Saranli, U., Schwind, W.J., Koditschek, D.E., 1998. Towards the control of a multi-jointed, monoped runner, leuven, Belgium. In: Proceedings of the IEEE International Conference on Robotics and Automation, pp. 2676-2682.
20. U. Saranli, M. Buehler, and D.E. Koditschek Rhex A simple and highly mobile hexapod robot Int. J. Robotics Res. 20 7 2001 616 631
21. J. Schmitt, and P. Holmes Mechanical models for insect locomotion dynamics and stability in the horizontal plane I Theory. Biol. Cybern. 83 2000 501 515
22. W.J. Schwind, and D.E. Koditschek Approximating the stance map of a 2-DOF monoped runner J. Nonlinear Sci. 10 2000 533 568
23. Seyfarth, A., Geyer, H., 2002. Natural control of spring-like running - optimized self-stabilization. In: Proceedings of the Fifth International Conference on Climbing and Walking Robots. Professional Engineering Publishing Limited, pp. 81-85.
24. Seyfarth, A., Apel, T., Geyer, H., Blickhan, R., 2001. Limits of elastic leg operation. In: Blickhan, R. (Ed.), Motion Systems 2001. Shaker Verlag, Aachen, pp. 102-107.
25. A. Seyfarth, H. Geyer, M. Günther, and R. Blickhan A movement criterion for running J. Biomech. 35 2002 649 655
26. A. Seyfarth, H. Geyer, and H.M. Herr Swing-leg retraction a simple control model for stable running J. Exp. Biol. 206 2003 2547 2555
27. E.T. Whittacker A treatise on the analytical dynamics of particles and rigid bodies Fourth ed. 1904 Cambridge University Press New York
28. S.J. Wickler, D.F. Hoyt, E.A. Cogger, and K.M. Hall Effect of load on preferred speed and cost of transport J. Appl. Physiol. 90 2001 1548 1551