Journal of the Korean Society for Precision Engineering (한국정밀공학회지)

Korean Society for Precision Engineering (한국정밀공학회)
권호 표지

Correlation between the Displacement of Center of Gravity and Lyapunov Exponent during Treadmill Walking

트레드밀 보행에서 무게중심 이동과 리아프노프 지수 사이의 상관관계

  • Kim, Soo-Han (School of Mechanical Engineering, Pusan Univ.) ;
  • Park, Jung-Hong (School of Mechanical Engineering, Pusan Univ.) ;
  • Son, Kwon (School of Mechanical Engineering, Pusan Univ.)
  • 김수한 (부산대학교 기계설계대학원) ;
  • 박정홍 (부산대학교 기계공학부) ;
  • 손권 (부산대학교 기계공학부)
  • Published : 2010.02.01
Download PDF
⟨ Previous Next ⟩

Abstract

The purpose of study is to investigate the correlation between the Lyapunov exponent (LE) and the displacement of the center of gravity (DCG) for clarifying walking stability on the treadmill. From fifteen young healthy subjects volunteered, lower extremity joint angles were recorded using a three-dimensional motion capture system with reflective markers. The anteroposterior DCG and the LE were calculated by a commercial software. A linear correlation between LE and DCG (p<0.05) showed that LEs compensated for walking distance on the treadmill walking. However, LEs were found to be independent of self-selected walking speeds by a negligible correlation between LE and the Froude number (p>0.05).

Keywords

References

  1. Sutherland, D. H., Olshen, R. A., Biden, E. N. and Wyatt, M. P., "The development of nature walking," Mac Keith Press, pp. 20-35, 1988.
  2. Stergiou, N., Moraiti, C., Giakas, G., Rastanis, S. and Georgoulis, A. D., "The effect of the walking speed on the stability of the anterior cruciate ligament deficient knee," Clin. Biomech., Vol. 19, No. 9, pp. 957-963, 2004. https://doi.org/10.1016/j.clinbiomech.2004.06.008
  3. Buzzi, U. H., Stergiou, N., Kurz, M. J., Hageman, P. A. and Heidel, J., "Nonlinear dynamics indicates aging affects variability during gait," Clin. Biomech., Vol. 18, No. 5, pp. 435-443, 2004.
  4. Dingwell, J. B., Cusumano, J. P., Srernad, D. and Cavanagh, P. R., "Slower speeds in patients with diabetic neuropathy lead to improved local dynamic stability of continuous overground walking," J. of Biomech., Vol. 33, No. 10, pp. 1269-1277, 2000. https://doi.org/10.1016/S0021-9290(00)00092-0
  5. Dingwell, J. B. and Cusumano, J. P., "Nonlinear time series analysis of normal and pathological human walking," Chaos, Vol. 10, No. 4, pp. 848-863, 2000. https://doi.org/10.1063/1.1324008
  6. Alexander, R. M., "Stride length and speed for adults, children and fossil hominids," Am. J. Phys. Anthropol., Vol. 63, No. 1, pp. 23-27, 1984. https://doi.org/10.1002/ajpa.1330630105
  7. Karen, S. N. and Timothy, D. W., "Froude number corrections in anthropological studies," Am. J. Phys. Anthropol., Vol. 131, No. 1, pp. 27-32, 2006. https://doi.org/10.1002/ajpa.20404
  8. KWON3D Manual, www.visol.co.kr
  9. Rapp, P. E., "A guide to dynamical analysis," Int. Phys. Behav. Sci., Vol. 29, No. 3, pp. 311-327, 1994. https://doi.org/10.1007/BF02691335
  10. Ko, J. H., Son, K., Park, J. H. and Suh, J. T., " Gait study on the normal and ACL deficient patients after ligament reconstruction surgery using chaos analysis method," J. of KSPE, Vol. 23, No. 2, pp. 164-171, 2006.
  11. Park, J. H., Son, K. and Kim, K. H., "Chaos analysis of major joint motions for young males during walking," Trans. of KSME(A), Vol. 31, No. 8, pp. 889-895, 2007.
  12. Kim, M. K., Son, K., Park, J. H., Seo, K. W. and Park, Y. H., "Chaos analysis of major joint motions for women during walking," J. of KSPE, Vol. 25, No. 10, pp. 130-136, 2008.
  13. Baker, G. L. and Gollub, J. P., Chaotic Dynamics, Cambridge University Press, 1996.
  14. Fraser, A. M. and Swinney, M. L., "Independent coordinates for strange attractors from mutual information," Phys. Rev.(A), Vol. 33, No. 2, pp. 1134-1140, 1986. https://doi.org/10.1103/PhysRevA.33.1134
  15. Cellucci, C. J., Albano, A. M. and Rapp, P. E., "Comparative study of embedding methods," Phys. Rev.(E), Vol. 67, No. 6, Paper No. 066210, 2003.
  16. Rhodes, C. and Morari, M., "The false nearest neighbors algorithm: An overview," Computer & Chemical Engineering, Vol. 21, No. 1, pp. 1149-1154, 1997. https://doi.org/10.1016/S0098-1354(97)00204-4
  17. Wolf, A., Swift, J. B., Swinney, H. L. and Vastano, J. A., "Determining Lyapunov exponents from a time series," Phys. D: Nonlinear Phenomena, Vol. 16, No. 3, pp. 285-317, 1985. https://doi.org/10.1016/0167-2789(85)90011-9
  18. Nelson, R. C., Dillman, P. L. and Bickett, P., "Biomechanics of overground versus treadmill running," Med. Sci. Sports, Vol. 4, No. 4, pp. 233-240, 1972. https://doi.org/10.1249/00005768-197200440-00029
  19. Collett, J., Dawes, H., Howells, K., Elsworth, C., Izadi, H. and Sacklet, C., "Anomalous centre of mass energy fluctuations during treadmill walking in healthy individuals," Gait and Posture, Vol. 26, No. 3, pp. 400-406, 2006.