Abstract
An innovative lower extremity exoskeleton with hybrid leg structures is proposed in this paper. The compound pendulum model is applied to analyze the swing motion during walking for the wearer and the exoskeleton respectively. The expression of the resonant period for the human lower limb is obtained and the optimum stride frequency, at which the energy expenditure for walking is the least, coincides with the stride frequency of strolling well. As for the exoskeleton, the relationship between the inertial parameters and the resonant period of the hybrid leg is established. To minimize the walking energy cost for the exoskeleton, the inertial parameter design must guarantee that the resonant period of the hybrid leg coincides with the actual stride period of the wearer. The resonant period of the hybrid leg is also influenced by the scissor angle which determines the distance between the hip and the ankle of the lower extremity exoskeleton (SJTU-EX) and can be adjusted to match different stride frequencies of various motions by the proper scissor angle planning.
Similar content being viewed by others
References
Yang C, Zhang J, Chen Y, Dong Y, Zhang Y. A review of exoskeleton-type systems and their key technologies. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2008, 222, 1599–1612.
Chao E. Biomechanics of the human gait. Frontiers in Biomechanics, Springer, New York, USA, 1986, 225–244.
Zarrugh M, Radcliffe C. Predicting metabolic cost of level walking. European Journal of Applied Physiology and Occupational Physiology, 1978, 38, 215–223.
Zarrugh M, Todd F, Ralston H. Optimization of energy expenditure during level walking. European Journal of Applied Physiology and Occupational Physiology, 1974, 33, 293–306.
Cavagna G A, Willems P A, Franzetti P, Detrembleur C. The two power limits conditioning step frequency in human running. The Journal of Physiology, 1991, 437, 95–108.
Willems P, Cavagna G A, Heglund N C. External, internal and total work in human locomotion. The Journal of Experimental Biology, 1995, 198, 379–393.
Cavagna G A, Franzetti P, Heglund N C, Willems P. The determinants of the step frequency in running, trotting and hopping in man and other vertebrates. The Journal of Physiology, 1988, 399, 81–92.
Cavagna G A, Franzetti P. The determinants of the step frequency in walking in humans. The Journal of Physiology, 1986, 373, 235–242.
Danion F, Bonnard M, Pailhous J. Joint-dependent mechanisms to adapt to an imbalance between flexion and extension forces in human gait. Neuroscience Letters, 1995, 187, 185–188.
Danion F, Varraine E, Bonnard M, Pailhous J. Stride variability in human gait: The effect of stride frequency and stride length. Gait & Posture, 2003, 18, 69–77.
Meng Q, Li B, Holstein H. Recognition of human periodic movements from unstructured information using a motion-based frequency domain approach. Image and Vision Computing, 2006, 24, 795–809.
Li B, Holstein H. Recognition of human periodic motion-a frequency domain approach. Proceedings of 16th International Conference on Pattern Recognition, Quebec, Canada, 2002, 311–314.
Cooper R C, Prebeau-Menezes L M, Butcher M T, Bertram J E. Step length and required friction in walking. Gait & Posture, 2008, 27, 547–551.
Bertram J E. Constrained optimization in human walking: Cost minimization and gait plasticity. The Journal of Experimental Biology, 2005, 208, 979–991.
Bertram J E, Ruina A. Multiple walking speed-frequency relations are predicted by constrained optimization. Journal of Theoretical Biology, 2001, 209, 445–453.
Kuo A D, Donelan J M, Ruina A. Energetic consequences of walking like an inverted pendulum: Stepto-step transitions. Exercise and Sport Sciences Reviews, 2005, 33, 88–97.
Kuo A D. Energetics of actively powered locomotion using the simplest walking model. Journal of Biomechanical Engineering, 2002, 124, 113–120.
Kuo A D. A simple model of bipedal walking predicts the preferred speed-step length relationship. Journal of Biomechanical Engineering, 2001, 123, 264–269.
Högberg P. How do stride length and stride frequency influence the energy-output during running? Arbeitsphysiologie, 1952, 14, 437–441.
Ferris D P, Louie M, Farley C T. Running in the real world: Adjusting leg stiffness for different surfaces. Proceedings of the Royal Society of London. Series B: Biological Sciences, 1998, 265, 989–994.
Biewener A A, Farley C T, Roberts T J, Temaner M. Muscle mechanical advantage of human walking and running: Implications for energy cost. Journal of Applied Physiology, 2004, 97, 2266–2274.
Lee C R, Farley C T. Determinants of the center of mass trajectory in human walking and running. The Journal of Experimental Biology, 1998, 201, 2935–2944.
Farley C T, Gonzalez O. Leg stiffness and stride frequency in human running. Journal of Biomechanics, 1996, 29, 181–186.
Günther M, Grimmer S, Siebert T, Blickhan R. All leg joints contribute to quiet human stance: A mechanical analysis. Journal of Biomechanics, 2009, 42, 2739–2746.
Geyer H, Seyfarth A, Blickhan R. Compliant leg behaviour explains basic dynamics of walking and running. Proceedings of the Royal Society B: Biological Sciences, 2006, 273, 2861–2867.
Blickhan R. The spring-mass model for running and hopping. Journal of Biomechanics, 1989, 22, 1217–1227.
Loopez R, Aguilar H, Salazar S, Lozano R. Adaptive control for passive kinesiotherapy ELLTIO. Journal of Bionic Engineering, 2014, 11, 581–588.
Miao Y, Gao F, Pan D. Mechanical design of a hybrid leg exoskeleton to augment load-carrying for walking. International Journal of Advanced Robotic Systems, 2013, 10, 1–11.
Miao Y, Gao F, Pan D. State classification and motion description for the lower extremity exoskeleton SJTU-EX. Journal of Bionic Engineering, 2014, 11, 249–258.
Thomson W. Theory of Vibration with Applications, CRC Press, Boca Raton, USA, 1996.
Zheng X, Jia S, Gao Y, Hou M, Xi D, Yang H. Modern Sports Biomechanics, National Defense Industry Press, Beijing, China, 2002, 100–163. (in Chinese)
Rose J, Gamble J G. Human Walking, Lippincott Williams & Wilkins, Philadelphia, USA, 2006.
Lovejoy C O. Evolution of human walking. Scientific American, 1988, 259, 118–125.
Sutherland D, Kaufman K, Moitoza J. Kinematics of normal human walking, in Rose J, Gamble J G (eds), Human Walking, Lippincott Williams & Wilkins, Philadelphia, USA, 1994, 23–44.
Inman V T, Ralston H J, Todd F. Human locomotion, in Rose J, Gamble J G (eds), Human Walking, Lippincott Williams & Wilkins, Philadelphia, USA, 1981.
Miao Y, Gao F, Pan D. Prototype design and size optimization of a hybrid lower extremity exoskeleton with a scissor mechanism for load-carrying augmentation. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2014, 229, 85–96.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Miao, Y., Gao, F. & Pan, D. Compound pendulum modeling and resonant frequency analysis of the lower limbs for the wearer and exoskeleton. J Bionic Eng 12, 372–381 (2015). https://doi.org/10.1016/S1672-6529(14)60129-3
Published:
Issue Date:
DOI: https://doi.org/10.1016/S1672-6529(14)60129-3