Constant and Variable Stiffness and Damping of the Leg Joints in Human Hopping

[+] Author and Article Information
Svetlana Rapoport, Joseph Mizrahi, Eitan Kimmel, Oleg Verbitsky

Department of Biomedical Engineering, Technion, Israel Institute of Technology, Haifa 32000, Israel

Eli Isakov

Loewenstein Rehabilitation Center, Raanana 43100, Israel

J Biomech Eng 125(4), 507-514 (Aug 01, 2003) (8 pages) doi:10.1115/1.1590358 History: Received August 27, 2001; Revised February 26, 2003; Online August 01, 2003
Copyright © 2003 by ASME
Topics: Damping , Stiffness
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Two-dimensional hopping model in the sagittal plane. (a) absolute angles of the joints; (b) anatomical angles of the joints.
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Typical traces of hopping at 1.53 Hz: Joint angles are shown in the three upper traces and ankle power is shown in the lower trace
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Typical curves of vertical ground reaction force (GRF), normalized to body weight (BW), versus the vertical excursion of the hip during the ground-contact phase of hopping
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Typical moment/angle curves of the leg joints during the ground-contact phase of hopping. The moments were computed from inverse dynamics for the ankle, knee and hip joints. Variable stiffness, constant stiffness model solutions are also given for the ankle joint. Left curves (dotted)=2.20 Hz; central curves (dashed)=1.87 Hz; right curves (solid)=1.53 Hz.
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Typical stiffness/time curves for the ankle during the stance phase of hopping
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Average ankle moment at 2.20 Hz hopping as obtained from three different methods: Inverse dynamics; kinematics with overall (constant) stiffness; and kinematics with actual (variable) stiffness. Standard deviations for the constant stiffness and variable stiffness moment results are indicated by the corresponding vertical bars. The difference between the moments using these two models was found significant (P<0.05) in points 2–5 and 10–12 along the time axis.
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Average maximal stiffness versus average initial stiffness for each of the joints and hopping frequencies




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