Linear Approximations for Swing Leg Motion During Gait

[+] Author and Article Information
W. H. Lee

Department of Electrical Engineering and Computer Science, MIT, Cambridge, Mass. 02139

J. M. Mansour

Department of Mechanical and Aerospace Engineering, Case Western Reserve University, Cleveland, Ohio 44106

J Biomech Eng 106(2), 137-143 (May 01, 1984) (7 pages) doi:10.1115/1.3138470 History: Received July 01, 1982; Revised October 31, 1983; Online June 15, 2009


The applicability of a linear systems analysis of two-dimensional swing leg motion was investigated. Two different linear systems were developed. A linear time-varying system was developed by linearizing the nonlinear equations describing swing leg motion about a set of nominal system and control trajectories. Linear time invariant systems were developed by linearizing about three different fixed limb positions. Simulations of swing leg motion were performed with each of these linear systems. These simulations were compared to previously performed nonlinear simulations of two-dimensional swing leg motion and the actual subject motion. Additionally, a linear system analysis was used to gain some insight into the interdependency of the state variables and controls. It was shown that the linear time varying approximation yielded an accurate representation of limb motion for the thigh and shank but with diminished accuracy for the foot. In contrast, all the linear time invariant systems, if used to simulate more than a quarter of the swing phase, yielded generally inaccurate results for thigh shank and foot motion.

Copyright © 1984 by ASME
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