Numerical Nonlinear Analysis for Dynamic Stability of an Ankle-Hip Model of Balance on a Balance Board

[+] Author and Article Information
Erik A. Chumacero

Human-Centric Design Research Laboratory, Department of Mechanical Engineering, Texas Tech University, Lubbock, TX 79401

James Yang

ASME Fellow, Human-Centric Design Research Laboratory, Department of Mechanical Engineering, Texas Tech University, Lubbock, TX 79401

James Chagdes

Department of Mechanical and Manufacturing Engineering, Miami University, Oxford, OH 45056

1Corresponding author.

ASME doi:10.1115/1.4042693 History: Received October 03, 2018; Revised January 16, 2019


Study of human upright posture (UP) stability is of great relevance to fall prevention and rehabilitation, especially for those with balance deficits for whom a balance board (BB) is a widely used mechanism to improve balance. The stability of the human-BB system has been widely investigated from a dynamical system point of view. However most studies assume small disturbances, which allows to linearize the nonlinear human-BB dynamical system, neglecting the effect of the nonlinear terms on the stability. Such assumption has been useful to simplify the system and use bifurcation analyses (BAs) to determine local dynamic stability properties. However, dynamic stability analysis results through such linearization of the system has not been verified. Moreover, BAs cannot provide insight on dynamical behaviors for different points within the stable and unstable regions. In this study, we numerically solve the nonlinear delay differential equations that describe the human-BB dynamics for a range of some selected parameters (proprioceptive feedback and time-delays). The resulting solutions in time domain are used to verify the stability properties given by the BAs and to compare different dynamical behaviors within the regions. Results show that the selected bifurcation parameters have significant impacts not only on UP stability and but also on the amplitude, frequency, and increasing or decaying rate of the resulting trajectory solutions.

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