The study of upright posture (UP) stability is of relevance to estimating risk of falls, especially among people with neuromuscular deficits. Several studies have addressed this problem from a system dynamic approach based on parameter bifurcation analyses, which provide the region of stability (RoS) and the delimiting bifurcation curves (usually Hopf and pitchfork) in some parameter-spaces. In contrast, our goal is to determine the effect of parameter changes on the size of the basin of attraction (BoA) of the UP equilibrium and the amplitude of the limit cycle oscillations (LCOs) emerging from the Hopf bifurcations (HBs). The BoA is an indicator of the ability of the UP to maintain balance without falling, while LCOs may explain the sway motion commonly observed during balancing. In this study, a three degree-of-freedom model for a human balancing on a balance board (BB) was developed. Analysis of the model revealed the BoAs and the amplitude of the LCOs. Results show that physical parameters (time-delays and feedback control gains) have a large impact on the size of the BoA and the amplitude of the LCOs. Particularly, the size of the BoA increases when balancing on a rigid surface and decreases when either proprioceptive or combined visual and vestibular (V&V) feedback gain is too high. With respect to the LCOs, it is shown that they emerge from both the subcritical and supercritical HBs and increase their amplitudes as some parameters vary.
Skip Nav Destination
Article navigation
November 2019
Research-Article
Basin of Attraction and Limit Cycle Oscillation Amplitude of an Ankle-Hip Model of Balance on a Balance Board
Erik Chumacero-Polanco,
Erik Chumacero-Polanco
Human-Centric Design Research Lab,
Department of Mechanical Engineering,
Texas Tech University,
Lubbock, TX 79409
e-mail: erik.chumacero@ttu.edu
Department of Mechanical Engineering,
Texas Tech University,
Lubbock, TX 79409
e-mail: erik.chumacero@ttu.edu
Search for other works by this author on:
James Yang
James Yang
Fellow ASME
Human-Centric Design Research Lab,
Department of Mechanical Engineering,
Texas Tech University,
Lubbock, TX 79409
e-mail: james.yang@ttu.edu
Human-Centric Design Research Lab,
Department of Mechanical Engineering,
Texas Tech University,
Lubbock, TX 79409
e-mail: james.yang@ttu.edu
1Corresponding author.
Search for other works by this author on:
Erik Chumacero-Polanco
Human-Centric Design Research Lab,
Department of Mechanical Engineering,
Texas Tech University,
Lubbock, TX 79409
e-mail: erik.chumacero@ttu.edu
Department of Mechanical Engineering,
Texas Tech University,
Lubbock, TX 79409
e-mail: erik.chumacero@ttu.edu
James Yang
Fellow ASME
Human-Centric Design Research Lab,
Department of Mechanical Engineering,
Texas Tech University,
Lubbock, TX 79409
e-mail: james.yang@ttu.edu
Human-Centric Design Research Lab,
Department of Mechanical Engineering,
Texas Tech University,
Lubbock, TX 79409
e-mail: james.yang@ttu.edu
1Corresponding author.
Manuscript received August 23, 2018; final manuscript received April 13, 2019; published online July 31, 2019. Assoc. Editor: Brittany Coats.
J Biomech Eng. Nov 2019, 141(11): 111007 (9 pages)
Published Online: July 31, 2019
Article history
Received:
August 23, 2018
Revised:
April 13, 2019
Citation
Chumacero-Polanco, E., and Yang, J. (July 31, 2019). "Basin of Attraction and Limit Cycle Oscillation Amplitude of an Ankle-Hip Model of Balance on a Balance Board." ASME. J Biomech Eng. November 2019; 141(11): 111007. https://doi.org/10.1115/1.4043563
Download citation file:
Get Email Alerts
Cited By
Related Articles
Sensitivity Enhancement of Cantilever-Based Sensors Using Feedback Delays
J. Comput. Nonlinear Dynam (October,2010)
Passive Control of Limit Cycle Oscillations in a Thermoacoustic System Using Asymmetry
J. Appl. Mech (January,2008)
Numerical Nonlinear Analysis for Dynamic Stability of an Ankle-Hip Model of Balance on a Balance Board
J. Comput. Nonlinear Dynam (October,2019)
Stability of Controlled Mechanical Systems With Ideal Coulomb Friction
J. Dyn. Sys., Meas., Control (January,2008)
Related Proceedings Papers
Related Chapters
Dynamic Behavior in a Singular Delayed Bioeconomic Model
International Conference on Instrumentation, Measurement, Circuits and Systems (ICIMCS 2011)
Numerical Study of Limit Cycles for Three Planar Polynomial Systems
International Conference on Information Technology and Computer Science, 3rd (ITCS 2011)
Constraints
Nonlinear Regression Modeling for Engineering Applications: Modeling, Model Validation, and Enabling Design of Experiments