Effect of Ankle-Pivot Misalignment and Upward Ankle Vertical Displacement on Stability and Equilibrium Location for an Ankle-Hip Model of Balance on a Balance Board

2019 ◽  
Vol 15 (2) ◽  
Author(s):  
Erik Chumacero-Polanco ◽  
James Yang ◽  
James Chagdes
Keyword(s):  
Critical Role ◽  
Vertical Displacement ◽  
Pitchfork Bifurcation ◽  
Saddle Node Bifurcation ◽  
Parameter Spaces ◽  
Stability Regions ◽  
Stability Properties ◽  
Saddle Node ◽  
The Stability ◽  
Balance Board

Abstract During individual training on a balance board (BB), misalignment between the ankle joint and the BB axis of rotation may exist. The ankle-pivot misalignment influences the dynamics of human balance and more importantly, the stability properties of the equilibrium positions of the human-BB dynamical system. Similarly, ankle displacement in the upward direction with respect to the BB pivot also plays a critical role in the stability properties of the human-BB system. This paper investigates these effects through bifurcation analyses performed to the ankle-hip model of balance on a BB developed in our previous work. By using local bifurcation analyses, we have obtained the stability regions of the upright posture (UP) of a human-BB model of balance in different parameter spaces. The stability regions are delimited by Hopf, pitchfork, and saddle-node bifurcation curves in some selected parameter spaces. Results show that ankle-pivot misalignment has an impact on the location of the Hopf and unfolds the pitchfork bifurcation curves (found in the aligned case) into saddle-node bifurcation curves. Moreover, ankle-pivot misalignment breaks the mirror symmetry of upright static equilibrium positions and induces the establishment of equilibrium positions away from the vertical UP. With respect to the ankle vertical displacement, it has a minimal impact on the location of the pitchfork bifurcation curves but has a large impact on the location of the Hopf bifurcation curves, especially when combined with large BB time delay. This suggests that a larger ankle vertical displacement may result in sway oscillations of larger amplitude. The analyses also provide insight into different mechanisms of stability that can be found in the ankle-hip model of balance on a BB, namely, limit cycle oscillations and leaning postures. If an individual suffers from neuropathy, results from this study can be useful for researchers and clinicians in understanding what types of instabilities might be encountered, and during rehabilitation how to position the subjects carefully to avoid inadvertent instabilities.

Bifurcation analysis of steady natural convection in a tilted cubical cavity with adiabatic sidewalls

2014 ◽  
Vol 756 ◽  
pp. 650-688 ◽  
Author(s):  
J. F. Torres ◽  
D. Henry ◽  
A. Komiya ◽  
S. Maruyama
Keyword(s):  
Natural Convection ◽  
Rotation Axis ◽  
Numerical Technique ◽  
Continuation Method ◽  
Rotation Vector ◽  
Saddle Node Bifurcation ◽  
Saddle Node ◽  
Stable Solutions ◽  
The Stability ◽  
Cubical Cavity

AbstractNatural convection in an inclined cubical cavity heated from two opposite walls maintained at different temperatures and with adiabatic sidewalls is investigated numerically. The cavity is inclined by an angle $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\theta $ around a lower horizontal edge and the isothermal wall set at the higher temperature is the lower wall in the horizontal situation ($\theta = 0^\circ $). A continuation method developed from a three-dimensional spectral finite-element code is applied to determine the bifurcation diagrams for steady flow solutions. The numerical technique is used to study the influence of ${\theta }$ on the stability of the flow for moderate Rayleigh numbers in the range $\mathit{Ra} \leq 150\, 000$, focusing on the Prandtl number $\mathit{Pr} = 5.9$. The results show that the inclination breaks the degeneracy of the stable solutions obtained at the first bifurcation point in the horizontal cubic cavity: (i) the transverse stable rolls, whose rotation vector is in the same direction as the inclination vector ${\boldsymbol{\Theta}}$, start from $\mathit{Ra} \to 0$ forming a leading branch and becoming more predominant with increasing $\theta $; (ii) a disconnected branch consisting of transverse rolls, whose rotation vector is opposite to ${\boldsymbol{\Theta}}$, develops from a saddle-node bifurcation, is stabilized at a pitchfork bifurcation, but globally disappears at a critical inclination angle; (iii) the semi-transverse stable rolls, whose rotation axis is perpendicular to ${\boldsymbol{\Theta}}$ at $\theta \to 0^\circ $, develop from another saddle-node bifurcation, but the branch also disappears at a critical angle. We also found the stability thresholds for the stable diagonal-roll and four-roll solutions, which increase with $\theta $ until they disappear at other critical angles. Finally, the families of stable solutions are presented in the $\mathit{Ra}-\theta $ parameter space by determining the locus of the primary, secondary, saddle-node, and Hopf bifurcation points as a function of $\mathit{Ra}$ and $\theta $.

APPLICATION OF A TWO-DIMENSIONAL HINDMARSH–ROSE TYPE MODEL FOR BIFURCATION ANALYSIS

2013 ◽  
Vol 23 (03) ◽  
pp. 1350055 ◽  
Author(s):  
SHYAN-SHIOU CHEN ◽  
CHANG-YUAN CHENG ◽  
YI-RU LIN
Keyword(s):  
Hopf Bifurcation ◽  
Bifurcation Analysis ◽  
Sufficient Conditions ◽  
Type Model ◽  
Two Dimensional ◽  
Saddle Node Bifurcation ◽  
Trapping Region ◽  
Saddle Node ◽  
The Stability ◽  
Two Equilibria

In this study, we examine the bifurcation scenarios of a two-dimensional Hindmarsh–Rose type model [Tsuji et al., 2007] with four parameters and simulate some resemblances of neurophysiological features for this model using spike-and-reset conditions. We present possible classifications based on the results of the following assessments: (1) the number and stability of the equilibria are analyzed in detail using a table to demonstrate the matter in which the stability of the equilibrium changes and to determine which two equilibria collapse through the saddle-node bifurcation; (2) the sufficient conditions for an Andronov–Hopf bifurcation and a saddle-node bifurcation are mathematically confirmed; and (3) we elaborately evaluate the sufficient conditions for the Bogdanov–Takens (BT) and Bautin bifurcations. Several numerical simulations for these conditions are also presented. In particular, two types of bistable behaviors are numerically demonstrated: the BT and Bautin bifurcations. Notably, all of the bifurcation curves in the domain of the remaining parameters are similar when the time scale is large. Additionally, to show the potential for a limit cycle, the existence of a trapping region is demonstrated. These results present a variety of diverse behaviors for this model. The results of this study will be helpful in assessing suitable parameters for fitting the resemblances of experimental observations.

A Geometric Approach to a Quantum Counterpart of a Saddle-Node Bifurcation in a 1:1 Resonant Perturbed Oscillator

1998 ◽  
Vol 08 (05) ◽  
pp. 941-950 ◽  
Author(s):  
Yoshio Uwano
Keyword(s):  
Energy Levels ◽  
Geometric Approach ◽  
Pitchfork Bifurcation ◽  
Point Of View ◽  
Saddle Node Bifurcation ◽  
Bifurcation Set ◽  
Saddle Node ◽  
Geometric Point ◽  
Two Parameters ◽  
Quantum Counterpart

In previous papers [Uwano, 1994, 1995], it was shown that a degeneracy of energy levels is a quantum counterpart of a Hamiltonian pitchfork bifurcation of periodic trajectories of a certain 1:1 resonant oscillator with two parameters. As a continuation of those papers, a quantum study is made from a geometric point of view in order to find a quantum counterpart of a saddle-node bifurcation taking place in a certain 1:1 resonant perturbed oscillator with three parameters. The torus quantization method is applied to the perturbed oscillator to show that a degeneracy of energy levels is a quantum counterpart of that bifurcation: The bifurcation set for the saddle-node bifurcation in classical theory is viewed as a "bifurcation set" for the degeneracy of energy levels in quantum theory.

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

2019 ◽  
Vol 14 (10) ◽  
Author(s):  
Erik Chumacero-Polanco ◽  
James Yang ◽  
James Chagdes
Keyword(s):  
Dynamical System ◽  
Dynamic Stability ◽  
Point Of View ◽  
Local Dynamic ◽  
Stability Properties ◽  
Dynamical Behaviors ◽  
Local Dynamic Stability ◽  
The Stability ◽  
Delay Differential ◽  
Balance Board

Abstract 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 allow 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 to determine local dynamic stability properties. However, dynamic stability analysis results through such linearization of the system have not been verified. Moreover, bifurcation analyses 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 equation that describes the human-BB dynamics for a range of selected parameters (proprioceptive feedback and time-delays). The resulting solutions in time domain are used to verify the stability properties given by the bifurcation analyses and to compare different dynamical behaviors within the regions. Results show that the selected bifurcation parameters have significant impacts not only on UP stability but also on the amplitude, frequency, and increasing or decaying rate of the resulting trajectory solutions.

Attractor-preserving control to avoid saddle-node bifurcation

2014 ◽  
Vol 2 ◽  
pp. 150-153
Author(s):  
Daisuke Ito ◽  
Tetsushi Ueta ◽  
Shigeki Tsuji ◽  
Kazuyuki Aihara
Keyword(s):  
Saddle Node Bifurcation ◽  
Saddle Node

scholarly journals Quantum-mechanical hydration plays critical role in the stability of firefly oxyluciferin isomers: State-of-the-art calculations of the excited states

2020 ◽  
Vol 153 (20) ◽  
pp. 201103
Author(s):  
Yoshifumi Noguchi ◽  
Miyabi Hiyama ◽  
Motoyuki Shiga ◽  
Hidefumi Akiyama ◽  
Osamu Sugino
Keyword(s):  
Excited States ◽  
State Of The Art ◽  
Critical Role ◽  
Quantum Mechanical ◽  
The Stability

scholarly journals Velocity and acceleration level inverse kinematic calculation alternatives for redundant manipulators

Meccanica ◽  
2021 ◽  
Author(s):  
Dóra Patkó ◽  
Ambrus Zelei
Keyword(s):  
Degrees Of Freedom ◽  
Direct Method ◽  
Tracking Error ◽  
Inverse Kinematic ◽  
Linear Feedback ◽  
Joint Position ◽  
Stability Properties ◽  
Acceleration Level ◽  
Error Elimination ◽  
The Stability

AbstractFor both non-redundant and redundant systems, the inverse kinematics (IK) calculation is a fundamental step in the control algorithm of fully actuated serial manipulators. The tool-center-point (TCP) position is given and the joint coordinates are determined by the IK. Depending on the task, robotic manipulators can be kinematically redundant. That is when the desired task possesses lower dimensions than the degrees-of-freedom of a redundant manipulator. The IK calculation can be implemented numerically in several alternative ways not only in case of the redundant but also in the non-redundant case. We study the stability properties and the feasibility of a tracking error feedback and a direct tracking error elimination approach of the numerical implementation of IK calculation both on velocity and acceleration levels. The feedback approach expresses the joint position increment stepwise based on the local velocity or acceleration of the desired TCP trajectory and linear feedback terms. In the direct error elimination concept, the increment of the joint position is directly given by the approximate error between the desired and the realized TCP position, by assuming constant TCP velocity or acceleration. We investigate the possibility of the implementation of the direct method on acceleration level. The investigated IK methods are unified in a framework that utilizes the idea of the auxiliary input. Our closed form results and numerical case study examples show the stability properties, benefits and disadvantages of the assessed IK implementations.

scholarly journals Experimental Study on the Softening Characteristics of Sandstone and Mudstone in Relation to Moisture Content

2017 ◽  
Vol 2017 ◽  
pp. 1-14 ◽  
Author(s):  
Gui-chen Li ◽  
Chong-chong Qi ◽  
Yuan-tian Sun ◽  
Xiao-lin Tang ◽  
Bao-quan Hou
Keyword(s):  
Moisture Content ◽  
Vertical Displacement ◽  
Surface Porosity ◽  
Shear Tests ◽  
Moisture Contents ◽  
Dynamic Finite Element ◽  
Rock Types ◽  
Underground Roadway ◽  
The Stability ◽  
Kinetics Of

The kinetics of fluid-solid coupling during immersion is an important topic of investigation in rock engineering. Two rock types, sandstone and mudstone, are selected in this work to study the correlation between the softening characteristics of the rocks and moisture content. This is achieved through detailed studies using scanning electron microscopy, shear tests, and evaluation of rock index properties during exposure to different moisture contents. An underground roadway excavation is simulated by dynamic finite element modeling to analyze the effect of moisture content on the stability of the roadway. The results show that moisture content has a significant effect on shear properties reduction of both sandstone and mudstone, which must thus be considered in mining or excavation processes. Specifically, it is found that the number, area, and diameter of micropores, as well as surface porosity, increase with increasing moisture content. Additionally, stress concentration is negatively correlated with moisture content, while the influenced area and vertical displacement are positively correlated with moisture content. These findings may provide useful input for the design of underground roadways.

scholarly journals DNA Genome Size Affects the Stability of the Adenovirus Virion

2008 ◽  
Vol 83 (4) ◽  
pp. 2025-2028 ◽  
Author(s):  
Adam C. Smith ◽  
Kathy L. Poulin ◽  
Robin J. Parks
Keyword(s):  
Genome Size ◽  
Critical Role ◽  
Heat Stability ◽  
Helper Virus ◽  
Heat Inactivation ◽  
Similar Relationship ◽  
Viral Dna ◽  
A Genome ◽  
The Stability ◽  
Replication Defective Adenovirus

ABSTRACT Replication-defective adenovirus (Ad) vectors can vary considerably in genome length, but whether this affects virion stability has not been investigated. Helper-dependent Ad vectors with a genome size of ∼30 kb were 100-fold more sensitive to heat inactivation than their parental helper virus (>36 kb), and increasing the genome size of the vector significantly improved heat stability. A similar relationship between genome size and stability existed for Ad with early region 1 deleted. Loss of infectivity was due to release of vertex proteins, followed by disintegration of the capsid. Thus, not only does the viral DNA encode all of the heritable information essential for virus replication, it also plays a critical role in maintaining capsid strength and integrity.

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