Instant Equilibrium Point and Its Migration in Standing Tasks: Rambling and Trembling Components of the Stabilogram

Motor Control ◽  
1999 ◽  
Vol 3 (1) ◽  
pp. 28-38 ◽  
Author(s):  
Vladimir M. Zatsiorsky ◽  
Marcos Duarte
Keyword(s):  
Time Delay ◽  
Equilibrium Point ◽  
Ground Reaction Force ◽  
Reference Point ◽  
Reaction Force ◽  
Time Lag ◽  
Cubic Spline ◽  
Spline Functions ◽  
Restoring Force ◽  
Zero Time

A method of decomposing stabilograms into two components, termed rambling and trembling, was developed. The rambling component reveals the motion of a moving reference point with respect to which the body's equilibrium is instantantly maintained. The trembling component reflects body oscillation around the reference point trajectory. The concepts of instant equilibrium point (IEP) and discrete IEP trajectory are introduced. The rambling trajectory was computed by interpolating the discrete IEP trajectory with cubic spline functions. The trembling trajectory is found as a difference between the approximated rambling trajectory and the COP trajectory. Instant values of the trembling trajectory are negatively correlated with the values of the horizontal ground reaction force at a zero time lag. It suggests that trembling is strongly influenced by a restoring force proportional to the magnitude of COP deviation from the rambling trajectory and acts without a time delay. An increment in relative COP position per unit of the restoring force, in mm/N, was on average 1.4 ± 0.4. The contribution of rambling and trembling components in the stabilogram was ascertained. The rambling variability is approximately three times larger than the trembling variability.

A Soft Ground Reaction Force Sensor System Utilizing Time-Delay Recurrent Neural Network

2020 ◽  
Vol 20 (18) ◽  
pp. 10851-10861 ◽  
Author(s):  
Hyo Seung Han ◽  
Juyoung Yoon ◽  
Seungkyu Nam ◽  
Sangin Park ◽  
Dong Jin Hyun
Keyword(s):  
Neural Network ◽  
Time Delay ◽  
Recurrent Neural Network ◽  
Ground Reaction Force ◽  
Reaction Force ◽  
Force Sensor ◽  
Sensor System ◽  
Soft Ground

scholarly journals Running ground reaction forces across footwear conditions are predicted from the motion of two body mass components

2019 ◽  
Vol 126 (5) ◽  
pp. 1315-1325 ◽  
Author(s):  
Andrew B. Udofa ◽  
Kenneth P. Clark ◽  
Laurence J. Ryan ◽  
Peter G. Weyand
Keyword(s):  
Ground Reaction Force ◽  
Lower Limb ◽  
Reaction Force ◽  
Ground Reaction Forces ◽  
Vertical Ground Reaction Force ◽  
Time Patterns ◽  
Foot Strike ◽  
Reaction Forces ◽  
Vertical Ground ◽  
Force Time

Although running shoes alter foot-ground reaction forces, particularly during impact, how they do so is incompletely understood. Here, we hypothesized that footwear effects on running ground reaction force-time patterns can be accurately predicted from the motion of two components of the body’s mass (mb): the contacting lower-limb (m1 = 0.08mb) and the remainder (m2 = 0.92mb). Simultaneous motion and vertical ground reaction force-time data were acquired at 1,000 Hz from eight uninstructed subjects running on a force-instrumented treadmill at 4.0 and 7.0 m/s under four footwear conditions: barefoot, minimal sole, thin sole, and thick sole. Vertical ground reaction force-time patterns were generated from the two-mass model using body mass and footfall-specific measures of contact time, aerial time, and lower-limb impact deceleration. Model force-time patterns generated using the empirical inputs acquired for each footfall matched the measured patterns closely across the four footwear conditions at both protocol speeds ( r2 = 0.96 ± 0.004; root mean squared error  = 0.17 ± 0.01 body-weight units; n = 275 total footfalls). Foot landing angles (θF) were inversely related to footwear thickness; more positive or plantar-flexed landing angles coincided with longer-impact durations and force-time patterns lacking distinct rising-edge force peaks. Our results support three conclusions: 1) running ground reaction force-time patterns across footwear conditions can be accurately predicted using our two-mass, two-impulse model, 2) impact forces, regardless of foot strike mechanics, can be accurately quantified from lower-limb motion and a fixed anatomical mass (0.08mb), and 3) runners maintain similar loading rates (ΔFvertical/Δtime) across footwear conditions by altering foot strike angle to regulate the duration of impact. NEW & NOTEWORTHY Here, we validate a two-mass, two-impulse model of running vertical ground reaction forces across four footwear thickness conditions (barefoot, minimal, thin, thick). Our model allows the impact portion of the impulse to be extracted from measured total ground reaction force-time patterns using motion data from the ankle. The gait adjustments observed across footwear conditions revealed that runners maintained similar loading rates across footwear conditions by altering foot strike angles to regulate the duration of impact.

scholarly journals Small changes in ball position at address cause a chain effect in golf swing

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Sung Eun Kim ◽  
Jangyun Lee ◽  
Sae Yong Lee ◽  
Hae-Dong Lee ◽  
Jae Kun Shim ◽  
...  
Keyword(s):  
Ground Reaction Force ◽  
Reaction Force ◽  
Statistical Parametric Mapping ◽  
Golf Swing ◽  
Whole Body ◽  
Centre Of Mass ◽  
Body Segment ◽  
A Chain ◽  
Professional Golfers ◽  
The Right

AbstractThe purpose of this study was to investigate how the ball position along the mediolateral (M-L) direction of a golfer causes a chain effect in the ground reaction force, body segment and joint angles, and whole-body centre of mass during the golf swing. Twenty professional golfers were asked to complete five straight shots for each 5 different ball positions along M-L: 4.27 cm (ball diameter), 2.14 cm (ball radius), 0 cm (reference position at preferred ball position), – 2.14 cm, and – 4.27 cm, while their ground reaction force and body segment motions were captured. The dependant variables were calculated at 14 swing events from address to impact, and the differences between the ball positions were evaluated using Statistical Parametric Mapping. The left-sided ball positions at address showed a greater weight distribution on the left foot with a more open shoulder angle compared to the reference ball position, whereas the trend was reversed for the right-sided ball positions. These trends disappeared during the backswing and reappeared during the downswing. The whole-body centre of mass was also located towards the target for the left-sided ball positions throughout the golf swing compared to the reference ball position, whereas the trend was reversed for the right-sided ball positions. We have concluded that initial ball position at address can cause a series of chain effects throughout the golf swing.

scholarly journals Injury prevention in Super-G alpine ski racing through course design

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Matthias Gilgien ◽  
Philip Crivelli ◽  
Josef Kröll ◽  
Live S. Luteberget ◽  
Erich Müller ◽  
...  
Keyword(s):  
Ground Reaction Force ◽  
Course Design ◽  
Reaction Force ◽  
Global Navigation Satellite Systems ◽  
World Cup ◽  
Satellite Systems ◽  
Turn Radius ◽  
Energy Dissipated ◽  
Global Navigation Satellite ◽  
High Level

AbstractIn Super-G alpine ski racing mean speed is nearly as high as in Downhill. Hence, the energy dissipated in typical impact accidents is similar. However, unlike Downhill, on Super-G courses no training runs are performed. Accordingly, speed control through course design is a challenging but important task to ensure safety in Super-G. In four male World Cup alpine Super-G races, terrain shape, course setting and the mechanics of a high-level athlete skiing the course were measured with differential global navigation satellite systems (dGNSS). The effects of course setting on skier mechanics were analysed using a linear mixed effects model. To reduce speed by 0.5 m/s throughout a turn, the gate offset needs to be increased by + 51%. This change simultaneously leads to a decrease in minimal turn radius (− 19%), an increase in impulse (+ 27%) and an increase in maximal ground reaction force (+ 6%). In contrast, the same reduction in speed can also be achieved by a − 13% change in vertical gate distance, which also leads to a small reduction in minimal turn radius (− 4%) impulse (− 2%), and no change in maximal ground reaction force; i.e. fewer adverse side effects in terms of safety. It appears that shortening the vertical gate distance is a better and safer way to reduce speed in Super-G than increasing the gate offset.

scholarly journals A Type of Time-Symmetric Stochastic System and Related Games

Symmetry ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 118
Author(s):  
Qingfeng Zhu ◽  
Yufeng Shi ◽  
Jiaqiang Wen ◽  
Hui Zhang
Keyword(s):  
Nash Equilibrium ◽  
Time Delay ◽  
Differential Equations ◽  
Equilibrium Point ◽  
Stochastic Differential Equations ◽  
Stochastic System ◽  
Stochastic Systems ◽  
Necessary Condition ◽  
Nash Equilibrium Point ◽  
Doubly Stochastic

This paper is concerned with a type of time-symmetric stochastic system, namely the so-called forward–backward doubly stochastic differential equations (FBDSDEs), in which the forward equations are delayed doubly stochastic differential equations (SDEs) and the backward equations are anticipated backward doubly SDEs. Under some monotonicity assumptions, the existence and uniqueness of measurable solutions to FBDSDEs are obtained. The future development of many processes depends on both their current state and historical state, and these processes can usually be represented by stochastic differential systems with time delay. Therefore, a class of nonzero sum differential game for doubly stochastic systems with time delay is studied in this paper. A necessary condition for the open-loop Nash equilibrium point of the Pontriagin-type maximum principle are established, and a sufficient condition for the Nash equilibrium point is obtained. Furthermore, the above results are applied to the study of nonzero sum differential games for linear quadratic backward doubly stochastic systems with delay. Based on the solution of FBDSDEs, an explicit expression of Nash equilibrium points for such game problems is established.

scholarly journals Stochastic P-bifurcation in a bistable Van der Pol oscillator with fractional time-delay feedback under Gaussian white noise excitation

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Yajie Li ◽  
Zhiqiang Wu ◽  
Guoqi Zhang ◽  
Feng Wang ◽  
Yuancen Wang
Keyword(s):  
Time Delay ◽  
White Noise ◽  
Gaussian White Noise ◽  
Singularity Theory ◽  
Van Der Pol Oscillator ◽  
Order System ◽  
Damping Force ◽  
Van Der Pol ◽  
Restoring Force ◽  
White Noise Excitation

Abstract The stochastic P-bifurcation behavior of a bistable Van der Pol system with fractional time-delay feedback under Gaussian white noise excitation is studied. Firstly, based on the minimal mean square error principle, the fractional derivative term is found to be equivalent to the linear combination of damping force and restoring force, and the original system is further simplified to an equivalent integer order system. Secondly, the stationary Probability Density Function (PDF) of system amplitude is obtained by stochastic averaging, and the critical parametric conditions for stochastic P-bifurcation of system amplitude are determined according to the singularity theory. Finally, the types of stationary PDF curves of system amplitude are qualitatively analyzed by choosing the corresponding parameters in each area divided by the transition set curves. The consistency between the analytical solutions and Monte Carlo simulation results verifies the theoretical analysis in this paper.

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