Subject: ScienceDirect - Journal of Biomechanics : The equations of motion for a standing human reveal three mechanisms for balance
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Volume 40, Issue 2, 2007, Pages 451-457 |
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doi:10.1016/j.jbiomech.2005.12.016
Copyright © 2006 Elsevier Ltd All rights reserved.
Short communication
The equations of motion for a standing human reveal three mechanisms for balance
At L. Hof
Laboratory of Human Movement Analysis, Center for Rehabilitation, University Medical Center Groningen, Center for Human Movement Sciences, University of Groningen, PO Box 196, 9700 AD Groningen, The Netherlands
Accepted 20 December 2005. Available online 10 March 2006.
Abstract
The equations of motion for a standing multi-segment human model are derived. Output quantity of these equations is the horizontal acceleration of the whole-body centre of mass (CoM). There are three input terms and they can be identified as the three mechanisms by which balance can be maintained: (1) by moving the centre of pressure with respect to the vertical projection of the CoM, (2) by counter-rotating segments around the CoM, and (3) by applying an external force, other than the ground reaction force.
For the first two mechanisms the respective contributions to CoM acceleration can be obtained from force plate recordings. This is illustrated by some example data from experiments, which show that the contribution from mechanism 2 can be considerable, e.g. in one-legged standing.
Keywords: Balance; Balance strategy; Equations of movement; Centre of mass; Centre of pressure; Balance mechanisms
Nomenclature
The co-ordinate system is according to the ISB recommendations:
X-axis forward, Y-axis vertically upward, Z-axis to the right.
aCoM
acceleration whole-body CoM horizontal components aCoMx and aCoMz
ai
acceleration of body segment i
CoM
whole-body CoM
CoM′
vertical projection of CoM on the ground
CoP
CoP, point of attack of GRF
FE
external force
FG
GRF
g
acceleration of gravity (0 –9.81 0)T
h
leg length, trochanteric height
time derivative of angular momentum w.r.t. CoM, see (3)
component of in YZ-plane (medio-lateral)
component of in XY-plane (sagittal)
Ibody
moment of inertia of whole body w.r.t. CoM
Ii
moment of inertia of segment i w.r.t. segment CoM
l
effective pendulum length
m
body mass
mi
mass of segment i
ME
(rE−rCoM′)×FE=moment of FE w.r.t. CoM′
rE
point of attack of external force
ri
position CoM of segment i
rCoM
rCoM′
position COM′=(xCoM, 0, zCoM)T
r′CoM
position of equivalent CoM, corrected for pendulum length l
rCoP
xa
xe
xh
xCoM, xCoP, etc.
See rCoM, rCoP
za
ze
zh
zCoM, zCoP, etc.
See rCoM, rCoP
CoM
angular acceleration of pendulum
i
angular acceleration of segment i
Article Outline
1. Introduction
2. Theory
2.1. Equations of motion—moment equation
2.2. Three mechanisms for balance control
2.3. Equations of motion—force equation
2.4. Calculation of
3. Experiment
4. Discussion
Volume 40, Issue 2, 2007, Pages 451-457 |
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