Subject: ScienceDirect - Journal of Biomechanics : The equations of motion for a standing human reveal three mechanisms for balance



   

 

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Journal of Biomechanics

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

(rErCoM′FE=moment of FE w.r.t. CoM′


rE

point of attack of external force


ri

position CoM of segment i


rCoM

position whole-body  


rCoM′

position COM′=(xCoM, 0, zCoM)T


r′CoM

position of equivalent CoM, corrected for pendulum length l


rCoP

position  


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

Nomenclature

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

Acknowledgements

References





Journal of Biomechanics

Volume 40, Issue 2, 2007, Pages 451-457

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