Dear all,

Many thanks for all the people who replied to my enquiry about calculating

the Centre of Mass from force plate data. It seems that the method is

indeed valid, although because of the double integration method used, the

result is only a relative indication of CoM displacement. Also, sensitivity

of force plates may impose limitations on the use of the method to quantify

sway.

Here are some salient responses...

From: "S. Archer"

There is an article that compares a segmental approach to

calculate the COM and the double integration approach.

J.Eng & D. Winter (1993) Gait and Posture. Volume 1, Page 141-144.

I do not think Herman was the first to try the method. I think it was one

of these papers by Breniere.

Y. Breniere & M.C. Do (1991) Journal of Motor Behaviour. Volume 23(4),

Page 235-240.

Y. Breniere, M.C. Do & S. Bouisset (1987) Journal of Motor Behaviour.

Volume 19(1), Page 62-76.

I would not try to calculate COM from the force plate in quiet stance, as

the anterior/posterior forces are only just above a noise level.

From: dmeglan@merle.acns.nwu.edu (Dwight Meglan)

You will find this as an option of the force commands of ANZ [this is

Dwight's 3D joint kinetics package, freely available on ftp ... Chris].

What is done

is to integrate the force components to compute the displacement of the

center of mass.

Fx= m*ax -> ax= Fx/m

Fy= m*ay -> ay= Fy/m

Fz= m*(az+g) -> az= Fz/m - g

where Fx,Fy,Fz are force components from the force plate, m is the total

body mass, g is gravitational acceleration, and ax, ay and az are the

accelerations of the center of mass. Now integrate,

vx= integral(ax) + v0x

vy= integral(ay) + v0y

vz= integral(az) + v0z

x= integral(vx) + integral(v0x) + x0

y= integral(vy) + integral(v0y) + y0

z= integral(vz) + integral(v0z) + z0

where vx,vy,vz are the center of mass velocities, v0x,v0y,v0z are

integration constants, x0,y0,z0 are also integration constants, and x,y,z

are the displacement of the center of mass. v0x,vy0,vz0 are also the

velocity of the center of mass at the beginning of the time period over

which the force plate data was recorded. x0,y0,z0 are the position of the

center of mass at the same initial time.

The difficulty is the integration constants. If you start with the body at

rest standing (or sitting or whatever) then v0x=v0y=v0z=0. Then, the

computed displacement of the center of mass differs from the actual center

of mass only by a constant.

In ANZ, I estimate the initial center of mass position and velocity from

summing the individual segmental mass times their positions divided by the

total mass of the body. You can calculate the center of mass in ANZ using

both the segmental mass approach or the force plate integration and compare

them if you want:

SEG BCM/VEL ! estimate body center of mass and velocity from segment mass

FRC INT/BCM ! estimate body center of mass from integrating force plates

One caution is to make sure you have the coordinate systems correct. If you

estimate the body center of mass from the segment mass, the position has to

be in the same coordinate system as the force plate data. ANZ adjusts all

the coordinate frames as needed.

From: "Prof. Joe Mizrahi"

We have done this and have recently written a manuscript describing the

procedure. It is now submitted and I will be glad to send you a preprint,

as soon as it will become possible.

The Authors are: Oron Levin (my M.Sc. student) and myself.

The title is:

An Iterative Model for Estimation of the Trajectory of Center of Gravity

from Bi-Lateral Reactive Force Measurements in Standing Sway.

From: "DI. Josef Kollmitzer"

We are a Gaitanalysis Group in Vienna, Austria. We use Forceplates and

Video Analysis equipment. It is possible to measure the horicontal (i.e.

the anterio/posterio and lateral-left/right) Component of the movement of

the Centre of Gravity during quiet standing with only one forceplate.

The idea is easy:

In quiet standing there are nearly no dynamic forces. Hence the Ground-

Reaction Force Vector is vertical. This means that the movement of the

Center of Mass in horicontal direction is identical with the movement of

the Point of Application (PA) of the Ground Reaction Force.

The Forceplate measures 3 Components of Force Fx,Fy,Fz and 3 Components of

Moments Mx,My,Mz. As the Moment is Force timed by perpenticular Distance

to the Measurement Center of the forceplate and Fx,Fy

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# CoM from force plate: summary of responses

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