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

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: (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