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Ton Van Den Bogert
05-26-1999, 01:40 AM
I am posting this to the list, because it may be of general interest.

Lisa Carnes wrote:
> If the orientation of the accelerometer is changed, then gravity
> vector becomes a problem, and the mathematics are hairy. Does anyone
> have any advice?

There is no fundamental solution to this problem: Einstein in his
general
theory of relativity (1916) hypothesized that it is not possible to
distinguish
between accelerations of the reference frame and being in a
gravitational
field. That theory is widely accepted. Also this idea seems consistent
with
the structure of the equation that describes the output of an
accelerometer.
You can find that equation in:

Bogert, A.J. van den, L. Read and B.M. Nigg "A method for inverse
dynamic analysis
using accelerometry". J. Biomech. 29: 949-954, 1996.

We have some advantage in that we know the magnitude of the
gravitational field,
only its orientation relative to the sensor is unknown. But I still
think the
contributions from gravity and from acceleration are inseparable.

In my own work I circumvented the problem by doing an analysis (inverse
dynamics)
that did not require a separation of the contributions by accelerations
and
gravity.

If you need pure acceleration information, you could assume that the
accelerations are large compared to the acceleration of gravity, so
you would ignore gravity. This assumption may be OK for impact
situations (tibial acceleration 4-10 g). But probably not for upper
body movement.

[By the way, if you make the opposite assumption: accelerations are
much smaller than 1 g, the signal is only dependent on orientation of
the
sensor with respect to gravity. The accelerometer then becomes an
inclinometer.]

Or you can measure the orientation of the accelerometer and use
that information to calculate the contribution of gravity and
subtract that from the signal. This was done by Wu and Ladin in
their "kinematometer". See:

Z. Ladin & G. Wu (1991) Combining position and acceleration
measurements for joint
force estimation. J. Biomech. 24: 1173-1187.

G. Wu & Z. Ladin (1993) The kinematometer--an integrated kinematic
sensor for
kinesiological measurements. J. Biomech. Eng. 115:53-62.

If you can make certain assumptions about the system (e.g. there
is a point with zero acceleration) separation of acceleration and
gravity is also theoretically possible. See:

A.T.M. Willemsen, J.A. van Alste and H.B.K. Boom (1990) Real-time gait
assessment
utilizing a new way of accelerometry. J. Biomech. 23: 859-863.

Ton van den Bogert

--

A.J. (Ton) van den Bogert, PhD
Department of Biomedical Engineering
Cleveland Clinic Foundation
9500 Euclid Avenue (ND-20)
Cleveland, OH 44195, USA
Phone/Fax: (216) 444-5566/9198

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