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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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

---------------------------------------------------------------

To unsubscribe send SIGNOFF BIOMCH-L to LISTSERV@nic.surfnet.nl

For information and archives: http://isb.ri.ccf.org/biomch-l

---------------------------------------------------------------