Necip Berme wrote to Biomch-L:

> I was expecting Albert King from Wayne State University to respond to the

> "accelerometer gravity correction" listing. As he has not, I am doing so to

> set the record straight. In 1970's one of Dr. King's doctoral students

> showed that nine accelerometers appropriately positioned on a rigid body

> are necessary and sufficient to separate the effect of gravity from the

> other acceleration information. Hence, it is possible to calculate the

> position of a rigid body from acceleration data.

Dr. Berme is correct and it is important for anyone using 3-D accelerometry

to know about this work. The full reference is:

N.K. Mital and A.I. King (1979) Computation of rigid-body rotation in

three-dimensional space from body-fixed linear acceleration measurements.

J. Appl. Mech. 46: 925-930.

Mital and King were able to solve the angular acceleration vector of a rigid body

from multiple accelerometer signals, and successfully eliminated the effect of

gravity on that result. Obtaining the attitude then required a double integration

in order to obtain Euler angles. This works for movements of short duration with

accurately known initial conditions (initial attitude and angular velocity). For

movements of longer duration, the end result will drift noticeably due to

inaccuracies in the initial conditions of the integration. It would be hard to

predict at which duration this becomes a problem. My feeling is that it is not

a practical method for most applications. Movement analysis in automobile crash

testing is probably a feasible application, and I think this is the area that Dr.

King works in.

Angular velocity can also be solved directly, using the centrifugal terms in

the accelerometer signals, but this tends to be noisy for typical movements

(my own observations). On the other hand, then only a single integration

is required to obtain Euler angles. Attitude (or Euler angles) can not

be solved directly from the accelerometer signals. Integration is always

required.

Once attitude is known, the gravity contribution to the translational

acceleration of the rigid body can then be calculated and a correction can

be made to obtain the true translational accelerations. With a further

double integration, position and velocity of the rigid body will be known.

There is an even earlier paper where a similar analysis was used, although

no integrations were carried out. Only angular velocity and angular

acceleration were needed. Reference:

T.R. Kane, W.C. Hayes and J.D. Priest (1974) Experimental determination

of forces exerted in tennis play. In: R.C. Nelson and C.A. Morehouse (eds.)

Biomechanics IV, University Park Press, Baltimore, pp. 284-290.

For the sake of completeness, here is a later development of that method.

The methodology is presented, but to my knowledge it has not been applied

again. Reference:

W.C. Hayes, J.D. Gran, M.L. Nagurka, J.M. Feldman and C. Oatis (1983) Leg motion

analysis during gait by multiaxial accelerometry: theoretical foundations and

preliminary validations. J. Biomech. Eng. 105:283-289.

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

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> I was expecting Albert King from Wayne State University to respond to the

> "accelerometer gravity correction" listing. As he has not, I am doing so to

> set the record straight. In 1970's one of Dr. King's doctoral students

> showed that nine accelerometers appropriately positioned on a rigid body

> are necessary and sufficient to separate the effect of gravity from the

> other acceleration information. Hence, it is possible to calculate the

> position of a rigid body from acceleration data.

Dr. Berme is correct and it is important for anyone using 3-D accelerometry

to know about this work. The full reference is:

N.K. Mital and A.I. King (1979) Computation of rigid-body rotation in

three-dimensional space from body-fixed linear acceleration measurements.

J. Appl. Mech. 46: 925-930.

Mital and King were able to solve the angular acceleration vector of a rigid body

from multiple accelerometer signals, and successfully eliminated the effect of

gravity on that result. Obtaining the attitude then required a double integration

in order to obtain Euler angles. This works for movements of short duration with

accurately known initial conditions (initial attitude and angular velocity). For

movements of longer duration, the end result will drift noticeably due to

inaccuracies in the initial conditions of the integration. It would be hard to

predict at which duration this becomes a problem. My feeling is that it is not

a practical method for most applications. Movement analysis in automobile crash

testing is probably a feasible application, and I think this is the area that Dr.

King works in.

Angular velocity can also be solved directly, using the centrifugal terms in

the accelerometer signals, but this tends to be noisy for typical movements

(my own observations). On the other hand, then only a single integration

is required to obtain Euler angles. Attitude (or Euler angles) can not

be solved directly from the accelerometer signals. Integration is always

required.

Once attitude is known, the gravity contribution to the translational

acceleration of the rigid body can then be calculated and a correction can

be made to obtain the true translational accelerations. With a further

double integration, position and velocity of the rigid body will be known.

There is an even earlier paper where a similar analysis was used, although

no integrations were carried out. Only angular velocity and angular

acceleration were needed. Reference:

T.R. Kane, W.C. Hayes and J.D. Priest (1974) Experimental determination

of forces exerted in tennis play. In: R.C. Nelson and C.A. Morehouse (eds.)

Biomechanics IV, University Park Press, Baltimore, pp. 284-290.

For the sake of completeness, here is a later development of that method.

The methodology is presented, but to my knowledge it has not been applied

again. Reference:

W.C. Hayes, J.D. Gran, M.L. Nagurka, J.M. Feldman and C. Oatis (1983) Leg motion

analysis during gait by multiaxial accelerometry: theoretical foundations and

preliminary validations. J. Biomech. Eng. 105:283-289.

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

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