Jonas Rubenson

01-25-2004, 12:56 PM

Dear Biomech-L members,

I am interested in your opinion on how to best calculate and interpret

joint power in three dimensions.

I have calculated 3D joint powers using an inverse dynamic solution,

where the individual joint powers in flex/ext, add/abd and int/ext

rotation are calculated by the product of the joint moments (expressed

in the distal segment anatomical coord. system) and the corresponding

elements of the joint angular velocity matrix expressed in the same

coordinate system (calculated from the time derivative of the rotation

matrix , Rd, and its inverse), i.e.

Omega = Rd * Rinv

By positive joint power I understand that power is being generated and the

muscle-tendon units produce positive work, and when joint power is negative

power is being absorbed and negative work is done. However, my first question

is how one should treat positive

and negative power occurring simultaneously in the different planes of

the anatomical coordinate system. Because I am ultimately using the

joint power to get an estimate of the amount of power that muscle-tendon

units must generate or absorb at a joint it would seem that it may be

most appropriate to take the net power in all three planes, thereby

cancelling simultaneous positive and negative power. The reason being

that the rate of change of the muscle-tendon unit lengths depend on the

angular velocity about all three axes (for muscles with moment arms

about all three axes) and since they also produce a moment about all

three axes. For example, what has been measured as a negative and

positive joint power about two axes, respectively, may conceivably be

the result of a muscle that has in actual fact produced a moment about

the two axes but which has not had a very large change in length (since

the change in joint angle about one axis acts to lengthen the muscle

whereas the change in joint angle about the other axis acts to shorten

it). In the case of net joint power it could be calculated from the dot

product of the moment vector and the angular velocity vector:

Power = [Mx,My,Mz] . [wx ,wy,wz].

But perhaps this will lead to an underestimate of the true muscle power

if a set of synergistic muscles can not produce the moments required

for the measured joint power about the three axes. Can it be that

different groups of muscles (with actions predominantly about one axis)

must produce and absorb power simultaneously? I am only thinking

intuitively here and maybe this logic doesn't adhere to more fundamental

principles such as the total energy balance of the segments.

I also have a second question that pertains more to the calculation of

the joint powers themselves. Some time ago I recall that one of the

list members suggested to calculate the components of the joint power

from the product of the joint moments expressed in the joint coordinate

system (rather than the anatomical fixed coordinate systems) and the

euler anglular velocities. If one is to calculate a net power from all

three planes will this approach still be valid given that the joint

coordinate system is non-orthogonal?

Any comments will be greatly appreciated and as usual I will post a

summary of responses,

Sincerely,

Jonas Rubenson

Dept. Human Movement and Exercise Science

The University of Western Australia

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I am interested in your opinion on how to best calculate and interpret

joint power in three dimensions.

I have calculated 3D joint powers using an inverse dynamic solution,

where the individual joint powers in flex/ext, add/abd and int/ext

rotation are calculated by the product of the joint moments (expressed

in the distal segment anatomical coord. system) and the corresponding

elements of the joint angular velocity matrix expressed in the same

coordinate system (calculated from the time derivative of the rotation

matrix , Rd, and its inverse), i.e.

Omega = Rd * Rinv

By positive joint power I understand that power is being generated and the

muscle-tendon units produce positive work, and when joint power is negative

power is being absorbed and negative work is done. However, my first question

is how one should treat positive

and negative power occurring simultaneously in the different planes of

the anatomical coordinate system. Because I am ultimately using the

joint power to get an estimate of the amount of power that muscle-tendon

units must generate or absorb at a joint it would seem that it may be

most appropriate to take the net power in all three planes, thereby

cancelling simultaneous positive and negative power. The reason being

that the rate of change of the muscle-tendon unit lengths depend on the

angular velocity about all three axes (for muscles with moment arms

about all three axes) and since they also produce a moment about all

three axes. For example, what has been measured as a negative and

positive joint power about two axes, respectively, may conceivably be

the result of a muscle that has in actual fact produced a moment about

the two axes but which has not had a very large change in length (since

the change in joint angle about one axis acts to lengthen the muscle

whereas the change in joint angle about the other axis acts to shorten

it). In the case of net joint power it could be calculated from the dot

product of the moment vector and the angular velocity vector:

Power = [Mx,My,Mz] . [wx ,wy,wz].

But perhaps this will lead to an underestimate of the true muscle power

if a set of synergistic muscles can not produce the moments required

for the measured joint power about the three axes. Can it be that

different groups of muscles (with actions predominantly about one axis)

must produce and absorb power simultaneously? I am only thinking

intuitively here and maybe this logic doesn't adhere to more fundamental

principles such as the total energy balance of the segments.

I also have a second question that pertains more to the calculation of

the joint powers themselves. Some time ago I recall that one of the

list members suggested to calculate the components of the joint power

from the product of the joint moments expressed in the joint coordinate

system (rather than the anatomical fixed coordinate systems) and the

euler anglular velocities. If one is to calculate a net power from all

three planes will this approach still be valid given that the joint

coordinate system is non-orthogonal?

Any comments will be greatly appreciated and as usual I will post a

summary of responses,

Sincerely,

Jonas Rubenson

Dept. Human Movement and Exercise Science

The University of Western Australia

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

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

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

Please consider posting your message to the Biomch-L Web-based

Discussion Forum: http://movement-analysis.com/biomch_l

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