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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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