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Krisanne E. Bothner
02-21-1997, 10:24 AM
My earlier posting was apparently not descriptive enough to clearly formulate
the problem. The question is not related to a "bottom up" versus "top down"
calculation of the torques. Rather, it is a problem of which segment's
equation of
motion will be used to calculate the ankle muscle moment, since this torque
plays a role
in the motion of both the foot and the leg and appears in the equations of
motion
for each segment.

Using both Lagrangian and Newtonian methods, and a "top down" approach in
general, my equations of motion for the foot and shank segments are of the
following
form:

Segment 2 (leg)

(I2 +m2r2^2)theta2'' = T1 - T2 - .....

and Segment 1 (foot)

(I1 + m1r1^2)theta1'' = -T1 - .....

The remainder of these equations ( the .....s) is made up of contributing
motion
dependent (proportional to both accelerations, inertial torques, and
velocities of
the other segments) and gravitational torques. T1 in these equations is the
ankle
torque, acting on both segments 1 and 2, and T2 is the knee torque acting on
the
leg (and thigh). The ankle torque appears in both equations of motion, and
I expected that the two equations would provide the same muscle torque.
They do
not.

Thanks to the quick responders who helped me to see that the problem needed a
more complete description.

**An interesting note: I have also used a "bottom up" approach to this
inverse dynamics
problem, and find that the ankle torque (T1) in that calculation is
comparable to the
ankle torque produced by the "top down" approach when I use the equation of
motion
for the *leg* segment.

Krisanne



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Krisanne E. Bothner Motor Control Laboratory
Dept. of Exercise & Movement Science 330 Gerlinger Hall
1240 University of Oregon voice: 541.346.0275
Eugene, Oregon USA 97403-1240 FAX: 541.346.2841