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

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

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

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

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

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

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

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