Bill Powers

05-28-2003, 03:27 AM

I'm from a list concerned with applications of control theory to

modeling behavior. We're concerned with rather global models, but are

also engaged in simulation studies of motor behavior. Some time ago, a

friend supplied me with the forward dynamical equations for a 3 df arm

(angular accelerations as a function of torques), which I incorporated

into a model of visual-motor pointing behavior (see

home.earthlink.net/~powers_w, where there's an underscore between powers

and w.). Now I find that I need the inverse equations (torques as

function of angle, velocity etc) and no longer have the friend's

handwritten sheets on which the derivation was worked out.. Stupid,

yes,. but they're gone nevertheless. I'm one of those people who are

great with simulations but poor at the analytical math, so will be

grateful to anyone who can point me to a source, or just write them out

for me.

There are three big long equations, one for each degree of freedom:

shoulder pitch and yaw, and elbow pitch. Each one shows a torque about

one axis as a function of angles, angular velocities, and angular

accelerations in all three axes. They were derived from the Lagrangian,

I believe, or Newton-LaGrange, if that's the right term (which shows

you about where I am mathematically).

Many thanks and apologies for the intrusion,

Bill Powers

Durango, CO

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modeling behavior. We're concerned with rather global models, but are

also engaged in simulation studies of motor behavior. Some time ago, a

friend supplied me with the forward dynamical equations for a 3 df arm

(angular accelerations as a function of torques), which I incorporated

into a model of visual-motor pointing behavior (see

home.earthlink.net/~powers_w, where there's an underscore between powers

and w.). Now I find that I need the inverse equations (torques as

function of angle, velocity etc) and no longer have the friend's

handwritten sheets on which the derivation was worked out.. Stupid,

yes,. but they're gone nevertheless. I'm one of those people who are

great with simulations but poor at the analytical math, so will be

grateful to anyone who can point me to a source, or just write them out

for me.

There are three big long equations, one for each degree of freedom:

shoulder pitch and yaw, and elbow pitch. Each one shows a torque about

one axis as a function of angles, angular velocities, and angular

accelerations in all three axes. They were derived from the Lagrangian,

I believe, or Newton-LaGrange, if that's the right term (which shows

you about where I am mathematically).

Many thanks and apologies for the intrusion,

Bill Powers

Durango, CO

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

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

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

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