View Full Version : Help with dynamical equations

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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