Re: equations for inertial simulator

On Feb 22, 8:37 pm, nottoo <nottooo...@xxxxxxxxxxx> wrote:
Sounds like a very cool idea! Except don't they use electronic
controls to drive bells instead of people nowdays?

Sometimes, but perhaps surprisingly there is still quite a lot of
interest in human-powered bell ringing, where several ringers each
carefully control the period of one bell so as to make them ring in a
pre-arranged pattern.

For a real shaft, at some point in time, the total torque applied = I
* angular acceleration. Your applied torque would be the sum of:
Weight: Some simple trig with theta, m and r.
Rope: Trope=F*r

I think you'd have to control the speed as well as the torque. For
example if the guy lets go, the motor isn't driving any load but it
should still rotate with the correct angular acceleration.

Yes, if the rope is released, the motor should simulate the swinging
of an inertial pendulum. The complication of the simulator is that
you don't really know the force applied by the rope (unless perhaps
you could put some kind of strain gauge on it). I was hoping you
could make do just by observing the position of the shaft (and
deducing the speed) via the encoder, but I'm not sure if this is
possible. Even if it is, it may not be possible to make the
controller stable. (One quantity I left out of the original
formulation of the problem is the rotational inertia of the motor.
That might also be important.)

I wonder if it would suffice just to make the motor model the inertial
pendulum, ignoring the torque applied by the rope altogether. It
should be possible to come up with a differential equation for that.
Then the rope just does whatever it does.
.

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