Re: equations for inertial simulator
- From: Douglas Eagleson <eaglesondouglas@xxxxxxxxx>
- Date: Sun, 24 Feb 2008 06:43:08 -0800 (PST)
On Feb 22, 3:19 pm, Robert <renen...@xxxxxxxxxxx> wrote:
Hello -- Can anyone help me derive the equations required to simulate
the following physical system?
Imagine a horizontal shaft on ball bearings, with an unbalanced mass
rigidly attached to the shaft. We know the mass m, the rotational
inertia I, and the radial distance of the center of gravity from the
shaft r. With no external torque applied to the shaft, gravity will
cause the mass to settle with the heavy side down. Now imagine an
arbitrary time-varying torque being applied to the shaft. As a
result, the shaft will turn with an angular position at time t given
by theta(t), say. (To simplify things we can assume that -180 <
theta(t) < 180 degrees, where 0 is the equilibrium position.)
I want to build a physical simulation of this system without having to
construct the actual mass, which is very large. I want to use a large
D.C. motor attached to an optical encoder. The unknown time-varying
input torque is applied to the motor shaft. The encoder transmits the
angular position theta(t) to a computer, which computes the torque
T(t) required from the motor to simulate the system, and controls the
voltage applied to the motor accordingly.
Can anyone suggest how I would go about describing T(t) in terms of
theta(t), theta'(t), I, m, and r?
(BTW the motivation for the system is a massive church bell mounted on
bearings and being swung by a human ringer pulling on a rope attached
to a wheel mounted on the bell. The simulator would be used to train
bell ringers. They would pull on the rope and feel as though a large
heavy bell was attached, whereas it is only the motor.)
Regards,
Robert
A test of the system is to make the rope simulate the applied lever on
a mass. A small motor as the mass would have to move as the mass then
alter the rope length to simulate the lever. A difficult technical
machine would ensue.
It is not easy to shorten rope as on a drum and make the drum twist.
Try some drawings before you use a lot of time searching for a current
function. Spring mounts motor to allow twisting were the hard part
for me to figure out.
A motor to swing a spring like a compound bow might be the easy
solution. A fairly simple motor drive then allows for simulated free
swinging. A rocking function.
Switched to begin the rocking are at the start of bow stretching. And
a slow lead in rate or ramp up to full swing might match a larger
bell.
Just remember to safety shield the compound bow as it might self
destruct from alot of usage and make dangerous projectiles.
N-motor
___________________
bow axis
_____________
|O -pulley on motor mount-making leverage
point
|
|
| rope
A ramp function might be makable with an easy RC circuit.
The swing as synchronus with the rope pull was the training aspect and
to make the bow super hard to pull while back swinging would be
introduced by the lose of leverage as the bow axis turns. A control
as swing rate exactly follows a leverage function?? this is hard by
the way as a task!
My pulley negates a good leverage function unless it was sized
somehow. A disc shaped pulley oriented right might be necessary.
Maybe just try it without a fancy pulley an allow bow asymetric
pulling to make the function.
Douglas Eagleson
Gaithersburg, MD USA
.
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- From: Robert
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