Alt-BEAM Archive

Message #04895



To: beam@sgiblab.sgi.com
From: Bruce Robinson Bruce_Robinson@bc.sympatico.ca
Date: Sat, 26 Jun 1999 23:32:13 -0700
Subject: [alt-beam] Re: Photopopper problems


James Wilson wrote:
>
> Bruce one small correction, the diameter of the wheels used as idlers
> does matter the larger the wheel the greater torque and the smaller the
> step size.

Uh, uh. That's only true when the motor shaft is connected to the wheel
shaft. When the motor shaft is pressed against the surface of the wheel,
you have an entirely different situation.

For example:
Consider a pager motor, 1 mm dia shaft, running at 600 RPM (or 10
revolutions per second). First put the shaft directly in contact with
the ground. The circumference of the shaft is Pi x diameter, or 3.14
mm.
In one second, the shaft rotates 10 times, and the photopopper travels
31.4 mm.

Now, place a 20 mm (3/4") wheel between the motor shaft and the
ground.
The circumference of the wheel is Pi x 20 = 62.8 mm. Now the motor
shaft
running on the wheel surface is just like two gears meshing, so the
wheel
will turn more slowly than the motor, by the ratio of the diameters:
wheel speed = (motor shaft dia/wheel dia) x motor speed, or
wheel speed = (1 mm / 20 mm) x 10 rps = 0.5 rps
So the wheel is turning half a revolution per second. Now multiply
this
by the wheel circumference, and you get 0.5 x 62.8 = 31.4 mm in one
second -- exactly the same as when the motor shaft is in contact with
the ground.

This relationship holds true no matter what size wheel you are talking
about.

That's the mathematical view. Now here's an intuitive one, which some
people might prefer. Consider a wheel which has a small rubber band
around it to act as a traction tire. The motor shaft presses against
this band, and the band presses against the ground. Now we could take
this rubber band off the wheel, and use it like a belt, except we would
have to keep it somehow pressed against the ground and the motor shaft
-- kind of like and inside-out v-belt arrangement. Well, when you have
two pulleys connected by a belt, it doesn't matter how long the belt is
-- the relative speed of the two pulleys is determined by their
diameters.

The torque is simply power divided by speed. If you don't change the
power delivered by the motor, and you don't change the speed of your
vehicle, then the torque delivered by the motor will stay the same.

Remember, this is only true when the motor shaft presses against the
side of a wheel which can rotate freely and is in contact with the
ground. As soon as you try to drive the wheel in some other way, such as
by connecting the motor shaft to the wheel shaft, or using a gearbox, or
a chain with sprockets, the situation is entirely different.

Regards,
Bruce


First off

Imagine a wheel that will travel 10 cm (or 4") in one revolution.

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