Alt-BEAM Archive
Message #04904
To: beam@sgiblab.sgi.com
From: Bruce Robinson Bruce_Robinson@bc.sympatico.ca
Date: Sun, 27 Jun 1999 12:50:51 -0400
Subject: 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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