[DPRG] Robot math problems
Subject: [DPRG] Robot math problems
From: Mike McCarty
jmccarty at ssd.usa.alcatel.com
Date: Wed Feb 13 14:19:18 CST 2002
On Wed, 13 Feb 2002, Chuck McManis wrote:
> At 11:37 AM 2/13/02 0800, Clay Timmons wrote:
> >Just working out a few robot navigation issues
> >and thought I'd share a couple math problems
> >I've encountered. Have fun! Took me about
> >10 minutes.
>
> You've got to build more tracked robots :) This is essential knowledge for
> doing inverse kinematics computations to position one's bot.
>
> >If a 12" wide robot with 3" diameter wheels
> >has one wheel going 1/2 the speed of the other
> >it will go in a circle.
> >
> > 1) What diameter is that circle?
> >
> > 2) To make the robot go in a circle with
> > a 9" radius on the inside wheel
> > what speed should the inside wheel
> > go as a percentage of the outside wheel?
>
> I'm going to assume that the centerline of the two wheels are 12" apart,
> since your robot is "12 inches wide" that cannot be true in practice as you
> either measured from wheel edge to wheel edge in which case the center line
> is 1 wheel width less than 12", or you measured the body and the wheels
> were outside of that meaning they are 1 wheel width + 12" apart.
>
> Given that, there is no solution for #2 because the smallest radius turn
> you could possibly make that is *centered on the inside wheel* is 12".
> However by rotating one wheel in reverse you can translate the center of
> rotation along the axle between the two wheels.
I believe you do misinterpret the meaning of the second. I understood it
to mean that the inside wheel travelled on a circle with radius 9
inches. This certainly has a solution.
Mike

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