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[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.

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