Subject:
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Re: Spirograph Formulas??
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Newsgroups:
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lugnet.robotics
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Date:
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Thu, 18 May 2000 20:57:07 GMT
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Viewed:
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817 times
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in article 3923F01F.2834EA50@idt.net, Dan Novy at lego-robotics@crynwr.com
wrote on 5/18/00 6:29 AM:
> Hi, all! My daughter and I have built a robot that holds a piece
> of sidewalk chalk and draws "spirograph-like" patterns on the side
> walk. No sensors, it really just executes a repeated path with an off
> set.
Cool! Any pictures available on the web somewhere?
> Then I remembered an old math teacher had a set of the spirographs
> that he used as an extra credit assignment. That was so long ago I
> can't remember what the assignment actually was, but I remember it had
> something to do with predicting and graphing the patterns a spirogear
> WOULD make given certain variables. Does this sound vaguely familiar to
> anyone? My question is, are there basic formulas (or at least an area
> of research) governing the spirograph patterns that I could translate
> into code for the RCX.
I typed "spirograph" into my favorite search engine (www.google.com) and
came up with several good hits. These two are way too math-intensive for me
to comprehend:
http://www.csm.astate.edu/spirotest/spirotest.html
http://www.geom.umn.edu/docs/reference/CRC-formulas/node34.html
This one has a much simpler set of formulas, plus a cool applet for drawing
the curves.
http://www.wordsmith.org/~anu/java/spirograph.html
From the above page:
==
What is a Spirograph?
A Spirograph is formed by rolling a circle inside or outside of another
circle. The pen is placed at any point on the rolling circle. If the radius
of fixed circle is R, the radius of moving circle is r, and the offset of
the pen point in the moving circle is O, then the equation of the resulting
curve is defined by:
x = (R+r)*cos(t) - (r+O)*cos(((R+r)/r)*t)
y = (R+r)*sin(t) - (r+O)*sin(((R+r)/r)*t)
==
The applet lets you change the parameters but doesn't display the actual
numbers, darn it.
I don't have any handy tools to use to graph these equations, which I
believe are parametric. Pacific Tech makes a commercial version of the
Graphing Calculator that comes free with the Mac OS, and version 2 does
parametric equations and works with Mac or Windows. It's about $40, and
it's a severely cool piece of software. Check them out and download a demo
at http://www.pacifict.com.
It's not immediately obvious to me how to convert these equations into a
piece of RCX code. Perhaps someone else can help, or find more appropriate
equations.
> Right now we're having fun guessing and
> adjusting different variables to get different patterns, but it would
> also be fun to generate a pattern on paper with our real spirograph and
> then have the RCX duplicate the same pattern only much larger in the
> sidewalk chalk. If you have no idea what a spirograph toy is, I'm sure
> many of us would be willing to explain. It was, and is, one of my all
> time favorite toys.
Mine's still in the closet, much the worse for wear. I loved it too, but
instead of a Lego Dark Ages I went into a Spirograph Dark Ages :)
>
> --
> Dan Novy
> Visual Effects Technical Supervisor
> Flash Film Works
> dan@flashfilmworks.com
>
> /////////////////////////////////////
>
> Simia anaticulam caseis defricavit.
>
> /////////////////////////////////////
>
>
>
--
Doug Weathers, http://www.rdrop.com/~dougw
Portland, Oregon, USA
Don't spam me - I know how to use http://www.spamcop.net
"On a clear disk you can seek forever"
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Message has 2 Replies:
 | | Re: Spirograph Formulas??
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| Funny, I went to google right after I posted and found those same sites. Cool, aren't they? No pics of the result of the robo-graph, but soon. I have to redesign the chalk holder assembly first. Did you ever notice that the minute you add a non (...) (25 years ago, 18-May-00, to lugnet.robotics)
| | | Re: Spirograph Formulas??
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| I wrote a director program once to graph those equations and made it into a shockwave movie. Ill see if i can't dig it up. b ---...--- (...) (25 years ago, 18-May-00, to lugnet.robotics)
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Message is in Reply To:
| | Spirograph Formulas??
|
| Hi, all! My daughter and I have built a robot that holds a piece of sidewalk chalk and draws "spirograph-like" patterns on the side walk. No sensors, it really just executes a repeated path with an off set. Then I remembered an old math teacher had (...) (25 years ago, 18-May-00, to lugnet.robotics)
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