I loved playing with the Spirograph drawing toy as a kid.
The mesmerizing shapes that a Spirograph makes are called hypotrochoids, which have some interesting mathematical properties.
I decided to design my own hypotrochoid-drawing-machine toy as one of my first lasercutter projects at Ace Monster Toys.  I'll describe the process here, and maybe it will inspire you to design your own!

You need:
  • a spreadsheet (such as in Microsoft Excel, Open Office Calc, or in Google Docs)
  • Inkscape (open source)
  • a laser cutter
  • 1/8" acrylic
  • pencils or pens
  • paper

Step 1: Choose some ring and gear sizes

The number of teeth on the outer ring and the inner gear determine the number of "points" on the resulting full drawing. When setting out to design a spirograph, I first fiddled around with a few different size rings and gears.  I found that, for a given ring and gear size, the number of "points" can be determined by taking the least common multiple (LCM) of the number of teeth on each of the two elements (ring and gear), and dividing it by the number of teeth on the gear.*  

Using this equation you can make a spreadsheet with columns as ring sizes and rows as gear sizes to help you choose the numbers of teeth for the elements of your toy.

Excel has a function for least common multiple, and thus it's easy to write a formula this purpose:


where B1 contains the number of teeth in the outer ring and A2 contains the number of teeth on the gear; see the screenshot.  

...Or just download the Excel file below.

As you might expect, for rings with a prime number of teeth, the number of points is always that number.  For gears which have a prime number of teeth, they result in designs with a number of points equal to the number of teeth in the ring.

* Perhaps this value has another name, but I'm no mathematician; please let me know if there's a more simple name.
Thanks for th Excel-Formula! I can use that one for a COMPLETELY other field (work) :)
Just curious, for what?
deep inside a formula to check for correlations of problems with a product vs the used lot's of materials to build the product.
Yepp. :) I am an Investigation Engineer for a company which develops and builds medical-technical products.
Pretty cool maiden Instructable! Keep it up :-)
Thank you!
<p>What diameter did you make the holes for the pens/pencils?</p>
<p>I suggest trial and error. But you can also refer to the .dxf attached in step 3. The holes in there work with most pens an pencils, but I do remember that they were too small for some ball point pens.</p>
<p>Great design! <br></p><p>Also on how to do marquetry with a laser using ImagePaint software by Amazon Canvas (www.amazoncanvas.com)</p>
<p>We just laser cutted it! The kids will love it! Thanks for the idea</p>
<p>Nice! I like your organic design.</p>
<p>Cool! The design reminds me of an etch-a-sketch! I loved those things!</p>
<p>So nice! I&acute;m about to do it thanks!</p>
<p>I loved these things when I was a kid! It never occurred to me that I now have the power to create my own! &lt;3</p>
Great Job !! Brings back childhood memories of my playtime. And Thanks for Inkscape, I'm going to install it later today.
oh nostalgia, i haven't seen one of these in ages.

About This Instructable


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Bio: scientist, educator, maker, and member of Ace Monster Toys
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