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Design a laser-cut Spirograph-like toy

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Picture of Design a laser-cut Spirograph-like toy
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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
 
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Step 1: Choose some ring and gear sizes

Picture of Choose some ring and gear sizes
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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:

=LCM(B$1,$A2)/$A2

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.
Orngrimm1 year ago
Thanks for th Excel-Formula! I can use that one for a COMPLETELY other field (work) :)
safay (author)  Orngrimm1 year ago
Just curious, for what?
Orngrimm safay1 year ago
deep inside a formula to check for correlations of problems with a product vs the used lot's of materials to build the product.
safay (author)  Orngrimm1 year ago
wow!
Orngrimm safay1 year ago
Yepp. :) I am an Investigation Engineer for a company which develops and builds medical-technical products.
ynze1 year ago
Pretty cool maiden Instructable! Keep it up :-)
safay (author)  ynze1 year ago
Thank you!
AntalToth1 year ago
Great Job !! Brings back childhood memories of my playtime. And Thanks for Inkscape, I'm going to install it later today.
HollyMann1 year ago
awesome!!!
MonkiMan1 year ago
oh nostalgia, i haven't seen one of these in ages.
Cool!
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