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*Project Completion Update!*

*Gear Sets can now be found for sale at:* *http://www.ponoko.com/showroom/wonders* _________________________

What Are You Making?

I am designing sets of gears that can be used to make beautiful art. I started this project when I bought a spirograph and found that it didn't have the precision, size, or versatility that I wanted. I learned how to design and fabricate my own precision gear set.

Wild gears is a project dedicated to making a superior spirograph. Each set of gears will be laser cut from a sheet of clear acrylic. It will also include triangular, square, and even pentagonal gears. It will include newly designed technology to allow for the creation of previously impossible designs. It will be fun.

I’ve already made two prototypes and they work well. With your help I can share my love of mathematical art with the world.

Using my gear sets makes art like that possible

How does it work?

It works using simple gear interaction. By placing a gear in a larger hollow gear and rolling the gear around the inside of the hollow gear a multitude of interesting patterns can be created.

The class of shapes generated are called hypotrochoids. When one gear is held in place (I use tape) and another gear is rolled around it, a different class of shape is generated which are called epitrochoids.

Examples can be found in the introduction video at the top of the page.

Hypotrochoids are more flowery with rounded petals or pointed tips whereas epitrochoids are almost circular with an open space in the middle where the stationary gear was. Both types of shape have an amazing variety in appearance.

Epitrochoid

Hypotrochoid

What makes these gears special?

In addition to the fact that they are precision laser cut gears and that they are made from fantastic clear acrylic, I have developed a new design technology and learned how to make triangular gears.

Laser cutting offers supreme precision. This is critical because if the gears have irregularities or too much play in the teeth when you finish a pattern and your pen reaches the line at the beginning it will not match up. This can be hidden, to some extent, by using large felt tipped pens. I have been experimenting with using fine lining pens, 0.1mm and smaller, with no problems.

Clear acrylic is great because it enables you to see how your design is proceeding much better than if your gears are opaque or colourful.

Triangular gears are exactly what they sound like. I spent some time and figured out how to make gears with any number of sides. So far I've made 3, 4, and 5 sided gears. Obviously the points and the sides are rounded but the curvature can be varied to make a very circle-like triangle or one with much more defined edges and corners.

Triangular, Square, and Pentagonal gears

The new design technology allows for the creation of designs that are otherwise impossible to generate using conventional gear and pen methods. As you can see in the picture above, most gears have many small holes in a row. When you select a gear and start at the outermost hole and roll it around to make a hypotrochoid, you can then move your pen one hole down the line and repeat the process, making a similar but different shape. Many beautiful designs can be created this way. The hypotrochoids created by using the two holes in the gear invariably cross each other at acute angles. One evening I decided that I really wanted to make designs with parallel patterns. (Note: parallel is probably the technically incorrect way to describe the relationship of the two patterns although I have yet to find a better term. If you know one please let me know.)

This simple pattern

A triangle

Can be made into a standard 'crossing' design

See the corners, they cross!

or it can be made into a parallel design, where the lines do not cross.

a parallel design

The ability to generate both types of designs widens the range of possible art with stunning effect. I have not encountered another gear set with this unique design feature.

As an additional cool feature, it is possible to put several gears together in on outer ring.

4 gears in 1 ring = cool design

This is a) really fun to play with, b) looks really cool, c) allows for the shrinking of a design without otherwise changing its appearance. This is especially interesting because if you have a design you want to make, perhaps a 17 pointed shape, its size is dictated by size of the outer gear. If you want to make that shape smaller but want it to still have its unique 17 pointed geometry that is possible using this method.

Why are some of the gears in the photos clear others are brown?

When the gears are laser cut, they have a protective paper backing on both sides. It peels off and leaves no sticky residue behind. I've left the paper on some of the gears to make them easier to photograph although I had to take it off of most of the gears so that it would be easier to use them.