Analemma Fourier Series Kinetic Art

The sun traces a shape in the sky throughout the year, and that shape is called an analemma. They are challenging to capture in an image, because they require a camera in the same place and orientation for an entire year, and the resulting pictures are superimposed on each other. Here is one such image – 

Image credit: Giuseppe Donatiello, CC0, via Wikimedia Commons

Funnily enough, NASA's Astronomy Pic of the Day for the day I'm publishing this model is also an analemma imaged by someone named Giuseppe, so I can't not post it.

Image credit: Giuseppe Petricca, via NASA APOD

By plotting these points and performing a Fourier transform on them, we can express the shape as a series of four vectors, each rotating at a constant rate, that trace out the analemma when added together. Then, we can animate those rotating vectors.  It looks like this:

This gear train is a physical implementation of those four vectors, rotating in sync with each other. When you turn the crank, the yellow dot traces out the analemma, just as the last vector traces out the red line in the animation above

If it helps, you can also print a mask that helps with following the dot as it traces its path.

The gear train is implemented with three planetary gearsets in series, representing the first three vectors. It uses the off-axis rotation of a planet in one gearset to drive the next gearset. The final vector is implemented with a single gear, since it doesn't need to drive any further elements of the gear train.

I've been unable to find anyone else on the internet implementing 2D Fourier Series like this – if you know of anyone please let me know! I think we'd probably get along.

See the attached PDF for detailed assembly instructions, with helpful pictures!