Sixty Wheels

a tool for visualizing Fourier series ยท 2002
Sixty Wheels drawing a square wave with a chain of turning wheels

Sixty Wheels is a Windows program that demonstrates Fourier series and harmonic analysis. It simulates up to 60 turning wheels, each attached to the rim of the one before. You can set each wheel's radius, phase and speed. The program shows the wheels from the front and from the side, and plots the side view against time.

With I draw graph checked, you can draw a periodic waveform on the graph. The Fourier button then works out the size, phase and speed of each wheel needed to reproduce it.

Sixty Wheels also includes a simulation of a hypothetical mechanical harmonic analyzer (first harmonic only, unfinished), inspired by Tatjana J. van Vark's account of the history of mechanical harmonic analyzers and her collection of mechanical integrators. See also the Helix Harmonic Analyzer.

Download

Download Sixty Wheels for Windows

The ZIP file (150 kB) contains a single program, sixtywheels.exe: extract it and run it. There is no manual; feel free to experiment. To get started:

  1. Click Turn.
  2. Click 60. You now see 60 wheels turning.
  3. Click one of the four buttons with waveform shapes under Fourier. Each loads a preset waveform and the wheels that reproduce it.
  4. Check I draw graph, draw a waveform on the graph, and click Fourier to work out the wheels that reproduce it.
Sixty Wheels reproducing a square wave
A square wave, drawn by a chain of wheels
Sixty Wheels in line mode, zoomed in to 10000%
Line mode, zoomed in to 10000%
The mechanical harmonic analyzer simulation analysing a square wave
The mechanical harmonic analyzer