Fourier Machine Mimics Michelson Original in Plywood

It’s funny how creation and understanding interact. Sometimes the urge to create something comes from a new-found deep understanding of a concept, and sometimes the act of creation leads to that understanding. And sometimes creation and understanding are linked together in such a way as to lead in an entirely new direction, which is the story behind this plywood recreation of the Michelson Fourier analysis machine.

For those not familiar with this piece of computing history, it’s worth watching the videos in our article covering [Bill “The Engineer Guy” Hammack]’s discussion of this amazing early 20th-century analog computer. Those videos were shown to [nopvelthuizen] in a math class he took at the outset of degree work in physics education. The beauty of the sinusoids being created by the cam-operated rocker arms and summed to display the output waveforms captured his imagination and lead to an eight-channel copy of the 20-channel original.

Working with plywood and a CNC router, [nopvelthuizen]’s creation is faithful to the original if a bit limited by the smaller number of sinusoids that can be summed. A laser cutter or 3D printer would have allowed for a longer gear train, but we think the replica is great the way it is. What’s more, the real winners are [nopvelthuizen]’s eventual physics students, who will probably look with some awe at their teacher’s skills and enthusiasm.

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Harmonic Analyzer Mechanical Fourier Computer

If you’re into mechanical devices or Fourier series (or both!), you’ve got some serious YouTubing to do.

[The Engineer Guy] has posted up a series of four videos (Introduction, Synthesis, Analysis, and Operation) that demonstrate the operation and theory behind a 100-year-old machine that does Fourier analysis and synthesis with gears, cams, rocker-arms, and springs.

In Synthesis, [The Engineer Guy] explains how the machine creates an arbitrary waveform from its twenty Fourier components. In retrospect, if you’re up on your Fourier synthesis, it’s pretty obvious. Gears turn at precise ratios to each other to create the relative frequencies, and circles turning trace out sine or cosine waves easily enough. But the mechanical spring-weighted summation mechanism blew our mind, and watching the machine do its thing is mesmerizing.

In Analysis everything runs in reverse. [The Engineer Guy] sets some sample points — a square wave — into the machine and it spits out the Fourier coefficients. If you don’t have a good intuitive feel for the duality implied by Fourier analysis and synthesis, go through the video from 1:50 to 2:20 again. For good measure, [The Engineer Guy] then puts the resulting coefficient estimates back into the machine, and you get to watch a bunch of gears and springs churn out a pretty good square wave. Truly amazing.

The fact that the machine was designed by [Albert Michelson], of Michelson-Morley experiment fame, adds some star power. [The Engineer Guy] is selling a book documenting the machine, and his video about the book is probably worth your time as well. And if you still haven’t gotten enough sine-wavey goodness, watch the bonus track where he runs the machine in slow-mo: pure mechano-mathematical hotness!

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