Three-Pendulum Harmonograph (#1)- an automatic drawing machine

Ladies and Gentlemen, you will like this. Here is a harmonograph in MS Excel 2003 which models a real one build by Karl Sims. Watch the video first to know what to expect. I could have built it from the bare drawing equations but that would have been too easy and no fun at all so I tried to model the real mechanism with 3 pendulums and the linkage rods.

It took me a weekend to make it. You can start or pause the drawing process with the green “Run-Pause” button. There is a “Reset” button too, use it whenever you want to erase the previous drawing.

Excel 2007 will work but it will be excessively slow with this file. There are six different configurations I saved, just dial a number from 1 to 6 and hit “Load”. If you create your own configuration, dial a number larger than 6 and click “Save”.  This way you can use it later. There is room for 100 configurations. The 6 pictures below correspond to the saved configurations.

I will add more explanations soon, plus I want to build it in 3D. Don’t forget, a 90 degrees phase diference between orthogonal sinusoids means a circle, zero or 180 degrees means a segment and everything in between are ellipses. Just a word of caution, it’s addictive! 

Do you have something to say? I’d love to hear from you so leave me a comment below.





  1. Author

    Thanks Devan.

  2. Hi George, you seem like the guy who would like to tinker with this. You can write/create the gcode in Excel and save to a *.nc file. I have done this with good results on an eleksmaker. The plotter will need to be able to interpret gcode (most should be), but is essentially just a set of XY instructions which can be concatenated in the spreadsheet.

  3. Derek, I am afraid I don’t understand your question.

  4. Very interesting indeed. Is there a way to derive an output for an x/y plotter?

  5. Lech, I know what you mean but I cannot help you with that. I believe the best waqy to do this in a fancy way, graphic-wise, is to use Java which I personally don’t know.

  6. is there a way to transfer the drawing, or actually transfer the making of the video into something like illustrator or adobe product that can make this a really fancy video?

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