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This video is the result of me obsessing about pinning down the ultimate explanation for what is going on with the mysterious nothing grinder aka the do nothing machine aka the trammel of Archimedes. I think what I present in this video is it in this respect, but I let you be the judge. Featuring the Tusi couple (again), some really neat optical phenomenon based on the Tusi couple (I first encountered this here:, the ellipsograph and lots of original twists to an ancient theme.

Here is a link to a .zip archive containing 3d printable .stl files of the models featuring the Mathologer logo that I showed in the video:

I usually trim the corners and excess material off the (slightly slanted) vertical edges of the three sliders to make them run without catching on anything. I also sharpen the points of the pins a bit before pushing them into the sliders. They lock in place automatically, you don't have to glue them in.

Other 3d printable incarnations featuring different numbers of sliders are floating around on the net—for example search nothing grinder/do nothing machine/Archimedes trammel on

The wiki page on the nothing grinder is also worth visiting:

My current bout of nothing grinder obsession started with Naomi a year 10 student from Melbourne who did a week of mathematical work experience with me at Monash university a couple of weeks ago. As her project she chose to design a 3d printable version of the wooden model that you see in the video. Her Rhino3d files of the square and hexagon grinders served as the starting point for the models you can see in action in the video.


As usual thank you very much to Marty and Danil for their help with this video.

Enjoy :)

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