Introduction: 3D Printed Galton Board

About: Analog maker dabbling in digital manufacture

A Galton board (AKA a bean machine) demonstrates probability by allowing balls to drop through an array of pegs through which they have a 50/50 chance of going left or right at each point. They drop into bins and are collected there, and the heights of the accumulated balls in each bin approximate a bell curve.

This Galton board was 3D printed on a consumer-grade machine, and is topped with a piece of acrylic (plexiglass). I used sand instead of beans or ball bearings to keep the project inexpensive and accessible.

Step 1: Design

I used Galton's original sketch of his bean machine, and converted it into a 3D-printable object using Fusion360. I am a pretty ordinary 3D designer so it took a good couple of hours of fiddling around to end up with the design you see here. File available at https://a360.co/39j2YNg.

Step 2: Print and Cut

I designed the Galton board to be printed on a Creality CR-10 3D printer at 115% scale, and it only just fits on that. If you want to print it on a smaller machine, scaling it down a little will only be a problem for the part that holds the acrylic, because it may end up a little thick. I suggest you use a thinner acrylic sheet or just shave the edges a little. Don't forget to scale the sheet by the same amount you scaled the print!

You may end up with some stringing between the pins - do a quick pass with a heat gun to fix that.

The acrylic piece was an offcut of 3 mm thick clear acrylic which was designed based on the final print I made. I laser cut it in a few seconds of cutting time. If you don't have access to a laser cutter, acrylic is easy enough to cut conventionally and sand and polish.

Step 3: Assemble

Pour your (very dry!) sand on the board. Slide the piece of acrylic into the two side slots. You're ready to go!

Galton boards often come in frames, but I like the hand-held nature of this one. You can tilt it to make the sand run at whatever speed you find most satisfying, and tilt the board to bias the distribution. The distribution above is a bit wonky because I was tilting the board with one hand and filming with the other.

If you're a teacher and have access to a makerspace, put one together and pass it around the class when you're talking about probability in math class.

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