# Piston-Driven Wheel Simulation

Edit: I noticed a small mistake in the formulas below. I’ll try to get it fixed this week.

I visited a railroad museum today, and I saw a display showing how the piston is linked to the train wheel. For fun and learning I wanted to model the basic mathematics of how the linkage moves with the wheel and the piston, without looking up the answer on the Internet. That part seemed very simple:

Since l and p are fixed length, it was a matter of simple trigonometry, as seen above. Then I threw the math into a simple Racket program to simulate the movement. That part not hard, but it took an hour or two to add enough lines and circles to make the graphic look half-way decent. Here is a video recording of it running (about 10 seconds):

Here is the source code packaged with the video:

ftp://lavender.qlfiles.net/Racket/piston-driven-wheel.7z

One interesting part of the math is the connection point of l and p (see the diagram above). Until you get very long lengths of l, you get something close to the cosine function but not quite the same.

## 2 thoughts on “Piston-Driven Wheel Simulation”

1. Nice graphic! Very interesting math problem!

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2. I just noticed a typo in the trig diagram so I fixed that.

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