The four bar linkage
Three moving bars and a frame, and everything they can trace.
Four bars pinned in a loop, one of them fixed, is the simplest mechanism that does something interesting. Depending on the lengths, the input either turns all the way round or rocks back and forth, and Grashof's rule says which: add the shortest and the longest, and if that is less than the other two added together, something can rotate fully.
A point on the coupler — the bar with no fixed pin — traces a curve that is neither a circle nor a line, and choosing the lengths to get the curve you want is most of a century of engineering. Straight line linkages, film advance mechanisms and windscreen wipers are all this.
| Rule | What it says |
|---|---|
| Grashof | shortest + longest ≤ the other two, and a crank can turn fully |
| Beyond it | both moving bars rock, neither goes round |
Turn on trails in the app and drag the coupler point about. The curve it draws changes shape as the lengths change.
Open the fourbar scene in the app to watch this one run.