LogIn"Tinkering with gears."
This nice, completely physics-based setup was created by a Reddit user known as pattyfritters, who used custom collision on the gears to allow the teeth to interact fully and a physics handle on a character to grab the actual handle.
Apparently, the gears also work mounted on the wall, and the physics handle works best on the wall as depth interferes with converting the cursor to world space. The developer mentioned that they are gradually making progress towards adding them to the door. Here's how it looks with 85 gears at once.
Although these gears involve zero math, the lever in the background was entirely math-based:
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