> I feel like common mechanical subsystems like cams (which, for example, allow a rod to follow an arbitrary velocity curve when you move a knob), gears, and other devices may be abstracted away by a simple primitive
This is exactly how I was thinking before I pivoted the project to a more practical version, spot on. I feel like this project has moved on from that, but someone should really investigate this. Just off the top of my head imagine how easy it would be to run a genetic algorithm to find machines if we had an abstract description for them, or maybe there could be a whole branch of mathematics to prove that a certain machine does what we think it does (a lock is secure, this sort of thing).
This is exactly how I was thinking before I pivoted the project to a more practical version, spot on. I feel like this project has moved on from that, but someone should really investigate this. Just off the top of my head imagine how easy it would be to run a genetic algorithm to find machines if we had an abstract description for them, or maybe there could be a whole branch of mathematics to prove that a certain machine does what we think it does (a lock is secure, this sort of thing).