Well, I was really into formalizing stuff when I was in college, you know proving that a cryptographic algorithm was correct by formalizing them as black boxes talking to each other, that sort of thing. Then I just started thinking about how to formalize mechanical things. One of the very things I remember is coming to the conclusion that all motions of a machine can be implemented as a combination of linear and rotational motions (and that's where the two things that move on mockmechanics, the track and the wagon, come from), but I don't know if that is true. But I don't really have any prior art, I had a 2d version that didn't work years ago but I think I lost it.
You should check out Shannon’s work on the differential analyser if you haven’t already. Before computers came along they used mechanical machines to solve differential equations etc. There are more papers with beautiful drawings of mechanical machines from that era.
I think the prior art you're looking for kinematics and robotics... and I distinctly remember that e.g. for multi-joints robotic arms you can actually use methods from the algebraic geometry instead of calculus (so you solve polynomial equations instead of differential equations).
Also, no one in this thread mentioned Opus Magnum from Zachtronics which has some quite neat mechanical movement in it.
