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 metho

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.