Disney's research lab did something along these lines some years ago for making a point follow a path. You draw a path, and it generates the linkages required to match that path as closely as possible. They've had a lot of follow-up work since, but I remember this video for it: https://youtu.be/DfznnKUwywQ?si=F-5NZxKu4hP_mand

Really neat demo! I skimmed through the paper and it looks like they’re using a precomputed database to find an assembly that matches the motion (presumably as a seed to instantiate the solver). That’s definitely more efficient than what I have right now (though perhaps less versatile). I like that they manufactured a few of the characters using 3D printing! That was definitely on my mind, really happy to see they did it.

Some of the mechanisms (belt drives etc) might be a little tricky with 3D printers, but would be very cool to see the mechanism tangibly realized.