physics – Can one build a “mechanical” universal turing machine?

This question connects different disciplines so it’s awkward to choose a SE site for it, but I’ll go with this one because here (I hope) the shared culture will make information transfer easier.

So computers as we know them use electricity and I don’t know what other invisible things that I don’t understand. I was wondering, is this a matter of efficiency, or of necessity? Can one achieve universal computation with just “moving parts”? Perhaps “Newtonian physics” is some term for this, although I guess it includes gravity which isn’t really what I mean. You know, just good old solid pieces of matter moving around.

To get some picture of what I mean, here is a “LEGO turing machine”. I’m afraid that the big gray block on top uses electricity, but could one replace it with a “mechanical” thing, powered perhaps by rotating a piece? I have no idea how such things be designed, and the state transitions for a universal TM have to be fairly complicated, so I have no intuition for whether this is possible or not.