We’ve often said you can make a logic gate out of darn near anything. [The Action Lab] agrees and just released a video showing how he made some logic gates from chains and gears. Along the way, he makes the case that the moving chain is an analog for electric current. The demonstration uses a commercial toy known as Spintronics, but if you are mechanically handy, you could probably devise your own setup using 3D printing or gears.
A spring wound motor is a “battery.” Gears act like resistors and junctions to distribute “current” in multiple directions. Seeing series and parallel resistance as moving chains is pretty entertaining and might help someone new learn those concepts.
A spring acts like a voltmeter, which acts as an indicator. There are also switched gears that act as inputs. While it is possible to make a chained inverter, NAND gate, and NOR gate, it would quickly become unwieldy. But it is, at least in theory, possible.