Synchro type parts used to be used for analog computation. There were transmitters, receivers, differentials, a whole zoo of gadgets. Now computers do the math, and synchros are mostly used as position sensors.
If you're ever in Hawaii, take a day off the beach and go to Pearl Harbor. It's impressive and very moving. You can tour the sub USS Bowfin. It has a beautiful mechanical torpedo targeting computer in a glass case, like a lethal pinball machine, full of synchros and motors and gears and cams and mechanical integrators.
There's one in San Francisco, too: