That's a good one. Never heard of a Ball Resolver. A quick internet search shows that it's part of an analog computer used as part of a Nav Instrument package, probably used for polar or oceanic flight. Being 50s vintage and apparently primarily used in military applications, it almost cries out B-47 StratoJet. A description of the function can be read at
http://terry-kidd.blogspot.com/2009/...computers.html.
More data is available at
http://www.moog.com/literature/MCG/M...erAppGuide.pdf. In part it says: Resolvers provide accurate position and velocity
feedback as well as commutation in precision equipment, without the structural or temperature restrictions imposed by other electronic feedback devices. They are resistant to the shock and vibration levels often encountered in military and aerospace applications.
Last on the list from searching, I found a military handbook about ball resolvers dated 1962. The URL is pretty lengthy, but try this from a google search:
http://www.google.com/url?sa=t&rct=j...,d.aWw&cad=rja
Sorry I can't be of more help. You do have something that's pretty unique and new to me.
-Cub Builder