In 1866, Swasey and Warner met as fellow apprentices at the Exeter Machine Works in Exeter, New Hampshire. Within a few years they went together to Pratt & Whitney in Hartford, Connecticut, which was one of the leading machine tool builders of the era. There they both rose through the ranks, with Warner rising to be in charge of an assembly floor and Swasey rising to be foreman of the gear-cutting department. There Swasey invented the epicycloidal milling machine for cutting true theoretical curves for the milling cutters used for cutting gears.