A rotary fluid device having a housing that defines a pumping chamber, a shaft disposed in the housing, and a rotor disposed in the pumping chamber and engaged with the shaft. The rotor includes a body which defines a bore that includes an oblique tapered surface. A pivot line is disposed along the tapered surface. The pivot line is a circumferential line at which the rotor pivots. A method for manufacturing a rotor includes turning an outer peripheral surface of the rotor. A bore is formed in the rotor. The bore includes an oblique tapered surface that has a pivot line disposed along the tapered surface, wherein the pivot line is a circumferential line at which the rotor pivots.