Abstract: A self-aligning bearing construction including a ball which can be used in a pillow block mounting mode, or a flange mounting mode, or in special mounting for specific applications. A pair of generally parallel flats are formed on the ball on opposite sides of the shaft bore therein, and two cylindrical lands extend transversely around the ball, connecting the flats. As a result of a sizing step, the ball may be formed with a bead or rib running around the ball centered on the cylindrical lands and across the flats. The lands and flats provide clearance spacing so that the bead does not engage seats in a cap and a base between which it is clamped. The ball is cooperable with a series of different caps and bases for use in different mounting modes and can receive any of a series of bearing inserts to provide different bearing service.