In a bent axis hydraulic machine, a back plate and cylinder barrel vary in distance from a drive plate as a stroke angle of the cylinder barrel changes, thereby minimizing unswept fluid volume in the cylinders of the barrel at any stroke angle. Distance is controlled by one or more rollers, engaging respective tracks that define a profile of contact that determines the distance as a function of the stroke angle. Telescoping fluid supply channels are employed to maintain a fluid supply to the cylinder barrel as the distance changes.