A continuously variable hydraulic machine has a vane rotor (412) with a plurality of radial vanes (414) and a connection for a torque transmitting input shaft (422). A cam ring (404) supported in a position surrounding the vane rotor (412) has an interior surface facing the vane rotor (412). The interior surface of the vane rotor (412) define a working volume swept by the vanes (414). The cam ring (404) has flexible portions capable of flexing radially when inwardly directed radial forces are exerted thereon to change the shape of the swept volume within the cam ring (404). A control mechanism (530) exerts a squeezing force on the cam ring (404) to distort the cross-sectional shape of the came ring (404) and the swept volume within the cam ring (404). The cross-sectional shape of the cam ring (404) swept by the vanes (414) is continuously adjustable by the control mechanism for continuously adjusting the displacement of the vane rotor per revolution. The flexible portions of the cam ring (404) are subjected to the same fluid pressure on opposite radial sides around the circumference of the flexible portions of the cam ring (404) so that the cam ring (404) is pressure balanced radially.
