The apparatus includes a driving shaft with a first gear wheel, a frame able to rotate within limits about the driving shaft, a servo mechanism for controlling the angular position of the frame, a valve-lifting crankshaft with a second gear wheel supported by the frame, a rocker cam assembly, a connecting rod pivotally connected to the valve-lifting crankshaft and the rocker cam assembly, a cam follower operatively connected to a charge exchange valve, and a spring for urging the cam follower against a cam lobe. The engine rotates the driving shaft. The first gear wheel rotates the second gearwheel and the valve-lifting crankshaft. The connecting rod transmits motion from the valve-lifting crankshaft to the rocker cam assembly. Stroke, lifting duration, and phase can be controlled by the angular position of the frame.