A brewing device for a beverage preparation machine, in particular coffee or tea, the brewing device includes a frame, a brewing chamber carried by the frame and having a longitudinal axis and a loading/unloading aperture for a brewable material, a closing body movable relative to the frame from and to a closing position for the aperture, and an actuator device to move the closing body. The brewing device further includes a motor and a transmission arranged between the motor and the closing body; the transmission includes a rack-and-pinion mechanism including a driving toothing carried by the frame, and a driven toothing carried by the closing body and meshing with the driving toothing to move the closing body from and to its closing position.