Abstract: A mechanism for varying rotational speed between two rotary shafts, namely a drive shaft and a driven shaft. The mechanism is designed to replace gear boxes which are generally used in motor vehicles. The mechanism includes two truncated cones with concave surface generatrices attached to a shaft secured to the engine and to a shaft secured to the transmission members, respectively. A roller made up of an inverted double cone having convex surface generatrices is mounted on an arm via a pin and arranged to rotationally interconnect the truncated cones by means of the adherence caused both by the choice of materials and by the bearing force exerted on the truncated cones by the roller through a suitable pressure member. The roller is translationally movable over the convex surfaces of the truncated cones by means of a suitable position varying system for adapting the drive ratio to the various parameters which influence the operation of the whole mechanism, according to its position.