A mechanism for transforming rotary motion of a shaft into a translational motion of actuating members, comprising a casing (33) adapted for connection with a cylinder block (2) of an engine, said casing having a cavity coaxially formed relative to an engine shaft (11) and receiving an end of the shaft (11) on which a drive gear (41) is connected, said drive gear being in mesh with a gear wheel (42) installed in the casing (33) and kinematically connected to a ring-shaped member (68) having external radial projections (71, 72) and an internal ring gear (83) and kinematically connected to actuating members, and wherein a first zone (A) of engagement of the drive gear (41) and gear wheel (42) communicates with a header (54) of oil fed to friction surfaces, while a second zone (B) outside the engagement of the drive gear (41) with the gear wheel (42) communicates with a lubrication source.