A transmission device for controlling the translational movement of an element includes: an exterior planetary gear equipped interiorly with teeth; an interior planetary gear connected to the controlled element and bearing a rack in the direction of translation; a satellite carrier having satellites with helical teeth engaged with the interior teeth; and a stationary housing accommodating the exterior planetary gear, the interior planetary gear, the satellite carrier. The rack is used to control the translational movement of the interior planetary gear. The transmission device is driven by a motor with a transmission acting either on the exterior planetary gear or the satellite carrier.