Control device for displacing movable parts of a covering element for vehicle passenger compartment

The invention relates to a device for controlling the movement of mobile elements of a covering part of a passenger compartment (2) of a motor vehicle which comprises successively a fixed element (11), a first mobile element (12) and a second mobile element (13). The device comprises at least one guiding means for each mobile element (12, 13), means for sliding displacement of the mobile elements (12, 13), on one hand, between the deployed position in which the mobile elements (12, 13) are aligned and contiguous and the retracted position in which said mobile elements are superposed and, on the other hand, between the retracted and deployed positions and means for locking and unlocking each mobile element (12, 13) in the deployed position.