A mechanism for installing a door or other similar closure device with rotary and translational motion, of the type comprising the following elements to be associated with a leaf first pivoting means, which form a first vertical axis (11) for the pivoting of the leaf (12), in a central region thereof, to means for translational motion arranged so as to slide in a corresponding guide (13) associated with the upper stringer (14) of the frame (15) of the door; second pivoting means, whose axis is parallel with respect to the axis of the first pivoting means, for the articulation of two arms (16, 17), a first upper arm (16) and a second lower arm (17), which are both pivoted by means of a first end (21, 22) thereof to the frame (15) of the door or window proximate to a jamb (18) so as to form a second rotation axis (20), third pivoting means, which are formed by the second ends (23, 24) of the arms (16, 17), which are hinged to the leaf (12) so as to form a third rotation axis (26) that passes through the leaf (12) parallel to the first and second axes and in an intermediate position between the two first and second axes when the leaf is in the closed configuration. The second pivoting means comprise a pivot (27) arranged in a compartment (28) formed within the jamb (18), the pivot (27) joining the first ends (21, 22) of the arms (16, 17) and thus causing their joint rotation.The mechanism according to the invention facilitates and improves the installation of doors with rotary and translational motion.