Articulated quadrilateral mechanism (50, 50') for moving a swing closure element for doors, windows or the like, said mechanism (50, 50') comprising: - a fixed member rigidly constrainable to a fixed structure, - a first movable member rigidly constrainable to a first movable wing and pivotably constrained to said fixed member by a first hinge constraint, - a second movable member (52, 52') rigidly constrainable to a second movable wing and pivotably constrained to said first movable member by a second hinge constraint and - a third movable member (53, 53') connected to said fixed member and to said second movable member (52, 52') by a first pin and a second pin (53b, 53b'), characterized in that respectively said articulated quadrilateral mechanism (50, 50') is pivotable according to a predetermined opening rotation direction starting from a first closed configuration wherein said four members (10a; 51; 52, 52'; 53, 53') are parallel to each other, said first and second hinge constraints (21, 31) being arranged in said closed configuration so that a first plane (Z1Z3) containing the axis of said first constraint and the axis of said first pin is spaced from a second plane (Z2Z4, Z2Z4') containing the axis of said second constraint and the axis of said second pin (53b, 53b'), said rotation direction being oriented from said second plane (Z2Z4, Z2Z4') to said first plane (Z1Z3), said articulated quadrilateral mechanism (50, 50') further comprising at least one first stiffening member (61, 61') pivotably constrained to a said first movable member and to a said third movable member (53, 53') so that in said closed configuration: - said first stiffening member (61, 61') is parallel to and spaced with respect to a plane containing said second axis and the axis of said second pin (53b, 53b') and - said rotation direction is oriented from said second plane (Z2Z4, Z2Z4') to said first stiffening member (61, 61'). - a fixed member rigidly constrainable to a fixed structure, - a first movable member rigidly constrainable to a first movable wing and pivotably constrained to said fixed member by a first hinge constraint, - a second movable member (52, 52') rigidly constrainable to a second movable wing and pivotably constrained to said first movable member by a second hinge constraint and - a third movable member (53, 53') connected to said fixed member and to said second movable member (52, 52') by a first pin and a second pin (53b, 53b'), characterized in that respectively said articulated quadrilateral mechanism (50, 50') is pivotable according to a predetermined opening rotation direction starting from a first closed configuration wherein said four members (10a; 51; 52, 52'; 53, 53') are parallel to each other, said first and second hinge constraints (21, 31) being arranged in said closed configuration so that a first plane (Z1Z3) containing the axis of said first constraint and the axis of said first pin is spaced from a second plane (Z2Z4, Z2Z4') containing the axis of said second constraint and the axis of said second pin (53b, 53b'), said rotation direction being oriented from said second plane (Z2Z4, Z2Z4') to said first plane (Z1Z3), said articulated quadrilateral mechanism (50, 50') further comprising at least one first stiffening member (61, 61') pivotably constrained to a said first movable member and to a said third movable member (53, 53') so that in said closed configuration: - said first stiffening member (61, 61') is parallel to and spaced with respect to a plane containing said second axis and the axis of said second pin (53b, 53b') and - said rotation direction is oriented from said second plane (Z2Z4, Z2Z4') to said first stiffening member (61, 61').