A rotary damper includes a rotating input member rotating about a rotation axis; a first cylinder and a second cylinder coaxially arranged on opposite sides of the rotation axis; a first and a second pistons slidable inside the first and second cylinders and defining a first and a second working chambers containing incompressible working fluids, respectively; motion conversion mechanisms converting the rotary motion of the rotating input member about the rotation axis into reciprocating motion of the first and second pistons; a third cylinder; a fourth cylinder; and a third and fourth pistons, slidable inside the third and fourth cylinders, respectively and separating the inner volume of the respective cylinder into a respective main chamber in fluid communication with the first working chamber and auxiliary chambers; and the second working chamber and auxiliary chambers respectively.