Transmission system for oscillating systems comprising: - a drive pulley operable in rotation about an axis of rotation of the drive pulley; - a driven pulley; - a first and a second flexible transmission element (130A, 130B) operatively coupled to the drive pulley and the driven pulley for the transmission of a movement between said pulleys (110, 120), the first and second flexible transmission elements (130A, 130B) each comprising a first and a second connection portion (131A, 131B, 132A, 132B), each of said first connection portions (131A, 131B) being attached to the drive pulley; and - a connection member including a connection element configured to connect the transmission system to a payload (4, 5) the connection element being integral in rotation with the driven pulley around an axis of rotation; wherein the drive pulley is adapted to drag the driven pulley and the connection element in rotation in a first and in a second direction of rotation opposite to each other respectively by means of the first and second flexible transmission elements (130A, 130B); wherein said connection element is arranged to rotate around the axis of rotation of the drive pulley; wherein said transmission system further comprises a fixed part with respect to said drive and driven pulleys (110, 120), said second connection portions (132A, 132B) being attached to said fixed part; wherein said rotation axis around which the driven pulley and the connection element are integral in rotation is the axis of rotation of the drive pulley; said transmission system being characterized in that: said transmission system further - comprises a coupling shaft connected to the driven pulley and to the connection member for coupling the driven pulley to the connection member, the driven pulley being coupled to the coupling shaft so as to be able to rotate around a rotation axis of the driven pulley that is parallel to the rotation axis of the drive pulley; wherein said transmission system has a transmission ratio ρ obtainable as follows: ρ = Tc ∗ Rc T ∗ Rm wherein Rc is the radius of the trajectory of the centre or rotation axis of the driven pulley, Rm is the radius of the drive pulley, T is a pull on the first transmission element and Tc is the effective component of resultant of the pulls T acting on the driven pulley. - a drive pulley operable in rotation about an axis of rotation of the drive pulley; - a driven pulley; - a first and a second flexible transmission element (130A, 130B) operatively coupled to the drive pulley and the driven pulley for the transmission of a movement between said pulleys (110, 120), the first and second flexible transmission elements (130A, 130B) each comprising a first and a second connection portion (131A, 131B, 132A, 132B), each of said first connection portions (131A, 131B) being attached to the drive pulley; and - a connection member including a connection element configured to connect the transmission system to a payload (4, 5) the connection element being integral in rotation with the driven pulley around an axis of rotation; - comprises a coupling shaft connected to the driven pulley and to the connection member for coupling the driven pulley to the connection member, the driven pulley being coupled to the coupling shaft so as to be able to rotate around a rotation axis of the driven pulley that is parallel to the rotation axis of the drive pulley;