Coupling device of a system for operating a horological movement

An operating system (1) for operating a horological movement of a watch, which system comprises a coupling device (40) provided with first and second coupling ends (32, 33) and first and second drive zones (36, 37), said coupling device (40) being configured to operate at least one function of this movement by comprising a control device (2) and a support piece (3) intended to be unmoving relative to the horological movement of the watch and in which piece (3) this control device (2) is movably mounted, the control device (2) comprising:

• a gripping element (7) capable of being driven in a rotational motion about a longitudinal axis (A) of the coupling device (40);
• a first drive element (31) including the first coupling end (32) and the first drive zone (36);
• a second drive element (8) mounted such that it is rigidly connected to the gripping element (7), this second drive element (8) including the second coupling end (33) and the second drive zone (37), said second zone (37) being able to be joined to the first drive zone (36) in order to drive the first drive element (31) such that it rotates;
• said elements (31, 8) being configured to transmit this rotational motion to a functional member of the movement when said gripping element (7) is arranged in an axial position for operating said function.