A medical appliance including a medical instrument that is separable from an actuator support, the appliance including a connection and disconnection system including a connector carried by the instrument and including a guide for guiding at least one actuator rod retained elastically in the guide by a head, and a coupling endpiece carried by the support and including at least one engagement mechanism that is guided in rotation and that defines a reception setback for receiving the head of the actuator rod. The engagement mechanism is fitted with a rotary coupling member complementary to the rotary coupling member presented by the connector, and the endpiece also presents at least one hook connected to an actuator system.