A medical apparatus including a medical instrument separable with respect to an actuating support, the device including a connecting and disconnecting system between the instrument and the support, including: - a connector supported by the instrument and including a guide for at least one actuating rod provided with a head protruding at the free end of the guide, the connector being provided with a rotational coupling member, and - a connecting tip supported by the support and including at least one engagement mechanism, this engagement mechanism being equipped with a rotational coupling member complementary with respect to the rotational coupling member of the connector, the tip and the connector occupying a connection position after they are brought axially closer together leading to the rotational coupling between the connector and the engagement mechanism, characterized in that: - the head of the actuating rod has a semi-hemispherical or prismatic shape, kept elastically bearing on a transverse end face (9 1) of the guide, by means of a return spring, - the tip having at least one hook connected to an actuating system and having a housing for receiving the head of the rod to provide a translational connection between the rod and the actuating hook, - the engagement mechanism is a cam guided in rotation and defining a recess for receiving the head of the actuating rod, the cam being mounted to extend in the position awaiting connection, inside the hook with the recess situated outside the hooks so as, following the axial approach movement, to receive the head of a rod released relative to the guide, the axial approach being followed by a rotational movement between the connector and the connecting tip to drive the rotation of the engagement mechanism, which moves the head of the rod until it cooperates with the hook order to provide a mechanical connection of the head of the rod with the actuating hook, the engagement mechanism extending, after rotation, outside the hook, which is then positioned inside the recess so as to be able to slide freely. - a connector supported by the instrument and including a guide for at least one actuating rod provided with a head protruding at the free end of the guide, the connector being provided with a rotational coupling member, and - a connecting tip supported by the support and including at least one engagement mechanism, this engagement mechanism being equipped with a rotational coupling member complementary with respect to the rotational coupling member of the connector, the tip and the connector occupying a connection position after they are brought axially closer together leading to the rotational coupling between the connector and the engagement mechanism, characterized in that: - the head of the actuating rod has a semi-hemispherical or prismatic shape, kept elastically bearing on a transverse end face (9 1) of the guide, by means of a return spring, - the tip having at least one hook connected to an actuating system and having a housing for receiving the head of the rod to provide a translational connection between the rod and the actuating hook, - the engagement mechanism is a cam guided in rotation and defining a recess for receiving the head of the actuating rod, the cam being mounted to extend in the position awaiting connection, inside the hook with the recess situated outside the hooks so as, following the axial approach movement, to receive the head of a rod released relative to the guide, the axial approach being followed by a rotational movement between the connector and the connecting tip to drive the rotation of the engagement mechanism, which moves the head of the rod until it cooperates with the hook order to provide a mechanical connection of the head of the rod with the actuating hook, the engagement mechanism extending, after rotation, outside the hook, which is then positioned inside the recess so as to be able to slide freely.