Method of producing drive element for a timepiece barrel including a barrel arbor and mainspring

A method of producing a drive element for a timepiece barrel, comprising at least one spiral strip mainspring of determined type comprising a first inner coil with a defined first width and first thickness, said first inner coil comprising, for the holding thereof on a barrel arbor, at an inner end, a holding or hooking means having a defined profile, said drive element further comprising a barrel arbor, the method comprising:

• drawing, in a first wire drawing operation, a bar so as to form, about an axis parallel to a direction of the drawing, a progressive profile in a shape of a snail between a smaller radius and a larger radius, with a step between points on said larger radius and said smaller radius, said profile in the shape of a snail comprising a support sector for said inner coil;
• and
• machining or turning, in a second touching-up or bar turning operation of said drawn bar about a touching-up axis parallel to or merged with the direction of the drawing, a complete external contour of said arbor, the complete external contour comprising at least one cylindrical shoulder for pivotally guiding said arbor,
• wherein said step is used, either as a stop means for said means of holding or hooking said mainspring when said step is used as drawn, or as a complementary stop or hooking means for said holding or hooking means for said mainspring when said step is re-machined during said second touching-up or bar turning operation, and
• wherein, in said second touching-up operation, a peripheral groove is machined, of a revolution about the touching-up axis parallel to the direction of the drawing, and a width of the groove is adjusted along the direction of said touching-up axis, to hold in position said inner coil of said mainspring in the direction of said touching-up axis, on at least one point on the revolution thereof, said groove being secant with said step, between the surfaces thereof of smallest radius and of largest radius, and said groove being substantially tangent to said profile in the shape of a snail in a zone substantially diametrically opposite to said step relative to said touching-up axis of revolution of said groove.