Restoration of a Miniature Patek Philippe
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Personally, I think the Swiss style stop-work mechanism, if used in a watch this small, would be likely to fail.  The force placed on the tiny parts during manual winding could be overwhelming causing deformation of the parts or sheering of the boss on the thin barrel lid. You can see from this photo of the movement placed on a dime that the mechanism is very small.  This is the smallest cylinder watch I have ever seen.   Making and fitting a cylinder is a demanding job and one this small is more so.

Making the Cylinder
A cylinder must be the right size inside and outside in order to interact properly with the escape wheel teeth. The dimensions are determined by the space between the teeth and the width of the tooth.  The outside diameter of this cylinder is close to 0.50mm.  The inside is very near 0.35mm.  That leaves the wall thickness at about 0.075mm.  It must also be hardened and polished in order to reduce wear and friction or the watch will not run for long if at all.  Temper must be drawn from the ends to allow the plugs to enter without fracturing the cylinder.

After carefully measuring the movement dimensions and making a drawing of the missing cylinder, the cylinder was produced using a WW pattern, American Style, Watchmakers lathe.  I used oil hardening drill rod reduced to about 0.80mm diameter. First the blank was drilled with a #80 drill producing a hole about 0.33mm diameter.  Then it was parted off at just slightly over finished length. I made three of these blanks while I was at it. Often something goes wrong during a later step in the production. It is great to have an extra blank on hand.  Next the blanks were strung on a tense steel wire charged with oilstone powder and worked back and forth to dress the holes, smoothing and removing burs etc.  Then the blanks were rinsed with ultrasonic action in solvent.  I made a mandrel by placing a hardened and tempered steel wire in the lathe and turned it carefully to accept the blank and be supported at the end by the tailstock center.  The blank was placed on the mandrel, cut, ground to length and about 0.52 mm diameter. This produced the rough cylinder (concentric) with evenly distributed wall thickness.

The cut out of the cylinder was done very carefully with a custom made lap, charged with oil stone powder, while it was on the mandrel. Removed from mandrel, the piece was placed on a strait, close fitting wire and hardened. It was then tempered to a straw color. The result is shown next to the point of a sewing pin. Hardening and tempering is a process, described in many references for Watchmaking, involving the use of heat to “heat treat” the carbon steel part.