The Swiss Screw Thread

In 1876 the Société des Arts de Genève formed a committee to standardize small screw threads for instruments, clocks and watches, Geneva being a center of the watch industry. The committee consisted principally of persons actually active in horological manufacturing. They began by forming an extensive collection of screws and documents related to screws, and then placed these materials in the hands of Professor Marc Thury. In 1877 the Society convened a conference in Geneva to agree upon a thread series.

The goal was to create a thread series that, while it differed as little as possible from current practice, was based on a simple, mathematical regularity. This Thury achieved. 

A screw diameter of 6 millimeters was chosen as size 0 and assigned a pitch of 1 mm. The 6 mm diameter was selected because that was roughly the diameter of currently-used screws that had a pitch of 1 mm. 

From size zero, progressively higher numbers identified progressively smaller screws, ending with number 25, the smallest. Sizes of screws larger than 6mm were negative numbers, beginning with minus 1 and ending at minus 20, the largest size. Thus in both cases, the bigger the number, the smaller the screw.

Pitch

The pitches of adjacent sizes differed by a factor of 0.9, which was determined empirically. One consideration in choosing this factor was that it was felt that the sizes in existing thread series were so close together that it was difficult for workers to distinguish sizes by eye; fewer, not more, sizes were desired.

Pitches of screws smaller than 6 mm were successive powers of 0.9, rounded off to 2 or 3 significant places. For example, the pitch of size 1 = 0.9¹; the pitch of size 2is 0.9² = 0.81; the pitch of size 3 is 0.9³ = 0.729, and so on.

Pitches of screws larger than 6 mm were determined by dividing the pitch of the previous size by 0.9 and rounding off to 2 or 3 significant places. For example, size −1 has a pitch of = 1 mm/0.9 = 1.1111… mm = 1.11 mm.

Diameter

The diameter (D) of the screw can be calculated from the pitch (P) by the formula

D = 6P^6/5

So, for example, a #1 screw, with a pitch of 0.9 mm, would have a diameter of 6 × 0.9^6/5 = 6 × 0.9 to the 1.2 power = 6 × 0.881233526… = 5.287401156…, which, again, is rounded off, here to 5.29 using the rule that the second figure is increased by 1 when the third figure is 5 or more.

Thread form

Two different thread forms were defined. The first was used for the screws 6 mm in diameter and smaller. The depth of the thread was 3/5 the pitch. Crests were rounded with a radius equal to 1/6 of the pitch. Roots were rounded with a radius equal to 1/5 of the pitch. Given these requirements, the thread angle will be about 47.5°. When these small screws are threaded in a screw-plate, the circular arcs are compressed into parabolic curves, a desireable profile.

The second thread form was for the larger screws, and intended to be cut on a lathe. The form is an isoceles triangle whose base and height are equal to the pitch. The thread depth is ¾ of the pitch; roots and crests are rounded with a radius of 0.1011 times the pitch. As a result, the thread angle is 53° 8′. Thury credits “M. Steinlen of Mulhouse” for this thread form.

Relief threads

In repairing watches and clocks one sometimes encounters tapped holes that have become enlarged. In this situation a special class of screws with “relief threads” may be used. Such a screw has a diameter half-way between the diameter of the standard screw whose pitch it shares, and the diameter of the next larger standard screw.

Marc Thury.
Systèmatique des vis horologères.
Geneva, 1878.