The theory behind the Stevens winder is very simple.
This is a drawing I colorized showing the missing parts of my winder
and how it all works.

My winder was originally only supplied with the 'upper' colorized drive parts,
so I will use that to show how my winder is supposed to work.

The main drive pulley is at the far left. This is driven by a motor and power supply (not shown)
to control how fast or slow the winder runs. This also controls the 'clock' turn counter
at the top of the winder and also the blue gear shown inside the gearbox. If the main drive pulley
rotates once, the blue gear inside the gearbox rotates once and the 'clock' also goes to its next 'tick' position.

The blue gear rotates the green gear and the yellow gear (behind the red heart shaped cam)
to set how fast the red cam rotates. The red cam is the heart of the winder... for real. The traverse rod
assembly (the orange rod) rides on the red cam, and the cam makes the traverse rod move
to the left or right to feed the wire evenly onto the coil. The gears inside the gearbox are chosen
to make the traverse assembly move only a very small amount per each revolution of the main drive.
The traverse assembly guides the coil wire onto the pickup bobbin depending on which gears and cams
are in the gearbox when it's being used.

The lower colorized parts are only used on later winders but I include them
here to demonstrate how cams work.

The orange traverse rod rides on the red cam. The zigzag drawing between the part
mounted to the traverse rod and the main gearbox's side is in real life a long coil spring
like the one you would find on an 'old school' house
screen door. If you turned the crank
on the cam counterclockwise, the traverse rod would move to the right. If you turned the crank
far enough, the flat area on the cam would make the traverse rod move very quickly
back to the left. Basically, a coil wound with this cam assembly would have only one
even winding from the left side of the coil to the right, and a quick movement back to the
left side when the winding was done.

Here are some more photos demonstrating how a cam works.
This is a bobbin winder from a very old treadle sewing machine with a
heart shaped cam mounted on it.

The pulley at the far right hooks onto the sewing machine's belt drive to power this winder.
The screw thread at the top of the winder is really a worm gear driving the large main gear.
The cam is bolted to the main gear so when the main gear rotates, the cam does too.

The worm gear is much smaller than the main gear, so one full rotation of the top worm
gear would only move the main gear a very small amount.

The traverse lever is the lever riding on the cam, and it's resting on the tip of the cam so it's
at the farthest lefthand point of its movement.

The drive pulley has rotated about 50 turns, and the main gear has rotated about 90
degrees. The traverse rod has moved about halfway across its movement.

The drive pulley has rotated another 50 turns or so, and the main gear has rotated
180 degrees around so the traverse rod has moved to the farthest right point
of its movement. The drive pulley will rotate about 100 times for every half a turn
of main gear and cam movement, so each single complete rotation of the main gear
equals two complete layers of windings of about 100 turns each.

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