This was exhausting and I hope I haven't done it wrong

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I think I am starting to understand the logic of the correlation between the bolt coils travel and the drum coil(s) travel so that triangulation is kept to a minimum.
It goes like this: the coil on the bolt moves up or down with "P-pitch" mm at every bolt rotation so the coil on the drum must travel the same Z distance to keep the line between the two entities parallel at all times. Since only so much string can be accommodated by the bolt at a complete turn, the compensation on the drum is in the steeper angle of the "imaginary" groove (capstan groove?).
For example, an M8 bolt typically has a pitch of 1.25mm (coarse). The threading is a helix with a radius smaller than the 4mm, about ~3.325 actually, plus the radius of the spectra line used (ex: 0.32/2). I used the calculator at
https://www.easycalculation.com/physics/classical-physics/helix.php and got a spectra helical length of ~23mm for a 3.45mm radius helix over 1.25mm of height at an angle of 60deg.
So for each rotation of the bolt the coil on the bolt travels 1.25mm on Z and winds or unwinds 23mm from the larger drum.
To keep up with this travel, the angle of the spectra line on the drum should accommodate 1.25mm in height for each 23mm, which translates to about 3deg of an angle (
http://www.pagetutor.com/trigcalc/trig.html). Also to be noted that the "pitch" on the drum is about 12.5mm which equals to 10 coils.
Here's a sketch of some of the math:

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With 120mm drums, the Spectra helical length is about 422mm for 180deg of rotation. So the bolt will rotate 18.33 times for this 180deg swipe of the shoulder from side to side. Over these 18.33 rotations the coil will travel on the Z of the bolt 18.33*1.25=23mm. With an initial coil height of 12.5mm, it totals up to 35.5mm in Z height on the bolt, which should be the height of the shoulder drum.
@Nic: I know I got to a number we both previously agreed upon but I needed to understand the process mathematically. I hope I didn't screw up again

. My sketch finally resembles yours provided in the Ideas for Next Wally thread but I didn't get it at the time.
I have two issues with this approach.
1) It's pretty bad news that 35.5mm+ will be the height of the drum, a lot more plastic than a solution with extended motor couplers but the bonus of less moving and potentially fragile parts.
2) The spectra line in the example above is a closed loop, resembling a belt and it is pretty difficult to tighten it or at least I don't know a good way to tension it because it moves up and down and no line end is fixed.
I got an idea though, which is inspired by your explanation in the other thread. If I was to split the coil and have half wound up in one direction at one end of the drum and the other half at the other side I would be left enough free space in the middle to use for the redirect line that drives the elbow pulley. I would also be able to use a tensioning mechanism that is away from the pulleys. Something like this:

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