Hi,
I have managed to get a working node file for my problem as follows.
As before there are 3 segments
1) entry constant pitch. 720 degrees ( 2 rotations ) 10 pitch
2) Variable pitch middle. 1800 degrees ( 5 rotations ) 10 start end 30 pitch
3) exit constant pitch. ( 2 rotations ) 30 pitch
I have a slider set max to 5 rotations same as the middle section.
There is a bottle for each section with its own move profile.
The slider or in my case the quartz node controls all 3 segments.
The bottles are positioned as if all 3 segments had 5 rotations so
bottle 1 is placed 5 x 10 pitch away from start of segment 2
bottle 2 at start of segment 2 and bottle 3 at end of segment 2
It's basically a relay race if that makes sense.
In the animation the bottle seams to travel the full length of the screw
but in fact it is each bottle for its own section.
It's not an elegant solution but it allows to animate the movement and
check for clashes using Karsten's Boolean intersect.
Cheers
Barry