UKH

On a maillon how do they make sure the "phase" of the thread at the top matches the thread at the bottom?

I'm guessing that the body of the maillon isn't quite as rigid as you may think, and that a tiny elastic movement of a less than a millimetre is easily achieved without obvious strain, especially seeing as it will be achieved by turning the thread screw, which will be adding a substantial gearing ratio to further reduce any perceived effort.

I’d guess the threads are sort of pressed on rather than cut individually on either side with a traditional style die and collar.

Probably a bit of hope it works and/ or a bit of adjustment after bending to shape if it's not aligned within tolerance. 

I have always been more intruiged as to how they get the gate bit on.

Easy, it's called engineering.

If a thread has a 1mm pitch for example as long as the gap between 2 threads is divisible by 1mm the female thread will join the 2 ends together. I have never looked at how a mallion is made but I suspect it starts as a streight bar, cut to length, the nut is put on, the ends are up set (heated and pushed in to increase the diameter), a thread is simultaneously rolled on to each end leaving a bit un rolled as the stop collar then its bent in a jig to the correct shape. 

This video shows some aspects of the manufacture but crucially not how they deal with non alignment of the threads.

youtube.com/watch?v=rl7P0wTocMs&

I suspect it is a hand made adjustment of those that don't match first time.

They do indeed have a row of people skilfully wielding hammers.

Ok - the video shows what I need to know - the threads are made with the bar straight, the sleeve is attached then it is bent.  I guess the thread rolling both end is done at the same time and the bending carefully calibrated.

Ta!

That seems the sensible approach for mass production.

jk