Could this mean that before the development of accurate screws, we could see the development of phonographs but have them very individualised devices.
Tormsen,
Possibly, but I believe it to be very unlikely.
MacCaulay in Post #15 neatly explained how standard screws with fixed thread pitches are made to today and have been made since ~1800 when Maudslay put together all the disparate pieces that make up a modern screw lathe. Before that screws were made by hand and not only did thread pitch very from screw to screw but thread pitch
varied with the same screw. (Great descriptions in that post, Mac!)
Having a varied thread pitch in a screw really doesn't matter if you're simply using it as a fastener, having a varied thread pitch matters a great deal if you're using the screw as a drive shaft however. You could revolve the screw at a steady speed but the component being driven by the screw would move at an irregular speed because of the variations in the pitch. It would next to impossible to recreate the "rhythm" of those variations by varying the speed at which you crank.
There could be one-off machines as you suggest, a record can only be played on the machine that recorded it, but almost obviates the reason for having such a machine in the first place.
So, yes, Ben Franklin could have built such a machine. However, if he ever needed to replace the drives screws or gearing in that machine, it would be unlikely that he or anyone else would be able to play back recordings made before the replacement of those parts.
This question of "recording speed" and the existence of variations in "recording speed" is one of the major reasons why no useful data was returned from those pots mentioned earlier. We don't know the speed at which the pots were thrown and we don't how that speed varied as they were thrown. Imagine a record whose RPM requirement repeatedly jumps between 33 1/3, 45, 78, and a wide range of other numbers with no warning and no pattern. How could you "play" that record?
Bill