by Joe Jarski » Mon Dec 20, 2010 12:49 pm
Ahh, the old chicken and egg... I'm not sure how it was really done back then. When they started cutting them on a machine, my guess is that it was done using gearing and a rack. That would give consistent results with a periodic error that could probably be lapped out. Though the lead may not have been accurate, neither were the measurements. There have been some pretty clever people that mapped the lead screw errors using optics, I believe, on a relatively inaccurate screw and then built a compensating cam mechanism to take the errors out. This was done with something like 30k tpi for ruling diffraction gratings.
There's a pretty good book called “Foundations of Mechanical Accuracy” by Wayne R. Moore who founded Moore Tools and it explains a lot of the hoops they had to jump through to get to extreme levels of accuracy. It's an interesting read if you've ever wondered how to make something flat or square within 50 millionths of an inch using hand tools and no master reference.