Building the most accurate DIY CNC lathe in the world [video]

For folks who are not familiar w/ machine shops, the lathe is a fundamental tool in a shop, and is the only tool in a shop which can replicate itself --- there is even a book series which uses this conceit, the "Gingery Books":

https://gingerybookstore.com/

where Vol. 1 has one setting up an aluminum casting foundry in one's backyard, and Vol. 2 has one using it to make a lathe which is then used to either improve itself or make a better lathe, then one uses it to make the balance of the tools in a machine shop.

A lathe can't actually replicate itself completely. Specifically, a lathe can only make ways smaller than its own cross slide's stroke. It would also be impossible to make a typical lathe bed on a lathe, though you theoretically could design an unconventional lathe bed that is possible to make on a lathe, even if grossly impractical.

The real starting point for machine precision is rubbing 3 granite plates together.

Lathes can certainly make cylinders, and a tube-based lathe bed is not a stretch.

A lathe can't replicate its own assembly, of course. It can't seat the spindle in the constraint bearings, for instance.

A CNC (without the word lathe) can make most of itself, and possible all. Nope: certainly all, if two of its dimensions fit within its work volume.

But it can't make cylinders as long as its own guide ways.