LOL!
Just sitting through a re-watch of the video I posted above, and marveling at the information it contains! The simplified OT Lathe, does very well show the basic principles, indeed!
Nice to see that I was not wrong in my remembered admiration for this video, it contains rather a LOT of great ideas for a home builder, (the use of the cams mounted at the ends of the spindle, instead of fixed in the middle, eg

, and it neatly shows the two most basic operations (rocking the spindle, vs. plunging it) in a Rose Engine Ornamental Turning Lathe, in very easy to understand visuals!
Needless to say, I have spent a fair amount of time reading about these processes, over the years, and no small part of that, in pre-youtube days, somewhat puzzled as to how exactly the whole process worked.
In pre-electronics days, the very high end of the ornamental Turning Lathes, were the playthings, quite literally, of Kings and their near peers, and they actively, in some cases, worked at having the 'best' finished project, whether by their own hand, or by a hireling, to use to entertain guests as an item of interest, usually made in Ivory or some exotic hardwood.. A cabinet full of curiosities that were both beautiful and interesting, made you a very fine host!
During one of the tours I did of a Castle in England near London, I did see a very nice, and quite complicated jewellery or snuff box, ornamentaly turned with several patterns, likely on a Holtzapffell lathe (if not one of their competitors) that was stated to have been made by the King's own hand, on display. Sadly, no sign of his lathe!
IIRC, the second Hotzapffell turning book has tables showing the progression of various gear ratios, through various versions of their Geometric Chucks.
And to think, some folks think trying to calculate a gear ratio, to cut a particular thread, when they know what the pitch of the leadscrew is, is "too hard!". Think on the maths that went in to accurately predicting the outcome of something like the five level Geometric Chuck that is shown on the last link I posted above!
Frankly, a LOT of these results CAN be recreated with CNC. But before you can make them, you need to understand all the vagary's of the geometry you are trying to create, or your project is a failure. If you cannot figure out how to make the CAM program understand what you want, you can't just push a button, and have it do all the work for you. Or you have to accurately draw out the end product, rather than have it generated by the equipment, whch is rather a different thing.
In the end, you have to understand the processes that you need, in order to get from here (raw material) to there (the end result you desire).
I kinda don't want to interject a Clickspring video, as there are those who have stated and objection to focused cameras, and high quality production values, but his video on guilloche, shows the difference rather well, to what I was talking about as Damanscening (or Damaskeening) Creative spelling for the win!
But anyway, for the pleasure of them what don't hate on clickspring...
I have said before, that the reason I LIKE his videos, is that I know and understand a LOT (nowhere near all) of his processes, and appreciate them showing clearly and well in the videos that are so well made.
Another video, worth a look, concentrating on Banknote stuff!
Cheers
Trev