Taps, reamers or other cutters were made on lathes in tool rooms equipped years ago with "Backing OFF attachments" or also called a relieving attachment. Very rare today . Attachment was a special compound rest with a cam which move the tool in and out the number of times per revolution for the flutes on the cutting tool. This was gearing to the lathe spindle and a u-joint drive shaft then connected to the special compound rest. Also a slow speed drive arrangement gearbox was necessary for a very slow spindle speed. This attachment was placed on lathe ways one side attached to the lathe spindle other was the chuck. I have only seen lathes with part of the attachment usually missing the special compound rest.
Today there are cutter grinders with relieving ability plus multi-axis CNC mills could make taps


Dennis Daugherty

.

I can think of a couple ways, you could machine inserts for the cutting surface, and then mount them in a carbon steel tool, that would function like a tap. The resulting tool would not have the same chip clearing ability of a true tap, but it would cut correctly.

Kelly The Hendy at the Huckberry Railroad Shop has the drive portion and drive shaft .
If you have the cam compound rest portion you should together with John Scott to see if it will work
Dennis Daugherty

Some of the mechanical attachments for those old lathes and milling machines are simply exquisite. They could be designed for all kinds of special shapes, gears, taps, etc.

The Gleason Works (in Rochester, New York) made a whole company out of special machines to cut the offset hypoid gears for automobile differentials, a wonder to watch one operate.

BUT now we have CNC milling machines, I think you can cut the taper for the tap and the threads on a good quality lathe (might have a hard time finding an old school mechanical only lathe with a lead screw/gear combination that supports 11 1/2 TPI).

Then take it to a good CNC milling machine (with the required computer wizard) and use a ball end mill (or maybe a couple different sizes to make the relief profile you want) to cut the flutes and make them follow right along the main taper of the tap body. With a real computer wizard you can probably make a spiral tap (but that's a bit much).

Then some heat treatment and a touch up grind to sharpen up the cutting edges (might get away with a hand stoning).

After all that labor and the cost of a big chunk of good tool steel to start with you can see why those big taps start to cost a "grand" each.

We could talk about "3-D" printing that tap, but that's way....... out there.

Good luck.

Kevin.