Long long ago I bought a set of collets to accurately hold smallish diameter metal for machining. The Unimat resisted my attempts at Plan A, adapting an existing collet chuck. The problem is to get the addition exactly concentric to the lathe spindle. The one I built had a runout (wobble) of .006” which is way too much for precision work.
For the Taig I decided to make on from scratch. This should result in one that is exactly concentric since it is built on the actual machine it will be used on. You can buy one for $23 but this way I learn some more skills, which will come on handy later.
Starting with a blank arbor ($3.60 at Lee Valley), I cut one end short and then turned it down to 22mm, the size of the collet nut. A 9mm hole through the center, tapped for M10x1.5 metric. Using a bolt (with head cut off) I then made a threading jig. As you turn the spindle the bolt threads into the part, dragging the tailstock and carriage along. The cutting bit cuts the thread, exactly mirroring the one on the bolt. No, I didn’t invent this method but it is gracefully simple. The lathe chuck is turned by hand giving total control over the operation. After about 10-12 passes, we have an M22x1.5 thread!
The overall dimensions of this one are: 1.5″ length overall, the M22 thread is 13mm long. The inside hole is bored out to 12.5mm before cutting the taper (happened to be the largest stub drill I have). This is I think overall shorter that the Taig and A2Z ones . You could go a bit shorter yet without the collet bottoming on the lathe spindle.
Next is the inside taper, 16 degrees total. I set the compound rest as close to 8 degree as possible and cut most of the taper. When I got close to the correct size I used a collet with an rod in it to test for wobble. The collet should just go in, no wobble. Adjusting the angle slightly and light cuts resulted in an accurate taper.
Two short cuts in the milling attachment to add wrench flats and we are done. All told maybe 2 hours work. The chuck itself has no detectable runout, a rod sticking out about an inch has .0005 runout. Should be good enough for most work