As you can see,I used a small drill chuck to hold the taps.I don't use it for anything bigger than about 3/16-5mm,as it gets to hard to turn.
I used an old drill base and column shaft,the rest is out of the recycling box.
As you say they are dead basic but it does the trick and it also gave me my first shop made tool and was the first time I worked steel in my lathe. I plan on making more for my other sized taps.
Great work Jeff, I'm still on baby steps. I looked at plans to make one like yours but decided my skill level was more suited to the one above.
I'm not on very good terms with steel, so I figured it best not to aggravate myself this early in the game.
For the larger stuff I can get the tap going in the lathe, then take it out and do it by hand in the usual way. This works an absolute treat for set screws, though, so I'm more than glad that you suggested it to me.