Bob
Proper tapping attachments as intended for use on drills and milling machine have a device to hold the square on the tap to provide drive. The hand tightened chuck is just for alignment purposes.
My Pollard tappers have chucks remarkably similar to those supplied with old style, inexpensive, hand cranked drills backed up by a floating square holder. The square holder is basically a pair of collars which draw together by means of an internal screw. The collar diameter is made large enough to grip perhaps half the square depth when its pushed hard up against the central screw.
If your chuck is hollow it ought to be possible to come up with something along similar lines. Given the limited number of sizes of square required it might be easier to just make inserts with a suitable cut out. Perhaps a pair od D shaped rods with matching slots milled into each side sliding into a cross drilling might work. Easy to amok but no obvious way of arranging for things to tighten up so tap driver engagement will be slack.
You do need to arrange some form of self alignment floating.
Clive.
PS :- Interesting links from Michael. Not sure about the first one as the usual pin chuck type wrenches supplied with sets aren't very good. The four sided square gripper is cunning and obviously effective but may take a bit of making. Given that the commercial pollard tapping chucks simply grip two sides of the square between a pair of collars it may be over sophisticated for the job.
Edited By Clive Foster on 31/08/2018 13:08:19
Edited By Clive Foster on 31/08/2018 13:08:40
Edited By Clive Foster on 31/08/2018 13:09:24