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I kind of sense the reason you would like to equip your CNC router with a '3 jaw chuck' is to make it easy to drill precisely spaced holes, of varying sizes, using a CNC 'program' that automates the process.
Though many here might consider this technique to be reckless, if I needed to drill a lot of holes on a specific pattern and had a CNC platform, I would be doing what you are asking about.
That being said, I would be extra careful in a couple areas. Cutter care and inspection would be at their highest. Extra thick safety glasses on this one...I suspect that doing this a lot would result in some broken bits. Odds are the CNC isn't smart enough to know when a cutter fails in that way, so being prepared to shut it down at any point during the sequence is advised.
Awareness of grain patterns/knots in the workpiece that could cause a cutter to bend during the 'plunge cut' (if the material is wood). I would use as short of drills as available to minimize the 'bending' caused when it's easier for a cutting edge to 'walk away' during a plunge, than it is to cut.
If you have a lot of this kind of drilling that needs to be done, it might be worthwhile to find away to slow the rpm down.
The approach Bob mentioned is the simplest that I am aware of. A lot of chucks on hand drills just have a 'threaded' hole that they attach to the rest of the drill with. I didn't know that MLCS sold adapters like that, so thanks to Bob for speaking up!
I kind of want to rig up a 3 jaw friction tightened chuck on one of my Yankee push drills!
wbh1963 is flowing with the grain in Arlington, Washington, USA
A day without curls is like a day without sunshine!