You would want to make the scroll plate, with bevel ring gear on the back of it out of steel. Ideally a tough steel such as 4140, which would make it tough to machine also. Cast iron would be a bit brittle on those small bevel teeth.
Or you could look into the alternative type of three-jaw chuck that does not use the three bevel pinions and the main bevel ring gear. The whole body turns instead, using a lever in a hole in the body and one in the back plate. I forget what this type of chuck is called. But a bit of googling around might find one. They are usually small chucks, 50 or 65mm diameter but could be made bigger.
ISTR the Model Engineers Workshop 25 year special edition had drawings in it for making your own four-jaw chuck, which is a lot more do-able than a three jaw as you only have to screwcut a square thread for each barrel, instead of a bevel gear, then screw cut the chuck body to match. If it were me, that is the way I would go.
None of them would rate as a beginner's project or even close to it, IMHO.
Edited By Hopper on 25/06/2018 07:20:13