Accuratly bore the ID of a 6 inch OD aluminum gear from 3 1/2 to 4 5/8?

[Forty Niner]

The project is to replace a telescope drive gear assembly. The current main gear has a 4 5/8 bore to attach to the scope. The replacement gear currently has a 3 1/2 bore. I have a 9 inch South Bend lathe.
My first thought is to bore a 'jig' the OD of the new gear to hold the new gear without munging up the teeth. If the jig is not removed from the lathe between boring the hole to hold the new gear and boring out the new gear center there there should be no alignmnet issues with the new center hole. The only accurcy issue will be the actual boring of the center hole.
Is this correcth thinking?

If the "new" gear with the 3.5" bore is mounted on a face plate with spacers between the gear and the face plate, you can true up/ indicate on the 3.5" bore, and just go ahead and bore it out to the 4 5/8" you need.
That is IF you are confident that the new gear teeth are concentric with the 3.5" bore. IF it is a new gear you will be OK, I think.

 

[dansawyer]

Quick update: I finished the project. I had recently purchased a really nice 12 inch Bridgeport rotary table for my mill. I centered the gear by rotating the table 180 degrees and halfing the difference. It was a bit tricky consistently measuring to the teeth. The teeth have a distinctive cut and there is a small flat spot on each outer edge. I took several measurements to assure consistent readings. I then used an edge finder to center the mill bed on the rotary table.
Because of the excess material to be removed I use a small mill bit to cut a swath creating a ring. I then carefully measured and remeasured the new center to tooth distance with a tenth reading mic. These were plus or minus 1/2 a thousands. I was convinced my method was working so I continuded to remove the remaining 250 thou.
In the end I removed about 2 thou too much.

 

[epanzella]

I have a drawer full of various sized dowel pins. When machining the bore of a gear or sprocket I grab 3 or 4 of the same size and put them between the chuck jaws and the tooth valleys. Whether I use a 3 or 4 jaw chuck is dependent on the tooth count of the gear/sprocket.

 

[Illinoyance]

If you have a mill why not set the gear on 1 2 3 blocks and clamp it to the table? Then all you need to do is dial in the bore and have at it with a boring head.