[How do I?] Radius gauge for 'large' values of radius

You can machine a disc with a 4 3/4" hole in it, then split the disc. To save you time just assume the contour on the OD is spherical. That type of bearing is used in pillow blocks in a spherical cavity. The shape needs to be spherical in order for pillow blocks to self align.
 
With the associated tolerances in mind... perhaps assessing spherosity (not finding another radius) could be achieved by laying the part flat and clamping 3 squares, stacks of 123 blocks, etc. around the OD of the part... essentially creating three vertical lines that correspond to points on the OD. Then raise the part off the table and see if it can be spun without binding and without creating gaps.

Likely very loose tolerances given the presumably small degree of rotation that can be assessed (thin part in question, etc.) and other factors.
 
I would use the rotary table, DTI and DRO. But it depends on how much of the race is left.
 
You can machine a disc with a 4 3/4" hole in it, then split the disc.

Mm, I don't have anything to hand I can use for that. But the suggestion of a compass was brilliant. I just need to dig out my draughting tools and some stuff pasteboard for a first approximation.

To save you time just assume the contour on the OD is spherical. That type of bearing is used in pillow blocks in a spherical cavity. The shape needs to be spherical in order for pillow blocks to self align.
That... Is very interesting to know! Thanks for that insight.

The race has two holes for lubricant injection, but they're on a diameter chord which is useful for balance.
 
I would use the rotary table, DTI and DRO. But it depends on how much of the race is left.
It has some scratches, but is otherwise in pretty much pristine condition. It was a pre-assembly part, rather than salvaged from an assembled bearing.
 
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You could just look up the bearing number in the Timken-Fafnir or similar online catalogs and find the dimension you seek.
Here is a sample page: https://cad.timken.com/viewitems/ni...afnir--eccentric-locking-collar-ball-bearings.
Note that there are only 2 options for the OD: cylindrical or spherical.
Considering how old this pre-assembly part is, I'm not sure it would still be listed.

Considering it was still in production during a union strike, it was probably part of an important contract at least, if not just a standard part.
 
The race weighs roughly 565 grams, and I've always had the intention of making it the rotor for a gyroscope. It turns out that the diameter is just about perfect to use slices from some fire extinguisher canisters to make the gimbal rings.. but that's off topic for this thread.
 
Here's a photo of the race. The grey stuff is some corrosion preventive spray-on I got from Brookstone years ago.

From some of the replies, I'm pretty sure my description was inadequate. If this photo comes through, you can see the curvature of the outer surface, which is what I'm trying to measure.
PXL_20220301_173738083.jpg
 
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