The outer doorknob on the kitchen pantry became very loose and sloppy, with the screw holding the inner knob on the shaft remaining snug. Obviously, something else was wrong inside the door.
A spring clip should retain the outer knob in the escutcheon:

The flange holding the clip has worn away, letting the clip fall loose. A side view shows the problem:

Yes, the knob’s chrome plating is in sorry shape after six decades of wear. I’d rather keep using a solid knob, instead of force-fitting some contemporary half-assed / cost-reduced junk into the door.
Reference: beausage. I say it “beau-sage”, the beauty that comes from usage.
The shaft consists of three triangular rods, with the setscrew on the inner knob pressing against the smaller rod to lock all three of them in place and eliminate all rattle & play:

A tapered pin (!) locks the three shaft rods into the outer knob:

Some doodling, most of which turned out to be irrelevant, captured the essential dimensions and suggested how to replace the flange:

The stock is 11/16 inch O-1 oil-hardening rod, forever to remain unhardened:

I drilled a few holes to get up to 1/2 inch, the largest drill bit I have and just barely clearing the the boring bar.
With the hole bored out to fit the end of the knob, cut it off:

Trial-fit the ring on the knob with the spring clip:

Reinstall the shaft, tap in the retaining pin, then epoxy the ring in place with the knob supported from below to eliminate having to fiddle with the spring clip:

Add a few dots of oil here & there, reinstall the parts in reverse order, and the knob works perfectly again. Still looks heavily used, of course, but that’s OK.
They definitely don’t make ’em like that any more …