First of all I'm incredibly grateful to Mikey for starting this thread. Very glad I bought Mr. Smith's video (and I'm sad that he's passed). I can't wait to try my hand at hand turning. I'm starting to lust after one of those little Sherline lathes....
Re: the burnishing tool. His video makes it pretty clear. By rubbing the smooth burnishing tool down a piece of sandpaper, he creates very slight ridges in the burnisher. Sort of turning the burnisher into a micro file.
I'm definitely not a clock maker, but I do know they have their own terminology. Per Stan Bray's book on clock making: "A shaft or spindle is known as an arbor, and the bearing surface at the end is not a shaft or axle but a pivot."
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Rex