Making jigs is a substantial part of learning machining methods.
I'd probably make up a round block with two slits in it so that it will
compress around the part and hold it. The hole in the front will be
somewhat less than what the part finished surface needs to be so that you
don't cut the jig to finish the part. I'd also recomment a 4 jaw chuck for
this work and that you make sure that everything is clean before doing the
final work.

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Why do penguins walk so far to get to their nesting grounds?