Flexible?  Yes!
A "Wiggly" Lathe Center
© Frank Ford 2006; Photos by FF

Here's a little item I find quite handy for picking up a center punch mark when I want to center an item in the four jaw chuck.   It's a long, flexible tailstock center.  I set up my taper attachment, made a #2 Morse taper holder and drilled it to receive a piece of 5/16" cold rolled rod. Then I threaded the other end and made a regular 60 degree center from a piece of 1/2" square W-1 steel, hardened* it after machining, and cleaned it up with some 600 grit paper and a sanding block:


Now, with a work piece in my four jaw chuck, I can stick the center right into a small punched center mark, and as I rotate the chuck, the center will follow it wherever it goes because that shaft is so long and flexible:


The non-rotating "center end" has flat sides so the indicator doesn't even have to be particularly close to the center height of the lathe to get good consistent readings:

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* For this and similar noncritical jobs, I have a simple mild hardening routine that I use with water hardening steel.  I just heat the piece with a propane torch until it just gets nice and red, and dunk it in some used motor oil. The result is a "sort of hard" condition that seems fine for  this application. Quick and easy with no tempering needed, the result is not "file hard" and not particularly brittle.