A friend gave me this pen in kit form. She included the bushings for holding the barrel on the mandrel, but not a mandrel. I do not have a mandrel. I decided to make my own precision mandrel and do a good job of turning the acrylic barrel blank. That means it had to be correctly centered while turning and with no vibration.
Step 1: The parts
This pen is from Woodcraft. The barrel features a cylindrical circuit board in clear acrylic. In addition to the various parts, you see a 1/4 inch steel rod from my workshop. The barrel blank shows the two bushings for mounting the barrel blank on a mandrel. I inserted the bushings into the ends of the barrel blank so I could determine how long to cut the 1/4 inch steel rod I will use to make a mandrel. The holes in the bushings are just a little too small for the 1/4 inch rod. I suspect the holes are 6 mm, which would be just a tiny bit smaller than 1/4 inch. My finger marks the length I want to cut for the mandrel.