Here are some specialty mandrels.
The first one I made for Richard Grantham, it has a 1/2" end for the Jacobs chuck, a 5/8" pin lock center and a 1/4" end that goes to the tailstock that has a 60 degree center dimple. I got this mandrel back when he sold all of his equipment. Now it is one of my most prized possessions.
This mandrel was made for my deer grunt flutes, it has various steps to take into account the step drilling of the bore of the flute.
The turkey trumpet mandrel. This one got me into more hot water than they have in a Japanese bathhouse. The one on the left has a 5/8" shank and the a cut down to the #2MT end that goes into the bell of the trumpet. The small rod is the mandrel that fits into the top or tailstock end of the trumpet blank, it also has a 60 degree center dimple in one end.
I don't think I need to post the no mandrel method, it is on the archives somewhere in this part of the forum. If I do I have it saved,
Marvin