CNC Turning-Centre Finder
If there is no diameter or hole, you may have to mark out the centre on the work using a height gauge, and centre pop it with a centre punch. Then you can use a wobbler and a test indicator to set the work true. It was once possible to get a lathe centre finder consisting of a bar about 6in (150mm) long, pointed at both ends, with a universal joint about 1in (25mm) from the front end. In use, the short front end goes in the centre pop of the work in the chuck. When you rotate the chuck by hand, the pointed short end follows the eccentricity of the centre hole, which is magnified about six times at the tailstock end. You then just have to adjust the chuck until the tailstock end is running true, at which point the centre in the work will also be running dead true. I don’t know anyone who makes these and second-hand ones are extremely rare.
A simple home-made centre finder.
You can make a simple version of this that works well by using a milling machine pointed centre finder. This is a parallel bar with a separate moveable pointed end. The two components are held together with a spring inside. You need the pointed edge finder, a Morse taper parallel adaptor (the Morse taper should fit your tailstock), a spring and a short stub of bar that will fit inside the tapered holder’s bore to stop the spring going right through. Put the short stub of bar into the taper, insert the spring, follow up with the centre and put the Morse taper
