I promised to show some photos trying to illustrate the usage of my cut knurling tool. I don't have any dimensions as I just dig up some good looking pieces of steel and started to machine. I think anyone can figure their own version with possible improvements and I am happy to help if there something mystery.

These are the main parts:



Knurling tool set to toolpost, mounting shaft angled approx 5-degrees in the tool post to create relief angle for the cutting edge:
(In this picture the Knurling tool set to cut the second cut of the diamond pattern, lathe run in reverse)



Centering the knurling tool to workpiece with ruler method:



Position for cutting lathe spinning in normal direction:



Rest of the photos are here:
http://imgur.com/a/nzkag

You really need to flush the tool with coolant or use constant air blast to blow of all the chips so that they don't mangle between the tool and workpiece.