Recently I was doing some research online for information regarding the history of the Singer model 237 sewing machine. A wonderful place for sewing machine info is ISMACS - The International Sewing Machine Collector's Society. While looking through their pages, I found a link to a manual that I had been unable to find before - to a Military manual on repairing and maintaining sewing machines.
Military Manual Chapter 4 - pages 51 and 57 (top right navigation) have info on Singer 31-15