This document discusses different methods for holding workpieces on an engine lathe. It separates workpieces into categories based on their geometry - cylindrical, non-cylindrical, solid, hollow, tapered, straight, short, long, regular shaped, and irregular shaped. For each category, it describes the appropriate holding method, such as using a tapered mandrel for a hollow tapered cylindrical workpiece, a 3-jaw chuck for a short solid cylindrical workpiece, or mounting an irregular shaped workpiece on a plate fixture attached to a faceplate with a counterweight. The goal is to select the best holding method based on the geometric features of the specific workpiece.