Machine tools generate geometrical surfaces (flat, cylindrical, and contoured) through the combined motion of two abstract vectors: the generatrix, a line or curve defined by the form of the cutting tool or the locus of a moving point, and the directrix, the path along which the generatrix travels; their combination, produced by tool-work motions such as cutting motion and feed motion, determines the resulting surface geometry. This is a core concept in manufacturing processes / production engineering, specifically the classification and kinematic analysis of machine tools, relating tool and workpiece motion (cutting motion, feed motion, and auxiliary motions such as indexing or relieving motion) to the surface-generation methods of tracing, form-copying (form milling), tangent tracing, and generation.
Machine tools generate geometrical surfaces (flat, cylindrical, and contoured) through the combined motion of two abstract vectors: the generatrix, a line or curve defined by the form of the cutting …