Cutting-tool geometry (rake angle, clearance angle, and inclination angle) can be expressed in several reference-plane systems — the American Standard Association (ASA) system, the Orthogonal Rake System (ORS), and the Normal Rake System — each offering different advantages for manufacturing, inspection, research, or resharpening, and the angles defined in one system can be converted analytically or graphically into another. The graphical conversion method rests on the "master line" principle: the line of intersection between an extended tool surface (rake or flank/clearance surface) and the tool's bottom plane, whose intercepts along the machine longitudinal, machine transverse, orthogonal, and cutting-plane axes are trigonometric functions (tangent or cotangent) of the corresponding angles in each system, from which conversion formulas between systems are derived geometrically. This belongs to the mechanics of machining within manufacturing/production engineering, specifically the sub-topic of cutting-tool geometry and tool angle designation systems.
Cutting-tool geometry (rake angle, clearance angle, and inclination angle) can be expressed in several reference-plane systems — the American Standard Association (ASA) system, the Orthogonal Rake Sy…