1 Coordinate system 1. The coordinate system of the machine tool, including all the actual machine axes. 2. The reference point, tool and pallet exchange point are determined by the machine coordinate system. The machine coordinate system includes the coordinate system, the origin of coordinates, and the direction of movement. 3. ISO defines the coordinate system of CNC machine tools as follows: Cartesian Cartesian coordinate system, right-hand rule. Figure 1 Right-handed Cartesian Cartesian coordinate system 2 Coordinate axes and their naming principles 1. Regardless of the specific structure of the machine tool, the workpiece is stationary, the tool is moving, or the workpiece is moving, and the tool is stationary. The coordinate motion of the CNC machine tool refers to the movement of the tool relative to the workpiece. 2. It is specified that the workpiece is used as a reference, and the principle of the motion of the tool is assumed to be fixed. 3. It is programmed with the movement path of the tool. 4. The movement direction of the moving parts of the machine tool: The position of the machine coordinate system is related to the machine type. JB3051-82 stipulates that increasing the distance between the workpiece and the tool is the positive direction of the machine tool movement. a) CNC Lathe b) Vertical CNC Boring and Milling Machine c) Horizontal CNC Boring and Milling Machine Figure 2 The axes of the CNC machine tool and its direction of motion (1) Definition of Z-axis coordinate motion (2) Definition of X axis coordinate motion 1) Workpiece rotating machine (car, grinding) The X-axis is in the radial direction of the workpiece and is parallel to the horizontal slide; the positive X-axis direction is the direction in which the tool leaves the center of rotation of the workpiece. 2) For tool rotary machine (milling, drilling) Vertical: X axis: horizontal, parallel to the axis of the workpiece clamping surface; positive direction: viewed from the main axis column, the right column is positive. Horizontal: X axis: horizontal, parallel to the workpiece clamping plane axis; positive direction: viewed from the main axis workpiece, the right side of the workpiece is positive. (3) Definition of Y axis coordinate motion The positive direction of the Y-axis is determined according to the right-hand rule based on the X and Z axes. (4) Definition of coordinate motion of rotation axis The positive directions of the rotation axes A, B, and C are determined in the positive X-, Y-, and Z-axis directions, respectively, in the direction in which the right-hand thread advances. 5. The workpiece coordinate system can describe the workpiece geometry in the workpiece coordinate system. That is, the data in the NC program should refer to the workpiece coordinate system. Fig. 3 Workpiece coordinate system Fig. 4 Lathe coordinate system Figure 5 Vertical Milling Coordinate System Figure 6 Horizontal Milling Machine Coordinate System 3 coordinate origin Different positions of the origin and reference point can be determined on the NC machine. The role of these reference points is: (1) The machine origin (M) (Machine Origin or home position) is the starting point for establishing the machine tool motion coordinates. (2) The machine tool reference point (R) (reference point) is set with a physical position of the travel switch. The relative position to the machine's origin is fixed. The machine tool is determined by the machine manufacturer's precision measurement before leaving the factory. Generally speaking, the machining center The reference point is the automatic tool change position of the machine tool. Fig. 7 Machine coordinate system (3) Program Origin (W) Program Origin: Also called Part Origin It is the geometric reference point that the programmer defined on the workpiece during the NC programming process. (4) Mounting origin: Fixture Origin (also known as chuck zero), which can coincide with the origin of the workpiece. Figure 8 CNC Lathe Figure 9 CNC Boring and Milling Machine 4 Absolute coordinates and relative coordinates 1. Absolute coordinate representation: The coordinate value of the tool movement position is expressed as the distance to the origin of the coordinate. The representation of this coordinate is called absolute coordinate representation. As shown in Figure 10. Most CNC systems use absolute coordinates to program G90 instructions. Figure 10 Absolute coordinate representation Figure 11 Relative coordinate representation 2. Relative coordinate representation: The coordinate value of the tool movement position is expressed as the increment relative to the coordinates of the previous position, that is, the difference between the absolute coordinate value of the target point and the absolute coordinate value of the current point. The representation of this coordinate is called The relative coordinate representation. As shown in Figure 11. Most CNC systems use relative coordinate programming with the G91 command. Some CNC systems use X, Y, Z for absolute coordinate codes, and U, V, W for relative coordinate codes. A combination of these two coordinate representations can be programmed in one machining program. 
Z axis: The coordinate axis parallel to the machine spindle.
Positive direction: The direction from the table to the tool holding, that is, the direction of movement of the tool away from the table. 
1. For machine positioning;
2. Program the workpiece size. They are: 
Workpiece coordinate system: Cartesian coordinate system established with the workpiece origin as the coordinate origin. 
