Although the rectangular coordinate system can be used to define points on the circle, a method using angular values may also be specified. We still use the same origin or zero-point for the X- and Y-axes. However, the two values that are being considered are an angular value for the position of a point on the circle and the length of the radius joining that point with the center of the circle. To understand the polar coordinate system, imagine that the radius is a line circling around the center origin or zero-point. Thinking in terms of hand movements on a clock, the three-o’clock position has an angular value of 0° counted as the “starting point” for the radius line. The twelve-o’clock position is referred to as the 90° position, nine-o’clock is 180°, and the six-o’clock position is 270°. When the radius line lies on the X-axis in the three-o’clock position, we have at least two possible angular measurements. If the radius line has not moved from its starting point, the angular measurement is known as 0°. On the other hand, if the radius line has circled once around the zero point, the angular measurement is known as 360°. Therefore, the movement of the radius determines the angular measurement. If the direction in which the radius rotates is counter-clockwise, angular values will be positive. A negative angular value (such as –90°) indicates that the radius has rotated in a clockwise direction. Note: A 90° angle (clockwise rotation) places the radius at the same position on the grid as a +270° (counter-clockwise) rotation.
Figure 1-16 Polar Coordinate System Quadrants
Sometimes the engineering drawing or blueprint will not specify a rectangular coordinate, but will give a polar system in the form of an angle for the location of a feature. With some basic trigonometric calculations, this information can be converted to the rectangular coordinate system.
The same polar coordinates system applies regardless of the axis of rotation, as is shown once again in Figure 1-16. When rotation is around the X-axis, the rotational axis is designated as A; the Y-axis, the rotational axis is designated as B; and the Z-axis, the rotational axis is designated as C. These are considered additional axes and are known as the fourth axis.
All operations of CNC machines are based on three axes: X, Y, and Z.
1. (X0, Y0, Z0)
2. (X0, Y0, Z+)
3. (X0, Y–, Z+)
4. (X0, Y–, Z0)
5. (X–, Y–, Z0)
6. (X–, Y0, Z0)
7. (X–, Y0, Z+)
8. (X–, Y–, Z+)
Figure 1-17 Three-Axis Part Example
Figure 1-17 illustrates a box-like object in which one vertex (point 1) is located at the origin of the coordinate system. At the side of the drawing, the coordinate signs are given for each of the numbered locations. Note the position of the coordinate system on the following machines.
On vertical milling machines, the spindle axis is perpendicular to the surface of the worktable (Figure 1-18).
Figure 1-18 Axis Designation for a Three-Axis Mill
On horizontal milling machines, the spindle axis is parallel to the surface of the worktable (1-19).
Figure 1-19 Axis Designation for a Three-Axis Horizontal Mill
On turning centers, the spindle axis is also the workpiece axis (1-20).
Figure 1-20 Axis Designation for a Two-Axis Turning Center
When using CNC machines, any tool location is controlled within the coordinate system. The accuracy of this positional information is established by specific zero points (reference points). The first is Machine Zero, a fixed point established by the manufacturer that is the basis for all coordinate system measurements. On a typical lathe, this is usually the spindle centerline in the X-axis and the face of the spindle nose for the Z-axis. For a milling machine, this position is often at the furthest end of travel in all three axes in the positive direction.
Occasionally, this X-axis position is at the center of the table travel.
This Machine Zero Point establishes the coordinate system for operation of the machine and is commonly called Machine Home (Home position). Upon startup of the machine, all axes need to be moved to this position to establish the coordinate system origin (commonly called homing the machine or Zero Return). The Machine Zero Point identifies to the machine controller where the origin for each axis is located. Some machines today are equipped with absolute encoders so that homing is no longer necessary at machine startup.
The operator’s manual supplied with the machine should be consulted to identify where this location is and how to properly home the machine.
The second zero point can be located anywhere within the machine work envelope and is called Workpiece Zero; it is used as the basis for programmed coordinate values used to produce the workpiece. It is established within the part program by a special code and the coordinates are taken from the distance from the Machine Zero point. The code number in the program identifies the location of offset values to the machine control where the exact coordinate distance of the X, Y, and Z axes of Workpiece Zero is in relationship to the Machine Zero. All dimensional data on the part will be established by accurately setting the Workpiece Zero. A way of looking at the Workpiece Zero is like another coordinate system within the machine coordinate system, established by the Home position.
Tool offsets are also considered to be Zero Points as well and are compensated for with tool length and diameter offsets. The tool-setting point for a lathe has two dimensions: the distance on diameter from the tool tip to the centerline of the tool turret, and the distance from the tool turret face to the tool tip. The tool-setting point for the mill is the distance from the spindle face to the tool tip, and the distance from the tool tip to the spindle centerline.
Engineering Drawing or Blueprint Relationship to CNC
The standard called ASME Y14.5-2009 establishes a method for communicating part dimensional values, in a uniform way, on the engineering drawing or blueprint. The drawing information will be translated