rel="nofollow" href="#ulink_05b910a1-7e17-5d09-97e7-98d784332b1b">11 and 12)
Figure 10 Two-Dimensional Coordinate System
Figure 11 Part Drawing with a 2D Coordinate System Overlay
Figure 12 Two-Dimensional Turned Part Drawing
Think of the cylindrical work piece as if it were flat or as shown in the front view of the part blueprint. Next, visualize the coordinate system superimposed over the blueprint of the workpiece, aligning the X axis with the centerline of the diameter shown. Then align the Z axis with the end of the part, which will be used as an origin or zero-point. In most cases, the finished part surface nearest the spindle face will represent this Z axis datum and the centerline will represent the X axis. Where the two axes intersect is the origin or zero point. By laying out this “grid,” we now can apply the coordinate system and define where the points are located to enable programmed creation of the geometry from the blueprint. Another point to consider: on a lathe, is that the cutting takes place on only one side of the part or the radius, because the part rotates and it is symmetrical about the centerline. In order to apply the coordinate system in this case, all we need is the basic contour features of one-half of the part (on one side of the diameter). The other half is a mirror image; when given this program coordinate information, the lathe will automatically produce the mirror image.
Three-Dimensional Coordinate System
Although the mill uses a three-dimensional coordinate system, the same concept (using the top view of the blueprint) can be used with rectangular workpieces. As with the lathe, the Z axis is related to the spindle. However, in the case of the three dimensional rectangular workpiece, the origin or zero-point must be defined differently. In the example shown in Figure13, the upper left hand corner of the workpiece is chosen as the zero-point for defining movements using the coordinate system. The thickness of the part is the third dimension or Z axis. When selecting a zero-point for the Z axis of a particular part, it is common to use the top surface.
Figure 13 Three-Dimensional Coordinate System
The Polar Coordinate System
If a circle is drawn on a piece of graph paper so that the center of the circle is at the intersection of two lines and the edges of the circle are tangent to any line on the paper this will help in visualizing the following statements. Let’s consider the circle center as the origin or zero-point of the coordinate system. This means that some of the points defined within this grid will be negative numbers. Now draw a horizontal line through the center and passing through each side of the circle. Then draw a vertical line through the center also passing through each side of the circle. Basically, we’ve made a pie with four pieces. Each of the four pieces or segments of the circle is known as a quadrant. The quadrants are numbered and progress counter-clockwise. In Quadrant No. 1, both the X and Y axis point values are positive. In Quadrant No. 2, the X axis point values are negative and the Y axis point values are positive. In Quadrant No. 3, both the X and Y axis point values are negative. Finally, in Quadrant No. 4, the X axis point values are positive while the Y axis values are negative. This quadrant system is true regardless of the axis that rotation is about. The following drawings illustrate the values (negative or positive) of the coordinates, depending on the quarter circle (quadrant) in which they appear.
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 14 Polar Coordinate System Quadrants
Sometimes the 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 14. 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 an 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 15
Figure 15 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 the numbered locations. Note the position of the coordinate system on the following machines.
Figure 16 Axis Designation for a Three Axis Mill
On vertical milling machines the spindle axis is perpendicular to the surface of the worktable.
