Figure 9 Right Hand Rule
The Right-Hand Rule System
In discussing the X, Y, and Z axes, the right hand rule establishes the orientation and the description of tool motions along a positive or negative direction for each axis. This rule is recognized worldwide and is the standard for which axis identification was established.
Use Figure 9 above to help you visualize this concept. For the vertical representation, the palm of your right hand is laid out flat in front, face up the thumb will point in the positive X direction. The forefinger will be pointing the positive Y direction. Now fold over the little finger and the ring finger and allow the middle finger to point up. This forms the third axis, Z, and points in the Z positive direction. The point where all three of these axes intersect is called the origin or zero point. When looking at any vertical milling machine, you can apply this rule. For the Horizontal mill the same steps described above could be applied if you were lying on your back.
Visualize a grid on a sheet of paper (graph paper) with each segment of the grid having a specific value. Now place two solid lines through the exact center of the grid and perpendicular to each other. By doing this, you have constructed a simple, two-dimensional coordinate system. Carry the thought a little further and add a third imaginary line. This line passes through the same center point as the first two lines but as vertical; that is, it rises above and below the sheet on which the grid is placed. This additional line would represent the third axis in the three-dimensional coordinate system which is called the Z axis.
Two-Dimensional Coordinate System
A two-dimensional coordinate system, such as the one used on a lathe, uses the X and Z axes for measurement. The X runs perpendicular to the workpiece and the Z axis is parallel with the spindle centerline. When working on the lathe, we are working with a workpiece that has only two dimensions, the diameter and the length. On blueprints, the front view generally shows the features that define the finished shape of the part for turning. In order to see how to apply this type of coordinate system, study the following diagrams. (See Figures 10, 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