engineering fundamentals GDT: Two-Dimensional
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2D Datum Examples
It has been found that the most powerful (yet often misunderstood) use for GDT is in the area of sizing and positioning of holes which must mate with shafts. We will start with a two-dimensional geometry and progress to three dimensions.
Figure 2.1
Pictured in Figure 2.1 is a two-dimensional part. The roughness of its edges has been greatly exaggerated in order to clarify the discussion. It might be thought of as a part with plane dimensions large compared with its dimension into the page. For example, this might be a sheet metal part which is .125 inches thick with a length and width of about ten inches.
In this example we will determine the position of the hole and in the process, find out why mutually-perpendicular ordered datums must be defined in order to define the position. Figure 2.1 shows the part with possible ways to define the location of the hole. As has been made apparent, the linear dimensions originate from the sides of the part, but it is not clear from where on the sides the dimensions should begin. (We consider where the center of the hole is later.) The method of fixturing the part for measurement of its features is critical since many different groups of people will be measuring the part: design, fabrication, fabrication inspection, purchasing inspection, etc. Without a common agreement as to how the part will be measured, measurements become meaningless.

Figure 2.2
One way to define where the dimensions should originate is shown in Figure 2.2. A steel straight edge can be used to define a line for the two edges. One problem with this method is that the two defined lines are not necessarily perpendicular, as shown in the figure. Without perpendicularity, the part dimensions do not agree with print dimensions, since print dimensions are assumed to be perpendicular.
We can force the two defined lines to be perpendicular to each other by using a right-angle straight edge, as shown in Figure 2.3. Now when the part is pushed against these two edges so that it cannot move (rock), the two edges can be used as mutually perpendicular datums. However, as Figure 2.4 shows, the part position with respect to these two datums is ambiguous. The final orientation of the part depends upon which side contacts first.

Figures 2.3 and 2.4
Figure 2.5 illustrates an ordered datum scheme that prevents confusion. The first side that is pressed against one of the edges will contact at the two highest points of the part edge. The part now only has one degree of freedom left: it can slide back and forth against the straight edge.

Figure 2.5
Once we butt the perpendicular side of the part against the corresponding straight edge, we will have completely constrained the position and orientation of the part in 2D space, as shown in Figure 2.5. This second side contacts its straight edge at one high point since it is not able to rotate to contact more than one high point. Figure 2.5 labels the datums as A and B, in the order of fixturing hierarchy. These datums are referred to as "functional datums" since they contact the part and are physical hardware used, for example, on a factory floor.

With this ordering of datums, we have clearly positioned the part in 2D space. As we have seen, this clear fixturing of the part is critical since it defines from where features are to be dimensioned on the part. Please continue by selecting "2D Hole/Shaft" from the menu on the left.

SIDE NOTE: Since this is a two-dimensional example, the part has three degrees of freedom: two translational and one rotational. The reason for the first two high points of contact has to do with the rotational degree of freedom of the part: one point allows the part to rotate, two does not. The single point of contact for -B- is due to the fact that once the part can only slide along -A- without rotating, a single high point will contact first on -B-. The part cannot rock, so a second contact point does not occur.
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