# PARAMETRIC MODELING. David Rosen. December By carefully laying-out datums and geometry, then constraining them with dimensions and constraints,

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3 3 of 5 11/18/2004 6:24 PM We have done research here at Georgia Tech on the fastener instantiation and substitution problems that have some promise in supporting aspects of configuration design, but a general solution will require very different CAD technologies. One technology that would be useful is a computational model of behavior, such that behaviors distributed throughout geometric objects can be modeled. Finite element models are one example of such a distributed behavior model (behavior in terms of displacement throughout a spatial domain). However, only a handful of behaviors can be readily modeled using FEM. Example The example that will be used to illustrate parametric modeling was constructed in ProEngineer. It is a blank injection mold insert. The way that parametric modeling CAD systems typically work is the user starts by sketching the part's cross-section, adding constraints, then specifying dimension values. I followed the ProEngineer guidelines of first setting up 3 datum planes and a datum coordinate system that coincides with the intersection of the 3 planes. Datum planes DTM2 and DTM3 can be seen in Figures 1 and 2, along with coordinate system CS0. All of these datums are parents of the part to be created. DTM3 was chosen as the sketch plane (XY). The mold insert cross-section was created with positive Y coordinates. Insert geometry consisted of two polylines and two 90 degree arcs. The arcs are tangent to the coincident line segments (constraints that ProE assumes correctly). After adding these geometric entities, I aligned the top line segment with DTM2. ProE assumes that line segments are horizontal or vertical, if nearly so, and are parallel or perpendicular to one another. In this case, these assumptions are appropriate. It is important to note that these assumptions are implemented internally by ProE as constraints. All parametric modelers are really uptight about properly constraining the geometric entities. This is where the choice of parameterization schemes comes into play. I chose to dimension everything from the datum planes. Figure 1 shows the dimensions with default ProE values. Note that the height of the insert is controlled by a dimension from the DTM2 datum. The width is controlled by the dimension with default value of Note that the horizontal location of the insert is controlled by a dimension from DTM1, the vertical datum plane (dimension value of 120.4). Also, the circular arcs have their radii dimensioned. Figure 2 shows the mold insert with correct dimensional values specified. Note the change in shape. Since ProE correctly changed the shape, it means that the cross-section is completely parameterized. Each of these dimensions can be changed, which of course is the whole idea behind parametric modeling. Figure 1 Mold Insert Cross-Section Geometry and Dimensions.

4 4 of 5 11/18/2004 6:24 PM Figure 2 Mold Insert Cross-Section with Correct Dimensional Values. After completing the cross-section, a solid model can be created by extruding the cross-section. I set things up to extrude this cross-section along the positive Z axis. After creating the solid model, it is displayed by ProE, along with the dimensions, as shown in Figure 3. Figure 3 Solid Model of Mold Insert.

5 5 of 5 11/18/2004 6:24 PM Figure 4 shows the result of changing the insert width dimension from 4.5 inches to 5.5 inches. Note that the insert geometry is no longer centered in the CS0 coordinate system. This is because the dimension to the right arc was not changed (1.88). With a different parameterization scheme, the insert could have remained centered. Recall that I dimensioned everything from the datums, rather than dimensioning entities relative to one another, which would be necessary in order for automatic centering to work. Which is correct? Both are - it really depends upon what design freedom the designer intends to embody in the design. Figure 4 Modified Mold Insert.

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