Most of you realize that 3-D CAD can be used to develop complex geometry through surface modeling, such as injection-molded plastic & die-cast parts, but how often do we really think about the equations used that actually drive these part models? Although we may dimension points on the splines, add constraints (tangent, curvature, etc.), and / or use splines as bridges between curves, we may not always realize there is an equation that describes the shape of the curve.

This brief tutorial is intended to introduce the SolidWorks or Pro-E user to using equations.  Equation driven curves are frequently used in features for the purpose of modeling surface or solid geometry in the part model. Some examples include: springs, wave washers, and optical lenses. Although there are mathematical tools available that integrate into 3-D CAD software (ex: MathCAD with Pro-E), I would like to demonstrate curve driven equation using the existing tools within the CAD software to create 3-D curves starting with Euler’s Equation (http://www.songho.ca/math/euler/euler.html).

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On June 30th in Chicago this year, a Solidworks 2010 vs. Pro/ENGINEER Wildfire 5.0 Shootout (see here) occurred for the purpose of comparing Design Engine’s “rapid fire” surface modeling technique as applied in each CAD system. Design Engine defines “Rapid Fire” as work flow constructing sketches & surface model features for sequential rapid modification. I was invited to be on the SolidWorks team with Bart Brejcha that was in competition with the Pro/Engineer team at this event.

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For Pro-E, creating a round / fillet and selecting the conic option is probably the easiest method and the results will be close, but I would like to replicate the method in Pro-E similar to the method previously used in SolidWorks. The “delete face” tool in SolidWorks is useful for removing the face of a tangent fillet (C1) so that it can be replaced with a curvature continuous (C2) fillet. The technique of using a “Boundary Surface” was discussed in the previous posting, but how is this done in Pro-E as no exact equivalent exists for the “delete face” tool?

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When modeling a part in SolidWorks, there are specific situations where a curvature continuous (C2) fillet is desired, but a double hold-line fillet or the “atomic bomb” fillet (split line, delete face, and fill surface) is unable to be created. The delima is how to create these fillets using as few features in the model tree as possible.

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With the introduction of the iPhone, there has been much discussion among both the SolidWorks and Pro/Engineer communities about how to model this shape in 3-D CAD. Although it can be done in either CAD system, and has been previously discussed in Josh Mings’s SolidSmack blog (see here) and the Pro-E MCAD forum (see here), I will discuss what I believe to be the most robust / straight-forward approach in creating this model in SolidWorks.

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