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# Torsion vs Curvature vs Tangent vs Contact Continuity in SOLIDWORKS

With the release of SOLIDWORKS 2020, a new continuity type became available for spline geometry in sketches, torsion continuity. Torsion (or G3 or C3) continuity provides a higher level of curvature control when transitioning between two entities. Most examples and explanations I’ve seen of torsion continuity when compared to curvature continuity are confusing at best. To start, most examples of continuity start with an image similar to the image below.

Certainly, understanding C0 continuity is fairly straight forward. Any edge where there is no continuity is C0. For the remaining blends, continuity becomes a bit more difficult to understand. Even beginning with C1, it can be helpful to use SOLIDWORKS evaluation tools to better understand the part’s curvature. By using View > Display > Curvature, C1 curvature is fairly easy to detect.

As seen in the image above, there is a distinct hard line where the curvature color changes (in this case from blue to green). For C2 curvature, there is a gradient of colors indicating a gradual blend to the radius. And for C3 curvature, an even more gradual blend. Another popular technique is to use View > Display > Zebra Stripes which can be turned on and the part rotated to see how light reflects off the part.

Looking at a view tangent to the radius, it can be seen that for C1 curvature the reflections all remain connected, but at the radius begin immediately changing direction (forming the reverse c shape seen above). For C2 curvature the zebra stripes flow and have no break. And for C3 curvature they have an even smoother transition.

The last evaluation technique I use is curvature combs. These can be turned on at a surface level (View > Display > Curvature Combs) or as I prefer at a sketch level (right click on a sketch entity and select ‘Show Curvature Combs’).

In this example, C0 and C1 curvature can be easily understood. With C0 curvature the curvature combs have no relationship at the edge. For C1 curvature, the curvature combs are in the same direction but are immediately able to change magnitude at the transition.  For C2 curvature, the curvature combs are in the same direction and of the same magnitude at the start of the transition, but then are able to transition to the radius. And for the C3 curvature the curvature combs are of the same magnitude and same direction at the start of the blend, gradually transition away from that face, then gradually transition to the radius.

Now hopefully, if I’ve done my job you clearly understand C0 and C1 curvature, but you may be thinking C2 and C3 still seem very similar to one another. Perfect! The reason they seem so similar in the examples above is we’re comparing Apples and Oranges! Yes, they’re both fruit, but only one keeps scurvy at bay. What do I mean? Well in the examples above we are trying to achieve the blend over the same setback distances throughout. Which means we’re trying to do more and more “transitioning” and include the radius over the same space leading to tighter radius throwing the whole example off.

Let’s consider instead trying to achieve roughly the same radius using the various continuities.

Here all the radii are very close, but I’m allowing the transition period (or blend) to happen over progressively larger areas.

With the use of Curvature evaluation, we can see the blending for C3 curvature occurs over a greater span compared to C2 curvature blend.

And when looking at Zebra Stripes we can see that the C3 curvature is a smoother blend with less abrupt change in the flow of the lines.

But perhaps the clearest way to understand the difference between C2 and C3 curvature is to look at the curvature combs.

C2 Curvature is in the same direction and of the same magnitude, but transitions to the radius without regard to the original face, while C3 curvature blends away from the original face before it blends into the curve.

Consider the alternative image above. For C1, C2, and C3 the ‘radius’ occurs in the green zone. With C1 curvature the radius is all that matters, the curvature immediately changes (as we’re accustom to seeing). For C2 curvature, the purple zone is where the face blends into the radius, but the only constraint for the start of the blend is that the curvature must be equal to the original face (same direction and magnitude curvature combs). The key difference with C3 curvature is that not only is the purple region the blend into the radius, but the blue region is the blend away from the original face into the purple region. So for C3 Curvature there’s a blend away from the original face, a blend into the radius, but also blending between the blends.

Hopefully this clarifies the difference between C2 and C3 curvature for you. And if you’re looking to use Torsional curvature, be sure to give a greater distance for that transition to occur compared to a traditional radius or C3 will probably look a lot like C2.

Brandon Nelms