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Variational Revolution

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I have a cicular part that I need to subtract material from in a variational groove-like design. The trick is, the groove width varies. Its not quite 360 degrees long. I have a start sketch and an end sketch, I want to revolve the start sketch which is a small square and have it smoothly widen around an axis into the end sketch which is a large square on the same rotational plane. I do have x and y coords for this, but it may not come out smooth.

 

What feature could I use for this?


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