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conical

Helix inside non-conical surface - sweeping help needed for inverted auger.
I need to build an auger on the ID of a conical surface that extends beyond the ends of a cone. I have succeeded with the sweep on a cone, but the rest is beyond me at this point. I profiled a cone with extensions at either end, but now it is no longer a cone. What can I do to achieve this?

Helix inside non-conical surface - sweeping help needed for inverted auger.
I need to build an auger on the ID of a conical surface that extends beyond the ends of a cone. I have succeeded with the sweep on a cone, but the rest is beyond me at this point. I profiled a cone with extensions at either end, but now it is no longer a cone. What can I do to achieve this?