Constant Groove Width with Twist

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I'm trying to model what is best described as a ball screw with a custom profile and lead. I have attached a screenshot of what I'm trying along with the model in .f3d and .stp formats. The problem I am having is keeping the groove a constant thickness.
I've tried a couple of approaches, one of which is based on lofting two or more sketches:
- Sketch the screw end in the x-y plane.
- Copy and paste the sketch and offset it in the z-direction. Rotate the sketch 45deg around the z-axis.
- Create a loft between the two sketches.
The above results in a shape that looks correct, but if you measure the width of the groove as you move up the z-axis, you find that it increases.
The second approach is based on a lofted cut through a cylinder in an attempt to control the twist of the cut:
- Extrude a cylinder
- Extrude a coil with a triangular profile.
- Project the curve formed by the tip of the triangle into a new sketch to get a coiled line.
- Create a Plane Along Path at the top and bottom of the coiled line.
- Sketch the groove profile on each of those planes.
- Loft the two profile.
The above does not result in a correctly oriented profile. Even when I try to move the "control points" on the sketch profiles, the twist of the cut is not correct and the cut does not work.
I've also tried to model it as a surface and then thicken the surface, but I can't get that approach to work either because of the nature of the profile. Surface modeling is not my strong suit.
Any new insights are appreciated as I've been trying to model this for at least a week now.
Thanks,
Geoff