I'm trying to make a set of parts that have a curved profile in them that is described by a spherical cutter following a curtate cycloid path. No matter what I try, the cut either fails to complete, or results in a surface that doesn't match the true profile. For lack of a better adjective, all of the bodies that I can generate are lumpy, with weird knots and knuckles that deviate from the desired result.

My problem is simplified as follows:

I have this block, and I'd like to remove material by running a spherical tool along this equation-driven curve.

The curve equations are **x=(a*t)-(b*sin(t)),** **y=a-(b*cos(t)),** where a=1.875mm, b=1.375mm, and t goes from 0 to roughly 60*pi (30 cycles)

When I try to do a solid profile cut, it fails to build. When I try to do a swept cut of a full circle or partial circle with geometry that would double back on itself, it fails.

(In the image below, to build "successfully", the circled dimension must be smaller than the tightest radius of the circled segment of the cycloid)

I've figured out that I can get both cuts and bosses to build something when I remove the outside half of the tool, which is acceptable for my current needs since it never intersects. However, the resulting shape is still not right. Regardless of my sweep settings, the body that is produced changes shape in a number of unexpected ways, leaving weird squiggles, knuckles, and kinks in the surface. The zebra stripes and curvature analysis tool reveal that even the segments that aren't visibly flawed have variability over what should be a constant curvature profile, and that each individual lobe has its own unique set of problems even though they are all generated from the same operation on the same equation-driven path!

As a bonus, the final implementation will be circular, and that path produces even more issues where the profile is so deformed it doesn't always intersect with the target body:

I need to roll a ball through these pathways with tight tolerances, and right now I have no hope of producing something usable. I suspect I can bypass this problem when I reach the level of producing parts in metal and I can just give the toolpath to a machinist, but I'll never get there without a working model for analysis and 3D printed prototypes. Right now I'm working on the math to produce some accurate guide curves, but I'm not sure what else to even try. Help!