Rotary Milling / CNC Surface Puzzle

We have this conundrum at work that I am trying to get my head around...

Imagine a cylindrical cam with a sinusoidal (or other) surface around the top of a cylinder that a follower would, well, follow. You could draw a sine wave around the circumference of the cylinder and use this as a tool path for a simple rotary milling operation. So, the cylinder is rotated through 360 degrees on a 4th axis CNC machine and the cutting tool would plunge to depth of cut on the z-axis and then simply be moved in one other axis to create the cam surface.

Simple :)

BUT... If you create this cam surface by sweeping a perpendicular line along the sine wave path that is around a cylinder it is not the same surface that would be created in the milling process described above. Using lofts does not help either.

When we run this through Solid Works (sorry for blaspheming) and CAM Works (sorry again) it shows that if the tool is kept tangent to the outside edge of the cam surface it would clash with the surface and needs to be moved on another axis to be machined. We end up having to freeform surfaces like this when all we really want to do is a simple rotary milling operation.

I've created a Grasshopper file to try and visualise what is happening and my 1st question  (plea for help) is this:

How can I move the cylinder (representing the cutting tool) in one axis only to follow the curve along the outside edge of the cylindrical cam?

I can move it in the Y direction of the perp-frame I've created by the tool radius but this is not quite in the right direction and does not constrain the cutting tool to one axis of movement only.

I am pretty sure that if I managed to get my cutting tool moving tangent to the outer edge of the cam surface and in only one axis it would not be tangent on the inside edge (shown by the intersection of the tool cylinder and the inside curve).

So to my Second question:

How could I draw a cylindrical cam surface that could be machined using just a rotary axis and one linear axis?

I could just get the CNC to follow the sine wave curve around the cylinder but it is helpful to actually create the 3d surface so we can compare theoretical to actual on the CMM machine after machining.

I really hope someone has followed this and can help because our CAM Works Support have been a bit useless on this one and I'd love to use Rhino / GH to solve it!