SolidWorks is not primarily an academic geometric solver. Perhaps you would be better served by another type of software.
I don't see any way to control curves or sketches by constantly changing vector directions in SW. But if you are looking to create a helix-type curve that follows the diameter of a given surface, with a constant pitch, you can revolve the surface as you have done, then sweep a surface using the twist options, and get the intersection curve from the two surfaces, as shown below.
Another thing that might get you where you're going is using the Variable Pitch option in the Helix PropertyManager. You can define a constant pitch with a variable diameter, as shown below.
By the way. You might get more responses if you stop using the .rar. compression. Just upload the bare file, and the forum puts it in a zip. Your .rar. files are also zipped when they appear on the forum, and I would guess that there are several people here who don't have a .rar. reader.
test3matt.SLDPRT.zip 352.0 KB
Tx a lot for your ideas.
I tried the first one (the good result for me), but trying to project the reguler outside helix (the more classical and most known one ).
To project such curve on a surface didn't work anymore, but I didn't think about genetrating 2 surfaces, as you do, to get the intersection curve.
So a big tx for this solution