Sinusoidal sweep path on cylindrical face

[androo]

Hello,
I am trying to find a way to create a sinusoidal path on a cylindrical surface so that I can sweep my profile along it. Think of a pulley with a sinusoidal groove that oscillates perpendicularly to the rotation. The vector equation of the path is F(x,y,z,theta) = R*cos(theta)x + R*sin(theta)y + A*sin(theta)z, where R is the radius of the cylinder and A is the amplitude of the sinusoidal path.

Is there any way to create geometry with an equation? Is there a way to force the Cylindrical Cam designer to make this feature?
Thanks for your help,
Andrew

 

[androo]

solved it

I figured it out. I restarted the model from scratch as a quarter revolution instead of extruding a disc. I then added more 3D sketch points between 0 and 90 degrees (total of 8, given below). With the higher point density it seems that the 3D spline will hug the well enough to make the feature; however there is some weird little facet/artifact surface at the start of the cut I haven't figured out. Also, I widened the cut for visibility but didn't amplify the sinusoid amplitude so it's still a little hard to see.

File: View attachment 765

X Y Z
2 0 0
1.961570561 0.390180644 0.002926355
1.847759065 0.765366865 0.005740251
1.662939225 1.111140466 0.008333553
1.414213562 1.414213562 0.010606602
1.111140466 1.662939225 0.012472044
0.765366865 1.847759065 0.013858193
0.390180644 1.961570561 0.014711779
1.22515E-16 2 0.015

UPDATE: add one more point to the spline to go past the last edge and that little facet will get cut away.