Pivoting cut

Dear Experts,

I have a following problem which I would like to find an elegant solution for.

There is a cylindrical part which should pivot on pins to certain angle (8 degrees) inside another part. The pivot axis is in the middle half height of the cylindrical part. How would you recommend modeling the socket/slit for such a part?

It is pretty clear how to manufacture such a part – have a cylindrical mill bit cutting inside the part while the part is turning.

The solid sweep looked like a nice solution, but I need the cutting cylinder to turn, not to just move along the path.

Any ideas?

Thanks

SolidworksToolbox