The first and seconde picture is an cut which i made with the logo as a solid. By creating the solid i cheated a little bit to show how it should looks.
The "F" solid was not that difficult, but with the gear i had to create the face with the outer wire and then created a circle to cut the hole. That is why the circle is not in the middle of the gear.
If i try to make the same thing on the zig zag surface this does not work, because i can not make any face out of the wires.
Maybe someone can also try this??
In the attached FC file i have added mainly 3 Parts:
Fc Logo Done --> is the solid with the cheated cut
FC-Logo --> is the sketch from the svg i have imported
FC-Logo Wire Bended --> is the wire of the logo on the bended surface
FC-Logo Zig Zag --> is the wire of the logo on the zigzag surface