The pictures tell the story - no welding, no machining required. It works great!
I got a few 1/4" dowels and on one I cut notches with 1/4" spacing, on the other 3/8" and by choosing either I can make any typical size cut. To cut the notches, since I don't have a lathe...I whipped up a little table out of plywood that would hold the dowel while it was chucked into a drill. A clamp held the drill powered on, a ruler was applied to the table with double sided tape, and the grooves were cut by holding a triangle shaped file on the dowel at the required interval.
I used both oak and pine, I think pine is fine for this and lower cost.
A piece of pine to span the pot rim with a hole approximately* in the center for the dowel
The wire cutter is 3/32 stainless steel welding rod, cut to fit inside the diameter of the pot, sharp edges smoothed with the grinder. (and...even tho I'm not a welder, somehow I used this need as justification to buy a tube of these rods for $17. I'll have to think of another use for them...)
Approximately...I worried about precision and came to realize that it's not really an issue. The wire is cut so that it is barely scratching the sides of the pot when spun. The pine top bar isn't clamped or held fast - forefinger and thumb twist the dowel while the whole unit free floats on top of the pot. The curds cut easily.
I put a flag of blue tape on top of the dowel, it acts like a weathervane so that I know when a sweep of the steel rod is complete.
Note: as the steel rod sweeps on both sides of center, the dowel only needs to rotate a little more than 1/2 a spin to completely cut a horizontal line.
The rubber band and paperclip are used to allow the dowel to advance and lock into a groove.