How to coordinate Welding Arm and Positioner to move coordinated as correct weldspeed

Yes, my goal is to have a constant welding speed, ie the tcp should move at a constant speed relative to the circumference of the pipe. The only way to achieve this (while staying in the 1F position) would be to have the positioner rotating at a sinusoidal speed. I’m ALMOST sure of this, but have been proven wrong many times before…If the pipe was centered on the axis of rotation then a constant positioner speed would work.

I can reason through this mathematically but solving it, then programming it seems daunting…there must be a better way!