Operate a CNC with waist ( radial ) X axes and linear Y axes

Hello ,
My question for the forum (and I hope I asking the right place) is , does any one know if/how to make LinuxCNC calculate X Y coordinates based on a radial waist axes and a lineal Y axes ...
I'm building a new CNC with a single post with a waist control and then a linear Y axes and i want to use normal G code to cut items.

You do this with a custom kinematics file.

There is a worked-example here:
linuxcnc.org/docs/2.7/html/motion/kinematics.html