Could you use the bot with a template. Trace the arch onto a paper or some sort of template that can lay flat on the table of your machine. Place the template square on the table and across the width of the template make reference marks say at 6" intervals. With a small 1/6" bit or small pointer move the spindle over the arch at the 6" intervals and record the readings from your screen. You should now be able to recreate the arch in your cad software. Make a sacrificial template to before cutting good material. I have done this once and it seem to work well. I am not good at geometry and complicated math so I find other ways. Hope I didn't confuse you too much.