When making a grandfather clock recently, I wanted to make the arches on the door frames, hood, and some other parts as precise as possible. My solution: Develop a jig to cut them with my table-mounted router.
My jig consists of a 1/4” plywood base, which mounts on the router table, and a pivot point. I use a dowel for the pivot, but you could also use a short nail.
To use the jig, I first set the distance between the pivot point and the 1/4” straight bit according to the radius I need to cut, and then bolt it to the table.
Next I make a 1/4” hardboard carrier somewhere larger than the workpiece, and drill a hole through it to fit over the pivot. I then adhere the workpiece to the hardboard, centering the work-piece's edge over the pivot hole. Finally, I drill start holes (larger than the bit) through the carrier just ahead of the workpiece where shown on the illustration.
To cut an arc, I place the workpiece and carrier over the pivot with the router bit positioned in one of the two start holes. I then rout the arc by slowly rotating the carrier and workpiece around the pivot. For best results, I'll make several passes to cut the part, elevating the router bit about 1/8” each time.
-L.K. Bolay, Oak Harbor, Ohio