I recently completed a project that required several 6" holes. I quickly discovered the 3" radius was too small for most router trammels. Here’s one solution you can use.

Lay out your circle using a compass, drill a 564 " hole in the center, and fit a 2d nail in the hole. Make an auxiliary subbase for your plunge router out of 12 " MDF, and drill a564 " pivot hole 2 78 " from the center of the bit hole (3" for the radius, minus the radius of a 14 " straight bit). Install the subbase, and clamp the workpiece to your bench on top of a backer board. Fit the hole in the router base over the nail and rout the hole by plunging and swinging the router around the nail.

To make 6" discs rather than holes, change the distance of the pivot hole from the base center to 318 " (the distance of the 3" radius plus half the radius of the 14 " straight bit).
—George Noeth, Fort Mill, S.C.