Just a thought here, but you could route out the background, leaving the letters raised. If the background looks a little 'rustic' after you've completed the carving, that's actually a good thing.
Why can't you just let the base ride on the high point of the circumference ie always perpendicular? If you're not trying to hog out a lot of material with a big bit, and/or deep cuts...assuming here you're doing this freehand(?), what could go wrong?

 

He challenged me to make him a sign with lettering on the outer radius of the de-barked slab.

Don't see any mention of routing there. Did he say rout, or not? If not, I'd just lay out the sign and then use carving chisels. Hehehe And if he did say rout, I'd just freehand rout it, same as with a flat piece. Might want to practice a bit before going for the final one tho.

 

will a palm router base ride on the material for free hand routing?

 

The radius of the log is a about 6" and the concern I have is stability. That is why I asked for ideas. If someone has done this successfully somehow, please chime in.

 

If you were to router on a flat surface you might clamp boards flat to support the router's path. Can you create a round or even arched support around the log or a portion of it? In my mind I'm picturing a couple of rings from an old wooden barrel acting as tracks to support the router.

 

How about instead of bearings or wheels take some 6/4 or 8/4 stock and cutting a curved shoe to match the outside arc of the log and attaching it to the base plate of the router? I did something similar for cutting flutes in a column when I didn't want to make an entire jig.

 

Routing the outside radius of a log

This is how I did It.

 

This is how I did It.

That was an inspired solution, Gary. I particularly like the ketchup bottle dust control. A simple, practical solution that obviously worked well. Nice job!

 

good job, Gary !! your son should be happy with it.
(try a piece of thin wall PVC pipe instead of the ketchup bottle).

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