Jere, please explain? Holding the router in your hands while the log spins on the lathe?
PS. Nice log on a Shopsmith.
Good eye on the shopsmith and the apple wood. The apple log has some wild grain and color to it.
The router sits on the tool rest, where the chisel usually sits (this may require a simple jig to hold the router depending on the routers shape.). You can move the router on the tool rest or keep a pivot screw loose on the tool rest and move the rest in small increments. Then turn the log feeding it into the router. Wider straight bits seem to work the best.
At first my router fit wedged between the base plate of the router like it was made for it with the Ss factory tool rest... This was until the original rest broke off while spinning a larger piece.
At the moment I am making a simple jig that the router base screws into. Basically a board has two u bolts with wing nuts that secures the board and router to the new tool rest(home made).