[ ... ]
No -- you simply keep the engraving cutter too high to touch the workpiece, and draw lines using it as an indication. These are not precise marks --just enough to tell you to not cut there yet.
That works -- if you are using a rotary table and a dial on the hand crank. But if you are using an index head (which is what I would be using, and which has no dials) you can set the arms so you move from one arm to the next (perhaps with two or three full turns between arms if you are marking angles greater than what a single turn of the crank provides. In the case of my index head, which has a 40:1 worm, you get nine degrees per full turn, so for the ten degree steps you would need to go one full turn plus the distance marked by the arms, which select a certain number of holes on a circle of N holes. Once you reach the new position, you move the arms (which are locked together) so instead of the trailing arm touching the index pin, the leading arm touches it, so when you crank again, you again move to the trailing arm.
For the 5 degree and 1 degree motions, you will be less than a full turn, making things even simpler.
Hmm ... You don't need to set the arms for the 10 degree setting anyway when just marking -- you simply set for five degrees, mark the starting position as blue, then crank five degrees out, mark in red, crank again for blue and so on until you reach the starting point. Then you set stops to limit the travel, lower the cutter to make contact with the workpiece, and cut, then crank out two five degrees steps and cut again. Once that reaches its start, you crank out five more degrees, set the stops for the medium length lines, and cut, again going in ten degree increments until you have completed the circle. Then you reset the arms for one degree increments and the stops for the shortest line length, and crank and cut on any stopping place which is not already cut.
Then you wash off the paint with solvent and figure out how you are going to engrave or stamp the numbers for the long lines.
The index head reduces the chances of mis-reading the dials, but you need a special index plate to do things like 127 (for making metric transposing gears).
Enjoy, DoN.