I do not think a 3 inch gear will translate in to the distance of the out side diameter, but what would be about at the diameter of the center of the tooth, because it pushes at the tooths center not it tip unless it is on the entering or exiting, teeth of the pinion, the diameter would be the pitch circle,
File:Gear words.png - Wikipedia, the free encyclopedia it has been a long time since I have studied gears, but
as the gear mesh there is a over lap that is do to the teeth of the gear, and there is the pitch circle which is the rolling diameter of the gear,
(I really doubt if this has any bearing on the discussion at hand or actual function of the splitter, but there is discussion on how far the pinion would move on a 3" gear, and it would depend on the pitch circle not the gears over all diameter, a finer toothed gear that was 3" over all, would move it faster than a coarse tooth gear that had big deep teeth as they both would have a different pitch circle, (in this instance the large coarse tooth would most likely be more robust and would deal with the shock load better, and would handle dirt and dust better),