Imagine we have two simple gears with different radii that are connected, with each gear on its own axis. If we fix the smaller gear so that it cannot rotate, then apply a force to the edge of the larger gear (perpendicular to its radius), the force applied to the smaller gear by the larger gear at the interface between them should be equal in magnitude to the force we are applying to the larger gear. Since all the forces involved are perpendicular to the gears they are acting on, it should be true that if a force is being applied to one part of a gear, to keep it from moving we must apply an equal force to the opposing side of the gear. In the scenario above where we want to keep the smaller gear fixed, it seems that if what I've said so far is correct, in order to prevent the two gears from rotating we would only need to apply a force equal in magnitude to the one acting on the larger gear. Obviously this is not correct, but I can't pin down exactly where the argument fails.