It may be explained now, why the thickness of the cutter if employed upon a wheel having more teeth than the cutter is correct for, interferes with theoretical exactitude.
Fig. 112.
Fig. 113.
First, then, with regard to the thickness of tooth and width of space. Suppose, then, [Fig. 112] to represent a section of a wheel having 12 teeth, then the pitch circle of the cutter will be represented by line a, and there will be the same difference between the arc and chord pitch on the cutter as there is on the wheel; but suppose that this same cutter be used on a wheel having 24 teeth, as in [Fig. 113], then the pitch circle on the cutter will be more curved than that on the wheel as denoted at c, and there will be more difference between the arc and chord pitches on the cutter than there is on the wheel, and as a result the cutter will cut a groove too narrow.
The amount of error thus induced diminishes as the diameter of the pitch circle of the cutter is increased.
But to illustrate the amount. Suppose that a cutter is made to be theoretically correct in thickness at the pitch line for a wheel to contain 12 teeth, and having a pitch circle diameter of 8 inches, then we have