[Fig. 1837] represents a die having three instead of four cutting points—that is, the point c of [Fig. 1835] is left out, and the remaining ones a, b, and d, are equally spaced. This, placed upon a similar bar and taking an equal cut, would produce a truly circular form until d had reached x—with a and b at z and y—after which the die would move laterally, tending to carry d toward the centre of the work and a and b away from it, so as to equalize the cuts on all three. Hence, when d had reached h and the three-cutter die attained the position shown by dotted lines in [Fig. 1837], h would have made an indentation inside the true circle, while e and f have travelled away from it, thus forming protuberances. From h to a the lateral movement is reversed, and finally upon the completion of a third of a revolution, the die is again central and a cut has been carried completely around the bar, leaving it as shown in [Fig. 1838]. Comparing this with [Fig. 1836], it will be seen that there are three truly cylindrical portions—viz., a z, b y, and d x instead of four in [Fig. 1836], but each one is longer; that there is a depressed place, x a, of equal length to that in [Fig. 1836], and two elevations, z b and y d, each of equal length to the one (y c) in [Fig. 1836].
Fig. 1839. Fig. 1840.
