Fig. 1836.
To take an example, in [Fig. 1835] is represented a die having four cutting points, placed upon a piece of iron of a round section, with the exception of a flat place, as shown. Now, in this position each one of the cutting points a, b, c, and d, is in contact with the true cylindrical part of the work only; hence, if the die were set to take the amount of cut shown, each point would enter the iron an equal distance, and the inner circle through the points would be the smallest diameter of the die. Upon revolving the die in the direction denoted by the arrow, an equal cut would continue to be taken off, and hence the circular form maintained, until cutter d had reached the edge x of the flat, the opposite one b, being at y (a at r and c at v), proceeding as d moved from x towards a, its cutting duty would continually become less and its pressure decrease, but as it is the cutting pressure of d that holds the opposite point b to its cut, as the pressure in d, after reaching x, continually becomes less, the die would gradually travel over so as to carry d toward the centre and cause it to take more cut, while b, on the opposite side, would travel out a corresponding distance and take less, thus keeping the duty equalized until the cutter d had reached h, the lowest part of the flat, when the die would have moved the greatest distance off the centre, assuming the position shown by dotted lines. Thus the cutting point at h has passed inside the true circle that all the cutters commenced to follow, while f has passed outside. Meanwhile, as h and f have shifted over, e and g have, of course, moved an equal amount and in the same direction, but the diameter of e and g being at right angles to that of h and f, the distances of e and g from the centre would be changed but an infinitesimal amount; hence, they would virtually continue to follow the true circle, notwithstanding the deviation of the other pair. As the die continues to revolve and h passes toward a, the lateral motion is reversed, the die tending to resume its original central position, which it does upon the completion of another quarter of a revolution, when the cutter that started at d has passed to h and finally to a. A cutting has now been removed from the entire circumference of the iron, leaving it of a form shown approximately in [Fig. 1836], where a z, b y, c v, and d x, are the four true circular portions cut respectively by the points a, b, c, and d, before the flat place was reached. After the flat place was reached x a is the depression cut by d, y c the elevation formed by b, and z b and v d are the arcs, differing almost imperceptibly from the true circular ones cut by a and c.
Fig. 1837.
Fig. 1838.