Fig. 1553.
In [Fig. 1553] is a diagram of the tool motion given when the slide is operated by a simple crank c, the thickened line r representing the rod actuating the slide and line on the line of motion of the cutting tool. The circle h denotes the path of revolution of the crank pin, and the black dots 1, 2, 3, 4, &c., equidistant positions of the crank pin.
Line m represents the path of motion of the cutting tool.
If a pair of compasses be set to the full length of the thick line r, that is from the centre of the crank pin to end b of line r, and these compasses be then applied to the centre of crank pin position 1, and to the line m, they will meet m at a point denoted by line a, which will, therefore, represent the position of the tool point when the crank pin was in position 1. To find how far the tool point is moved while the crank pin moves from position 1 to position 2, we place the compass point on the centre of crank pin position 2 and mark line b. For crank position 3 we have by the same process line c, and so on, the twelve lines from a to l representing crank positions from 1 to 12.
Now let it be noted that since the path of the crank pin is a circle, the tool point will on the backward stroke occupy the same position when the crank pin is at corresponding positions on the forward and backward strokes. For example, when the crank pin is in position 7 the tool point will be at point g on the forward stroke, and when the crank pin is in position 17 the tool will be at point g on the backward stroke, as will be found by trial with the compasses; and it follows that the lines a, b, c, &c., for the forward stroke will also serve for the backward one, which enables us to keep the engraving clear, by marking the first seven positions on one side of line m, and the remaining five on the other side of m, as has been done in the figure.
Obviously the distances apart of the lines a, b, c, d, &c., represent the amount of tool motion during equal periods of time, because the motion of the crank pin being uniform it will move from position 1 to position 2 in the same time as it moves from position 2 to position 3, and it follows that the cutting speed of the tool varies at every instant in its path across the work, and also that since the crank pin operates during a full one-half of its revolution to push the tool forward, and during a full one-half to pull it backward, therefore the speed of the two strokes are equal.
Fig. 1554.
We may now plot out the motion of the link quick return that was shown in [Fig. 1550], the dotted circle h′, in [Fig. 1554], representing the path of the pin a, and the arc h representing the line of motion of the upper end of link l, and lines n, o, its centre line at the extreme ends of its vibrating motion. In [Fig. 1554] the letters of reference refer to the same parts as those in [Fig. 1550]. We divide the circle h′ of pin motion into twenty-four equidistant parts marked by dots, and through these we draw lines radiating from centre c and cutting arc h, obtaining on the arc h the various positions for end z of rod r, these positions being marked respectively 1, 2, 3, 4, &c., up to 24. With a pair of compasses set to the length of rod r from 1 on h, as a centre, we mark on the line of motion of the slide line a, which shows where the other end of the rod r will be (or, in other words, it shows the position of bolt b in [Fig. 1550]), when the centre of a, [Fig. 1550], is in position 1, [Fig. 1554].