From 2 on arc h, we mark with the compasses line b on line m, showing that while the pin moved from 1 to 2, the rod r would move slide s, [Fig. 1550], from a to b, in [Fig. 1554]. From 3 we mark c, and so on, all these marks being above the horizontal line m, representing the line of motion, and being for the forward stroke. For the backward stroke we draw the dotted line from position 17 up to arc h, and with the compasses at 17 mark a line beneath the line m of motion, pursuing the same course for all the other pin positions, as 18, 19, &c., until the pin arrives again at position 24, and the link at o, and has made a full revolution, and we shall have the motion of the forward stroke above and that of the backward one below the line of motion of the slide.
On comparing this with the crank and with the Whitworth motion hereafter described, we find that the cutting speed is much more uniform than either of them, the irregularity of motion occurring mainly at the two ends of the stroke.
Fig. 1555.
Fig. 1556.
In [Fig. 1555] we have the motion of the Whitworth quick return described in [Fig. 1551], h′ representing the path of motion of the driving-pin d about the centre of b, and h′ the path of motion of x about the centre c, these two centres corresponding to the centres of b and c respectively in [Fig. 1551]. Let the line m correspond to the line of motion m in [Fig. 1551]. Now, since pin d, [Fig. 1551], drives, and since its speed of revolution is uniform, we divide its circle of motion h′ into twenty-four equal divisions, and by drawing lines radiating from centre b, and passing through the lines of division on h′, we get on circle h twenty-four positions for the pin x in [Fig. 1551]. Then setting the compasses to the length of the rod (r, [Fig. 1551]), we mark from position 1 on circle h as a centre, line a; from position 2 on h we mark line b, and so on for the whole twenty-four positions on circle h, obtaining from a to n for the forward, and from n to y for the motion during the backward stroke. Suppose, now, that the mechanism remaining precisely the same as before, the line m of motion be in a line with the centres c, b, instead of at a right angle to it, as it is in [Fig. 1551], and the motion under this new condition will be as in [Fig. 1556], the process for finding the amount of motion along m from the motion around h being precisely as before.