ward one below the line of motion of the
slide, and may compare the two.

[Illustration: Fig. 286.]

[Illustration: Fig. 287.]

[Illustration: Fig. 288.]

[Illustration: Fig. 289.]

Figures 286 and 287 represent the Whitworth quick return motion that is
employed in many machines. F represents a frame supporting a fixed
journal, B, on which revolves a gear-wheel, G, operated by a pinion, P.
At A is an arm having journal bearing in B at C. This arm is driven by a
pin, D, fast in the gear, G; hence as the gear revolves, pin D moves A
around on C as a centre of motion. A is provided with a slot carrying a
pin, X, on which is pivoted the rod, R. The motion of end N of the rod R
being in a straight line, M, it is required to find the positions of N
during twenty-four periods in one revolution of G. In Figure 288 let H'
represent 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 Figure 287. Let
the line M correspond to the line of motion M in Figure 286. Now since
it is the pin D, Figure 287, that 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
C, and passing through the lines of division on H' we get on circle H
twenty-four positions for the pin X in Figure 286. Then setting the
compasses to the length of the rod (R, Figure 286), 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 Figure 286, and the motion under this new condition will be as in
Figure 289; the process for finding the amount of motion along M from
the motion around H being precisely as before.

[Illustration: Fig. 290.]

In Figure 290 is shown a cutter-head for a wood moulding machine, and it
is required to find what shape the cutting edge of the cutter must be
to form a moulding such as is shown in the end view of the moulding in
the figure. Now the line A A being at a right angle to the line of
motion of the moulding a