[Illustration: FIG. 23.]
[Illustration: FIG. 24.]
[Illustration: FIG. 25.]
Moreover, in Fig. 22, the locus of the instantaneous axis of the trammel
bar (of which the part EH corresponds to the connecting rod, when a crank
OH is added to the elliptograph there discussed) was found to be a
circle. But in the present case this locus is very different. Beginning
at A', the instantaneous axis moves downward and to the right, as the
crank travels from A in the direction of the arrow, until it becomes
vertical, when the axis will be found upon C'R, at an infinite distance
below AB', the locus for this quarter of the revolution being a curve
A'G, to which C'R is an asymptote. After the crank pin passes C, the axis
will be found above AB' and to the right of C'R, moving in a curve HB',
which is the locus for the second quadrant. Since the path of P is
symmetrical with respect to DE, the completion of the revolution will
result in the formation of two other curves, continuous and symmetrical
with those above described, the whole appearing as in Fig. 24, the
vertical line through C' being a common asymptote.
In order to find the radius of curvature at any point on the generated
curve, it is necessary to find not only the location of the instantaneous
axis, but its motion. This is done as shown in Fig. 25.
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