This inference is so far correct, but the very common
impression that the middle point of the rod always describes an ellipse
is quite erroneous. The variation from that curve, while not conspicuous
in all cases, is nevertheless quite sufficient to prevent the use of this
movement for an elliptograph. To this there is, abstractly, one
exception. Referring to Fig. 22 in the preceding article, it will be seen
that if the crank OH and the connecting HE are of equal length, any point
on the latter or on its prolongation, except E, H, and F, will describe
an exact ellipse. But the proportions are here so different from anything
used in steam engines (the stroke being four times the length of the
crank), that this particular arrangement can hardly be considered as what
is ordinarily understood by a "crank and connecting rod movement," such
as is shown in Fig. 23.
The length DE of the curve traced by the point P will evidently be equal
to A'B', the stroke of the engine, and that again to AB, the throw of the
crank. The highest position of P will be that shown in the figure,
determined by placing the crank vertically, as OC. At that instant the
motions of C and C' are horizontal, and being inclined to CC' they must
be equal. In other words, the motion is one of translation, and the
radius of curvature at P is infinite.
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