HIGHER PAIRING AT CHANGE-POINTS.
�195
�in Fig. 145, the length of the link I be made equal to that of the
crank a, then when the crank makes a quarter revolution the centre
of the block c has been brought up to the axis 1 of the crank, and
it would be moved forward symmetrically as the rotation continued,
were it not that a change-point here occurred. The centre of the
��FIG. 155.
�pin 3 coincides with the centre 1, a and b cover each other, and
can together turn about their common axis 1. The chain thus
becomes at its point of change simply a pair of elements. This
can be prevented by pairing the link b with the opposite one d, for
which purpose we must find the centroids of both links.
��FIG. 156.
�An examination of the relative motions of b and d shows at
once that these centroids are Cardanic circles (Fig. 157), the
smaller having a radius a = b, and described about the point 2
(which is a point always of the link b), the larger having a radius
twice as great, described about the point 1 of the link d. It is
easy to see that the pairing at the point of change can be effected
by supplying b and d with such small portions of toothed profiles
as can come into action at that point.
o 2
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