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KINEMATICS OF MACHINERY.

G7. Anti-parallel Cranks.

By means of pair-closure we can, as we have already seen in 47, convert the crank parallelogram into an anti-parallelogram, 47 and this can be so constrained as to retain its special property in every position. Figs. 208 and 209 represent the two forms of this chain, pair-closed, which we have already considered. We may call the mechanisms to be formed from it anti-parallel

crank trains. Two different results can be obtained by the different modes of placing the chain, one if it be placed on d or &, the other if a or c be the fixed link. If d be fixed> as is supposed in both the figures, the two cranks turn in opposite directions, or reversely, for which reason 1 have already given the mechanism the name of reverse cranks ( 47, Fig. 155). If, however, the chain be placed on a (Fig. 210), so that c becomes the coupler and the former coupler and frame both become cranks, then b and d both revolve continuously, but in the same direction, or we may say conversely. In the first case the anti- parallelogram gives us reverse anti-parallel cranks, in the second converse anti^parallel cranks. It should be noticed that the nature of the relative rotations is the same in both cases. This arises from the equality, through the anti- parallelism, of the angles 123 and 143. We may therefore use a pair of congruent ellipses as reduced ccntroicls ( 9) for the