192 KINEMATICS OF MACHINERY.
the motion of c from left to right as itself a reversed motion to leave the whole conditions just what they were before.
Under similar circumstances, however, the case is quite differ- ent in the mechanism with two parallel cranks, which was described above. Let us suppose here (Fig. 152) that by turning in the direction of the arrow the link 2,3 takes the position 2'3' ; then in the absence of any provision for carrying it across the dead point, any forward motion of the crank a may cause c to move either back- wards or forwards ; thus, for example, when a has reached 2'" , c may have returned to 3, and so when a has arrived at 2" it may have again resumed its dead position 4 3".
Thence the backward motion may be continued through the other semicircle, a again passing through 2 and so on. In short the L. H, rotation of a may give to c either a right- or a left-
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�FIG. 152.
�handed rotation, and the latter would take place in a manner en-
tirely different from the former. The change from the one motion
to the other may occur at either of the dead points. Obviously
here again the chain is not closed at these points, and the methods
for passing them represented in Figs. 149 and 150 furnish also the
necessary closure at them. If such closure be not provided, a
complete change in the motion may take place at each dead point ;
the nature of the mechanism, that is, may be entirely altered.
Any position of a link of a mechanism at which this is possible
we shall therefore call a change-position or change-point.
The chain-closure of which we have shown two forms in Figs. 149 and 150 is arranged for constraining the two cranks to rotate similarly. Another question now presents itself ; how to make the closure complete and at the same time to constrain a and I to revolve in opposite instead of in similar directions.
This closure can here be effected, as in all chains which have change-points, by connecting those links which are unclosed
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