196 KINEMATICS OF MACHINERY.
The diametral ratio 1 : 2 of the centroids, and their simple figures, make this extremely easy. If, for instance, we connect with b at the point 5, opposite to 3, a pin, this will be at 5' at the first change point and at 5" at tlje second, and if suitable gabs be fixed in those positions, it will gear with them, and the mechanism will be completely closed, as can be readily seen from the figure. It is worth noting that, for every half revolution of the crank, the point 3 moves through a distance equal to four times the crank radius, while in the mechanism in Fig. 145 its path has only half this extent.
��This mechanism has been long known. It was applied by Dawes
with little alteration in 1816 to a steam-engine, which I shall have
to mention again. It must be remembered that this closure in no
way helps the crossing of the dead points 3' and 3" which occur if
the driving effort act upon the block c. Neither here, nor in the
case of Fig. 145, is this possible, for at these points the instan-
taneous centre lies upon the line of motion of the block, so that
the driving force passes directly through it.
Generally, the passage of the dead points by higher pairs is only possible if the centroids have suitable forms. These must be such that, at the moment when the dead point is reached, the driving effort must not pass through the instantaneous centre, for in that case the arm of its moment about that point, and therefore the moment itself, have become = 0.
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