Page:The Kinematics of Machinery.djvu/351

 CONIG CRANK TRAINS.

329

The parallel and anti-parallel cranks repeat themselves in the conic chain along with the others. The arrangements necessary for passing the dead-points are not, however, those examined before. If we join two conic parallel crank-chains in a way corresponding to Fig. 206, we obtain a mechanism by which it might appear at first sight that a uniform rotation could be transmitted between shafts whose axes are neither coincident nor parallel, a problem for which a solution has often been attempted. The formula of such a train would be 2 (0- 1| (?-) d . In reality, however, this combina- tion is an impossible one. For the chain (C- || C) has only four positions the four cardinal ones in which its opposite links lie parallel to each other ; in all other positions the opposite angles of what was the parallelogram are unequal, and the rotation of the cranks is therefore not uniform. While therefore the chain (C- || Cjf) has its own special interest, it will be seen that it is not entirely analogous with (<7J || C').

B. Conic slider-crank chain (C^C^), Fig. 258. The links d and c are right-angled, that is, the angle between the axes 1 and 4

FIG. 257.

FIG. 258.

and between 4 and 3 = 90. The comprehension of this chain^ which may present at first difficulties to some of my readers, may perhaps be made more easy by the help of Fig. 259. Here the principle of pin-expansion is applied to the mechanism. For the arm M 3 (which the figure shows as the projection of a quadrant like c, Fig. 258), turning about an axis at M (corresponding to the