Page:The Kinematics of Machinery.djvu/307

 LEVEE-CR 4 NK. 285

the other swings ; from this peculiarity we may call it a lever-and- crank train, or simply a lever-crank.

The mechanism (C" 4 ') b . If we now place the chain on b, that is, release the frame d and fix instead of it the coupler b (Fig. 202) we obtain a mechanism in which a and c again turn and swing respec-

.04"

FIG. 202.

tively, but now about the centres 2 and 3 instead of 1 and 4. The frame d has become the coupler, and the coupler b the frame. The whole is still a lever-crank, and differs from the former only in the relative lengths of the coupler and frame. There is therefore no difference in kind between the two mechanisms, and we have (C")* = (C" 4 ') b.

The mechanism (" 4 ') a - If the link a be made the frame, Fig. 203, we obtain the entirely different mechanism, one which we have previously examined in 9. The links b and d rotate about the axes 2 and 1, that is, they become cranks, c, on the other hand, becomes the coupler. The mechanism is known in practice as a drag-link coupling, we shall call it the double-crank. The cranks move with varying angular velocity ratio in a way which we were able to represent conveniently by the aid of re- duced centroids in Fig. 25.

The mechanism (G'") c . In this last arrangement the links b and d swing to right and left about their axes 3 and 4 ; c has become the frame, and a the coupler. In the position 4 V 2 3 shown in dotted lines, b has completed its swing to the right ; as it returns, however, d can move somewhat further to the right and then will swing in the same direction until at 1" it reaches the left limit of its travel. As it returns b in its turn moves further to the left and then returns as d did before : 4 I'" 2'" 3 shows an intermediate position with the links crossed. We may call this mechanism, which is frequently used in the parallel motions of machinery, but then not to the limits of its motion, the double