Page:The Kinematics of Machinery.djvu/287

 COMPOUND CHAINS. 265

to some extent difficult to attain the required distinctness. A little experience, however, enables this to be obtained, as a few examples will show.

We have before examined ( 3) the chain represented in Fig. 185, containing seven cylindric pairs. It is obtained from the familiar chain ((7") by the addition of two more links of the form (7...||...(7, and possesses a certain symmetry of arrangement in having two opposite three-cylindered links twice connected by a pair of two- cylindered links,* altogether, that is, by four such links. This is made more distinct by the schematic representation in Fig. 186, in which also the dimensions are so chosen as to make the chain symmetrical. The turning-pairs are here numbered

FIG. 185.

from 1 to 7. We may look at the whole chain as consisting of two five-linked cylinder-chains 1, 2, 3, 4, 5 and 1, 2, 6, 7, 5 in which the links 1, 2 and 1, 5 are common, the cylinders 2, 3, 6 united into one link containing three elements, and the cylinders 5, 4, 7 into another, To distinguish between links containing two, and links containing three elements, we may call them binary and ternary links respectively.

We may now proceed by first writing down these two five-linked cylinder-chains neither of which is by itself constrainedly closed singly, and then as it were adding them together that is putting a single sign only where pieces are common to both chains, and bracketing the elements brought together in the ternary links.

connection by k I and m n.
 * Firstly in the original connection by a d and e h, and secondly in the additional