568
�KINEMATICS OF MACHINERY.
�two of its links are ternary ; the water is paired with the three
elements 2, 3 and 5, and the frame d with the three elements 1, 4
and 5. Its formula is
�d
�v-
�'(... (P) ..
�Q,
��By itself, however, the chain is still not constrainedly closed,
force-closure is always a condition of its working.
One means of making such chains, as well as others containing
flectional elements, pair-closed, consists in doubling them. We
have found already that this method has been applied in the case of the belt-trains (cf. 44), and have also seen the nature of the doubling of the chain now before us. Fig. 422 repre- sents such a doubled chain. Its mo- tions are now completely pair-closed; but at the same time, although it con- tains only five links, it has become a compound chain even more completely than before. If we imagine the chain of Fig. 420, also, to be made pair- closed by any means, the addition for instance of a suitable lever-train, which could make the motions of the piston dependent upon those of another, we
see at once that we are again brought into the region of compound
chains. It may just be noticed that this method of doubling chains
can be applied also to ordinary pulley -tackle in such a way as to
transform it into a constrained closed chain.*
��FIG. 422.
�* I have illustrated this by a model in the kinematic collection of the Kouig.
Gewerb. Akademie in Berlin. .
�
