SCREW CHAINS. 555
that the links I and c be fixed together, the pair 3, that is, made immoveable, we see at once that the chain still remains moveable, and indeed has become simply that of Fig. 397.
154 - The Crossed and Skew Screw Chains.
In our development of the cylinder chain, ( 152), we found seven to be the limiting number of links in a simple chain. We were not there dealing, however, with the most general case, for the cylinder pair is not the highest form of the lower or closed pairs. This position is occupied, as we know, by the screw-pair (S). We shall therefore obtain the most general form of chain containing
only lower pairs if we place () instead of (C) in the most extended cylinder chain. The highest chain formed from closed pairs will therefore be the chain (S\). The complete synthetic examination of this chain, of which those already treated in 151 to 153 are really special cases, is part of the work still before synthetic kinematics. Further on we shall have to return to the question, it would suffice here merely to indicate the existence of the chain were it not necessary to look at some of the forms in which it is practically applied in machinery.
Kef erring again to the chain ((7+) which was shown in Fig. 394, it will be noticed that we can make the cylinder 2 oblique or crossed instead of normal, as for instance in Fig. 400, where an exceedingly complex motion can be obtained. Leaving this