484 KINEMATICS OF MACHINERY.
These form a kind of transition from the constructive elements to the complete machine. It will be remembered, however, that these three classes of trains are not the only ones occurring among the constructive elements. We had, for example, the screw-train (S'P'Cy among the rigid elements, while in the chain, rope and belt-trains of Class II. we had other complete mechanisms. We know too that the clutches are click- and brake-trains (cf. 123) while the moveable couplings are mechanisms formed from lower pairs of elements.
Our investigation of the constructive elements from a kinematic point of view has led us rather to a rearrangement of them than to any alteration in their number. It has furnished us, however, with explanations on some points by which, I believe, the treatment of the whole matter will be greatly facilitated.
The analysis has in several cases thrown a new and unexpected light upon very well known and apparently very thoroughly under- stood constructive elements. This has been specially the case in regard to valves and the machines fitted with.. them, pumps, blowing-machines, steam-engines, etc. The conclusions which we reached showed for the first time the close connection existing between many of the characteristics of these machines, and have thus greatly aided their comprehension. They enabled us to define relationships which before had not been proved, even where they had been recognised. In this way we have succeeded in effecting a real simplification of the subject, the advantages of which will be felt specially in the problems of Applied Kinematics. In reference to locks, too, our analysis has given us an explana- tion of which the want has often been felt. It has shown us that their kinematic principles are exceedingly simple, and that their treatment falls fairly within the limits of Applied Kinematics. Those arrangements which we have called curb-trains also (the special properties of which have not hitherto been distinctly recognised), and the escapements, we have been able to bring into their proper position among other mechanisms, and to examine from a general point of view instead of from the special one commonly adopted. The same is true also in the case of water- wheels, steam-engines and other complete machines, the more detailed examination of which we shall take up in the next chapter.
