Page:The Kinematics of Machinery.djvu/303

 THE SCREW.

281

of the drums. This, however, makes the problem simply a re- petition of that of the lever, which was not its original meaning.

The Screw. A screw placed vertically working in a fixed nut and loaded by a weight (Fig. 200) ; the force which has to be applied, normal to a radius and at some point not in the axis of the screw, in order to balance the load, is determined. We recognise at once the twisting-pair, written either

S~ S+ or S+ S~.

The " principle of the screw " is a very limited, indeed incom- plete, case of the equilibrium of forces in a twisting-pair.

The Funicular Machine. This, lastly, is a problem which, apart from its value in pure Mechanics when put into an abstract form, is so far removed from the machinal idea by its extended force- closure and the indefiniteness of its motions, that it obviously has no right to a place among " simple machines," and we need not there- fore consider it here.*

As a whole, the result at which we have arrived is very remarkable. We find in the simple machines, which of all others ought to ap- pear harmoniously related, a crude mixture of kinematic problems closed and unclosed pairs, and chains mistaken for pairs, arrangements mostly force-closed among them

the tension-organ with all its difficulties of treatment, and in addition an experiment in the inversion of a mechanism. We have been compelled to recognise, too, that in their usual treatment there is an extraordinary inexactness in stating the problems, which can hardly tend to give the beginner clear ideas. The explanation of

powers" is really the mechanism (C^C" 2 ') c which is shown in Fig. 183. Precisely the same chain placed upon another link, viz. (C+C^)*, forms an epicyclic train, which is treated not as a simple machine but as a moio or less difficult case of " aggregate motion."
 * The "toothed wheel" in the form in which it appears among the "mechanical

FIG. 200.