276 KINEMATICS OF MACHINERY.
could be done with them. .In short, such a comparison shows that there is no common idea really underlying the matter, for the differences are more than superficial ; it rather leads to doubt as to whether the " simple machines " have any right whatever to their name.
And yet there is something specially characteristic in these arrangements, at least in some of them, as, e.g., the lever and the inclined plane, which have so entirely passed from a special department into common language and ideas. There is something homely and familiar about them, they excite, I might almost say, a sentimental interest. Does this merely result from recol- lections of youthful mechanical study, or is it a breath from the childhood of science itself playing upon us ? Or has this sympathy, to which even the most abstract theorist would pro- bably have to acknowledge in his quiet moments, really no deeper
FIG. 192.
ground ? Kinematic analysis must give us a distinct answer to these questions ; it must show us whether we have really to give up these old heirlooms of mechanics, and if so it must enable us to remove them altogether, or whether there is not some- thing really indestructible in them. Let us proceed with the examination.
The Lever. A straight bar or knee-shaped body supported upon a fixed angular bearing, about which it can turn, (Fig. 192) ; two forces act on the bar on the one or the other side of the support; their equilibrium is to be studied. The problem has been stated thus since the time of Archimedes. In most cases the description is not exact. It is assumed, but not distinctly stated, that the support is so arranged that only plane motions can occur ; it remains unsaid that in cases where the direction of the forces is such as to move the lever from the support, this does not occur, in other words that it is prevented by suitable
