Page:The Kinematics of Machinery.djvu/299

 LEVER AND INCLINED PLANE.

277

restraint. We have here certainly an incompleteness in the statement of conditions which is very extraordinary in the case of an important fundamental proposition. If we supply these defects we have the bodies, lever, and support so arranged that their relative motions are constrained, and that each is free only to rotate relatively to the other. This, however, is nothing else than the arrangement of the turning pair R+R-, or (see 57) CiG~ t and will be called, according as one or the other elements be fixed

or otherwise

z or

and the " principle of the lever " is simply the conditions of equi- librium of the forces in a turning pair. The pair is usually

represented, however, as incomplete and force-closed, in principle

rt //+ as in Fig. 193, for which the formula stands : ^ -.

FIG. 193.

FIG. 194.

The Inclined Plane. A surface oblique to the plane of the horizon, having a body resting upon it, touching it throughout a plane section, and tending by its weight to slide downwards (Fig. 194) ; the magnitude of the force necessary to prevent this sliding is studied. Here again the description leaves much to be wished. It is, as a rule, left unexpressed that the body can only slide parallel to the greatest slope of the plane, that is, the necessary bodily restraint in other directions is imagined, and means are also imagined to exist by which it is prevented from leaving the plane. In other words, it is tacitly assumed that the sliding body with the one below it are paired for rectilinear motion, and the pair under the supposed conditions is simply a