Page:The Kinematics of Machinery.djvu/301

 THE FIXED AND LOOSE PULLEY. 279

The " principle of the wedge," if it be expressed in a sufficiently general form, gives the conditions of equilibrium of the forces in this chain. The traditional representation stands for a combina- tion of bodies, force-closed throughout, which, only roughly ap- proximates to the combination really intended.

The Pulley. A disc turning about a fixed pin, and having a grooved periphery over which rests a rope stretched at both ends (Fig. 197) ; the equilibrium of the forces acting at the ends of the rope and upon the pin is studied. The pulley takes a remarkable position among the simple machines. In the first place, we have here not two but three bodies used in combination. As a rule no mention is made of the assumption that the bearings of the pulley are supposed to be such as to prevent cross motions. Then again it is remarkable that while here a force-closed element, the rope, is employed, there is very insufficient recognition of its characteristic property of one-sided resistance. If the bracket for the pulley-spindle be considered as fixed, the kinematic formula for the chain is as follows :

/

T^ ' f

a mechanism of three links covering very indefinite motions, which approximate to machinal strictness only in consequence of force-closure.

The mechanism is commonly known as the fixed pulley, but under the head "pulley" another arrangement, the loose pulley (Fig. 198), is usually treated. Here the pulley frame is movable and loaded, and one end of the rope fixed, as in the formula.

!T~ _ ' / ,+'

This expression differs from the former only in the link which is fixed. The old mechanicians have busied themselves with the inversion of a kinematic chain ! In the loose pulley also force- closure is applied to the fullest extent.