Page:The Kinematics of Machinery.djvu/302

 280

KINEMATICS OF MACHINERY.

The Wheel and Axle. Two drums of different diameters fixed together and having a common shaft, each having one end of a rope which is loaded at the other fixed to it ; the shaft works in fixed bearings, or at least is imagined to do so, for the bearings are often enough omitted in the drawing (Fig. 199) ; the equilibrium of the forces is studied. Again the problem is wanting in clearness, and is only solved by the employment of a number of

FIG. 199.

FIG. 193.

abstract assumptions, for the most part not expressed. Supposing

the axle bearings fixed the chain runs

C-G+.

V^ + 'T

\ y*+

(...R+,-jT

All the indefiniteness which we saw existing in the assumptions in the former cases exists also here. Indeed they are increased by the helical winding off and on of the cords, which occurs, too, so that their axes must describe higher screw-lines if artificial means of preventing it are not supposed to exist, or if the difficulty be not got over by the supposition of infinitely thin cords. This last is very common. The sense of the necessity for eliminating these complicated motions of the cord has led many to omit it altogether, replacing it merely by tange'ntial forces acting upon the peripheries