Fig. 202.
In [Fig. 202] are two gear-wheels, a, which is fast upon its stationary shaft, and b, which is free to rotate upon its shaft, the link c affording journal bearing to the two shafts. Suppose that a has 40 teeth, while b has 20 teeth, and that the link c is rotated once around the axis of a, how many revolutions will b make? By reason of there being twice as many teeth in a as in b the latter will make two rotations, and in addition to this it will, by reason of its connection to the arm c, also make a revolution, these being two distinct motions, one a rotation of b about the axis of a, and the other two rotations of b upon its own axis.
Fig. 203.
Fig. 204.
A simple arrangement of gearing for reversing the direction of rotation of a shaft is shown in [Fig. 203]. i and f are fast and loose pulleys for the shaft d, a and c are gears free to rotate upon d, n is a clutch driven by d; hence if n be moved so as to engage with c the latter will act as a driver to rotate the shaft b, the wheel upon b rotating a in an opposite direction to the rotation of d. But if n be moved to engage with a the latter becomes the driving wheel, and b will be caused to rotate in the opposite direction. Since, however, the engagement of the clutch n with the clutch on the nut of the gear-wheels is accompanied with a violent shock and with noise, a preferable arrangement is shown in [Fig. 204], in which the gears are all fast to their shafts, and the driving shaft for c passes through the core or bore of that for a, which is a sleeve, so that when the driving belt acts upon pulley f the shaft b rotates in one direction, while when the belt acts upon e, b rotates in the opposite direction, i being a loose pulley.
If the speed of rotation of b require to be greater in one direction than in the other, then the bevel-wheel on b is made a double one, that is to say, it has two annular toothed surfaces on its radial face, one of larger diameter than the other; a gearing with one of these toothed surfaces, and c with the other. It is obvious that the pinions a c, being of equal diameters, that gearing with the surface or gear of largest diameter will give to b the slowest speed of rotation.