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FIG. 4.—PRIMITIVE GEAR WHEELS—TWO COACTING GROUPS OF LEVERS

If we take a number of levers radiating from a common fulcrum like the spokes of a carriage wheel, we have a primitive gear wheel. Two such groups of levers may be mounted on parallel shafts so that when one is turned its spokes will successively engage the spokes of the other group and make the latter turn (see Figure 4). Each spoke is first an effort arm on one side of the wheel and then a weight arm as it turns around to the other side of the wheel, and as the effort arms and weight arms are of the same length there is no multiplication of power. A pound on one side of the wheel cannot lift more than a pound on the other. The driven wheel receives the same power as the driving wheel except for such loss as may be due to friction at the bearings or where the spokes contact. The only advantage of such a pair of gears is that the direction of rotation of the driven wheel is the reverse of that of the driving wheel. If the spokes of one wheel are longer than those of the other, we have at once a variation in the rate of rotation proportional to the relative diameters of the two wheels. In Figure 5, for instance, the diameter of the driving wheel A is twice the diameter of the driven gear B, and so, for each revolution of A, B must make two revolutions, i.e., the driver must make two revolutions for each revolution of the driven wheel. In other words, the speed of revolution is doubled. However, if we make B the driver the speed of the driven wheel A will be half of that of wheel B.

FIG. 5.—COACTING LEVERS OF UNEQUAL LENGTH

In primitive machines spoke gears were seldom mounted on parallel shafts because of the difficulty of keeping the spokes in alignment. Instead, one shaft was mounted at right angles to the other so that one set of spokes would cross the other (Figure 6), thus producing the equivalent of a bevel gear. This was of advantage in changing the plane of rotation. A later development was the barrel or lantern gear, which permitted transfer of power without changing the plane of rotation. A cylindrical bundle of rods constituted one of the wheels (as shown in Figure 7). Instead of being crudely formed of spokes, the other wheel sometimes consisted of a disk with pins radiating from its rim. Such gears in far more refined form are still used in modern clocks and watches. A still further development for transmitting motion to a plane at right angles to that of the driving shaft is shown in Figure 8. Here we have a crown gear in which the pins instead of radiating from the periphery of the disk project from the side face of the gear.

FIG. 6.—PRIMITIVE EQUIVALENT OF THE BEVEL GEAR

FIG. 7.—PRIMITIVE LANTERN GEAR

Turning back to our first spoked wheels, it is very evident that we may put a rim over the spokes or even fill in between the spokes and convert the wheels into solid disks that are in frictional engagement with each other without getting away from the fact that we are dealing with levers. Each wheel, then, consists of a continuous revolving lever. Friction gears are used quite commonly in machinery when it is desirable to have the wheels slip if subjected to excessive strain.