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By forming teeth on one gear to mesh between similar teeth on the other, we convert the friction gears into a pair of spur gears (Figure 9). We need not go into the intricacies of the form of gear teeth. They are designed to be in continuous rolling contact while they are in mesh. The novice is apt to call all spur gears “cogwheels” and gear-teeth “cogs.” Mechanics, however, recognize a difference between cog wheels and spur wheels. In the former, the teeth, or cogs, are not cast upon or cut out of the wheel body, but are separate pieces fitted to the wheel. Such wheels are found in old water mills. They consist of wooden wheels with iron or steel teeth mortised in the wooden rim of the wheel. In general it is safer to speak of spur gears because there are few cogwheels now in use.

FIG. 8.—CROWN AND LANTERN GEAR

When a small gear engages a large one, the former is commonly known as a pinion.

FIG. 9.—SPUR AND PINION GEAR

FIG. 10.—BEVEL FRICTION GEARS

If two friction wheels are to turn at right angles one to the other, they must have conical bearing surfaces, as in Figure 10. The angle between the shafts of the two gears and the relative size of the gears may be changed as desired, provided each cone surface has its apex at the intersection of the two shafts or axes. It is easy to understand how such conical friction gears may be converted into toothed bevel gears (Figure 11), by forming teeth on the conical surfaces, and it will be evident that the teeth must taper toward the apex of the two cones. Two bevel gears of equal diameter, and with shafts set at right angles one to the other, are known as miter gears.

FIG. 11.—TOOTHED BEVEL GEARS

So far we have not shown any combination of gearing that will multiply power. In Figure 5, the driver A is twice the diameter of the driven wheel B, and the latter makes two revolutions for one of A, but the speed at the periphery of the two wheels is the same. A pull of one pound at the point a produces a pressure of one pound at b, and this in turn produces a lift of one pound at c because the levers in each wheel are perfectly balanced, that is, each lever has equal effort and weight arms. The way to obtain an increase of power and of peripheral speed is to fasten two wheels of unequal diameters together on the same center and apply the effort to one of the wheels (as in Figure 12) and the weight to the other wheel. This gives us what is technically known as a wheel and axle. The dotted lines show that we have here a lever of the first order which can be used to multiply power in the same way that a bar lever does. If one wheel is twice the diameter of the other then a pound of effort will lift two pounds of weight.

FIG. 12.—WHEEL AND AXLE OR REVOLVING LEVER OF FIRST ORDER

FIG. 13.—REVOLVING LEVERS OF THE 2D AND 3D ORDER

Figure 13 shows how the effort and weight can be shifted about in such fashion as to give us a lever of the second and one of the third order. The power may be enormously increased and the speed of the final wheel greatly reduced by setting up a train of gears in which the effort is received by the larger one of each couple and is delivered by the smaller one. In Figure 14 the smaller wheels are half the diameter of the larger ones. A pound of pressure at A will amount to 2 at B, 4 at C, 8 at D, 16 at E, and 32 at F. On the other hand, point A will have to move through 32 inches to make the point F move an inch.

RAISING WATER WITH A CHAIN OF POTS

A primitive pump still used in Egypt

A HORSE-OPERATED CHAIN-PUMP USED IN GREECE

MULTIPLE SPINDLE DRILL IN MOTOR CAR FACTORY

FIG. 14.—A TRAIN OF SPUR GEARS

FIG. 15.—PULLEYS OF THE 1ST, 2D, AND 3D ORDERS

FIG. 16.—TYPICAL ARRANGEMENT OF BLOCK AND TACKLE

A pulley is merely a modification of the wheel. Figure 15 shows how it may be arranged to correspond to the three orders of simple levers. If the pulley axis is fixed, as in the first order, the effort and weight arms are equal and hence balanced. In the second order the wheel is bodily movable, hence one pound will raise two pounds of weight because the power arm is twice as long as the weight arm, while in the third order it takes two pounds of lift to raise one pound of weight. There is no end of possible combinations of pulleys which will multiply power in the same way that bar levers do when compounded. A common arrangement of block and tackle is given in Figure 16. There is a four-sheave pulley block above and a three-sheave block below, but in order to trace the rope clearly the pulley wheels or sheaves are represented as of different diameters. The arrangement consists of a series of levers of the first order in the upper pulley block coupled to a series of levers of the second order in the lower block. To find the weight that a given power will lift, multiply the effort by the number of strands of rope that are supporting the weight. In this case there are seven such strands, not counting the strand E, to which the effort or pull is applied. This means that a pull of a hundred pounds at E will lift 700 pounds at W. Of course a pull of seven feet at E will raise the weight only one foot.

FIG. 17.—INCLINED PLANE WITH EFFORT PARALLEL TO THE INCLINED FACE