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Among the moving elements the first to be considered is the lever, which really forms a broad classification comprising many elements that will hardly be recognized as levers at first blush. Levers in some form are to be found in practically every machine. A wheel, a gear, and a pulley are really levers in disguise, as will be explained presently.

Of course everyone knows that a simple lever consists of a rigid bar that swings on a fulcrum. The fulcrum may be a knife edge, a shaft passing through the bar or any element on which the bar can be swung or oscillated. The purpose of the lever is to give a certain advantage in the application of a force to a load. This may be a change of speed and distance of travel, and hence of power, or merely a change of direction.

FIG. 1.—THREE ORDERS OF SIMPLE LEVERS

There are three types or orders of levers produced by varying the relative positions of the points where the fulcrum, the force or effort, and the weight or load are applied. These are shown in Figure 1. In the lever of the first order the fulcrum is placed between the effort and the weight; in the lever of the second order the weight is applied between the fulcrum and the effort; and in the lever of the third order the effort is applied between the fulcrum and the weight. In each case that part of the lever which extends from the fulcrum to the point where the effort is applied is called the effort arm, and that which extends from the fulcrum to the point where the weight is supported is the weight arm. The weight that can be lifted with a given effort depends upon the ratio of the effort arm to the weight arm. If the two arms are of equal length, the effort is equal to the weight, but twice the weight can be lifted with the same effort if the effort arm is twice as long as the weight arm. You can lift a ton with an effort of only 100 pounds if your effort arm is twenty times as long as your weight arm but the end of your effort arm would have to move twenty inches to raise the ton weight one inch. We are assuming in all these cases that the lever itself has no weight and that there is no friction at the fulcrum.

Of course levers are not used merely for the purpose of lifting weight, but to overcome any resistance or merely to apply pressure upon an object. In almost every household we may find examples of the three orders of levers. A pair of shears, for instance, is composed of two levers of the first order, swinging on a common fulcrum. The effort is applied at the handles, and the weight or load is the material that is cut by the blades or, speaking more technically, the handles are the effort arms and the blades are the weight arms. A material that is too tough to be cut at the tip ends of the blades may be easily cut if we move it in near the fulcrum or pin that hinges the blades together; for by doing this we shorten the weight arms, because the weight arm is measured not to the end of the blade, but to the point where it is cutting into the material. To cut very tough material, such as heavy tin or sheet steel, we use long-handled short-bladed shears. The cutting pressure depends upon the ratio of the effort arm to the weight arm. If the effort arms are twice as long as the weight arms, the cutting pressure is twice as great as that applied at the handles.

A nutcracker consists of a pair of levers of the second order. The fulcrum is at one end and the effort or pressure is applied at the opposite end of the levers or handles, while the equivalent of the weight (in this case the nut) is placed between the effort and the fulcrum. Again the effort arm is measured from the fulcrum or hinge pin of the tool to the point where the hand pressure is applied, and the weight arm is measured from the fulcrum to the nut. The effort arm may be four or five times as long as the weight arm, so that the pressure exerted on the nut is four or five times as great as that exerted by the hand on the ends of the handles.

FIG. 2.—AN ANGULAR OR BELL-CRANK LEVER

In the case of a pair of sugar tongs we have another tool something like the nutcracker in construction, but here the weight, i.e., the lump of sugar, is seized by the ends of the tongs while the hand pressure is applied somewhere between the fulcrum and the weight. Hence we have here a lever or pair of levers of the third order. The effort arm of a pair of tongs is always shorter than the weight arm and the pressure on the sugar lump is always less than that exerted on the tongs by the hand. Evidently the most powerful tool of the three is the nutcracker, because the effort arms extend over the full length of the tool and are always longer than the weight arms.

A lever need not consist of a straight bar; the effort arm may form an angle with the weight arm, forming what is known as an angular or bell-crank lever (Figure 2). When a common claw hammer is used to pull out a nail, the claws that slip under the head of the nail form the weight arm and the hammer handle the effort arm. A horizontal pull on the handle produces a vertical lift on the nail.

Sometimes two or more levers are interconnected, as in Figure 3, the effort arm of one being linked to the weight arm of the other. This serves to increase the lifting force at the weight and at the same time keep the mechanism within compact limits. Such compounding can go on indefinitely and is subject to all sorts of variations.

FIG. 3.—COMPOUND LEVERAGE

One thing we must not forget, and it is a matter that is commonly overlooked by perpetual motion cranks, namely, that while a pound of pressure on the effort arm may be made to lift two, four, or a hundred times as many pounds on the weight arm by varying the relative length of these arms, it has to move two, four, or a hundred times as far as the weight arm, so that the work done on one side of the fulcrum is always exactly equal to that done on the other side.