Ancient Principles Drive Mechanical Advantage

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A McCormick-Deering No. 9 mowing machine, a device chock-full of levers. Even the double tree is actually a second class lever with the weight being the load (mower) connected to the center hole of the evener.
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Drawing One: A simple lever. Another example is the pitchfork: The hay on the tines is the load, the fulcrum is the hand grasping the fork handle near its center, and the force is other hand pushing down on the handle end to lift the hay.
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Drawing Two: Top, a class 1 lever; middle, a class 2 lever; bottom, a class 3 lever.
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Drawing Three: An angular (or bellcrank) lever.
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Drawing Four: A compound lever.
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Drawing Five: A wheel, axle and gear as a continuous lever.

The ancient Archimedes of Syracuse (a Greek mathematician, physicist, engineer, inventor and astronomer, 287-212 B.C.) is supposed to have said, “Give me a firm place to stand and I will move the earth.” Archimedes was talking about the use of a lever and a fulcrum to move a heavy object.

Farm machines are full of levers. For example, everyone knows that the cutter bar on a horse-drawn mower is raised by a lever, but how about the eveners that equalize the load between the two horses pulling the thing? Or, the mower wheels that impart motion to the cutter bar knife that cuts the hay — could they be levers as well? The mower is a complex machine, but it’s made up of a lot of levers in one form or another. The evener, wheels and gears are really just levers in disguise, as we shall see.

Force arm is the key

The simple lever consists of a rigid bar that rotates around a fixed object called a “fulcrum,” as shown in drawing No. 1. The hand provides the force by pulling down on the one end of the lever. The lever rotates around the fulcrum and causes the weight at the other end of the lever to rise. The length of the lever between the weight and the fulcrum is the weight arm, while the force arm is the length of the lever between the hand and the fulcrum.

If the weight arm and the force arm are the same length, the amount of force necessary to lift the weight will be equal to the weight and there will be no mechanical advantage. If the force arm is twice as long as the weight arm, twice the weight can be lifted with the same amount of force. A ton of weight can be lifted with a force of only 100 pounds if the force arm is 20 times as long as the weight arm, assuming the lever itself has no weight and there is no friction at the fulcrum.

Levers, of course, do more than lift weights. Levers overcome any resistance, such as sliding a gear horizontally along a shaft, as in a tractor transmission, or application of pressure upon an object, such as with a pair of pliers or tweezers.

Class 1 levers

There are three classes of simple levers, depending upon the relative positions of the fulcrum, weight and applied force.

The class 1 lever has the weight at one end and the applied force at the other, while the fulcrum is placed somewhere between. Many levers used for moving and prying objects fall into this class.

A nail lifter and a pair of shears are examples of first class levers. The claws of a nail lifter form the weight arm and the nail to be pulled is the weight. The crook in the nail lifter bears against the board and is the fulcrum, while the long handle is the force arm.

A pair of shears consists of two levers sharing a single fulcrum: the bolt that holds the shearing blades together. The handles are the force arms, the blades are the weight arms, and the material to be cut is the weight.

In that case, the length of the weight arms is measured from the fulcrum to the point where the cut is being made. For that reason, a material that’s too tough to be cut at the blade tips can be easily cut if it’s moved nearer the fulcrum bolt, making the handles, or force arms, longer than the weight arms.

Class 2 levers

A class 2 lever has the applied force at one end of the lever and the fulcrum at the other, with the weight between them. A wheelbarrow is a good example of this class of lever. The wheel and axle of a wheelbarrow provides a fulcrum, while the handles are the force arms. The load in the wheelbarrow is the weight. Because the load is closer to the fulcrum than the handles, a heavy load can be lifted.

Class 3 levers

If the fulcrum is at one end of the lever and the weight at the other, with the applied force in between, it is a class 3 lever. A pair of tweezers is an example of a third class lever. To pluck an errant eyebrow hair, milady must first grasp it firmly with a tweezers. The two tweezer halves are joined at one end, forming the fulcrum. The open ends must be brought together to firmly grasp the offending hair, which is the weight. The pressure of the fingers is the force and is applied somewhere between the fulcrum and the weight.

Variations on a theme

A lever isn’t always a straight bar. The force arm and the weight arm can be at an angle to each other, forming an angular or bell-crank lever as shown in drawing No. 3. When a claw hammer is used to pull a nail, the claws that slip under the nail head become the weight arm, while the hammer handle is the force arm. A hammer used in this manner becomes an angular lever and a horizontal pull on the handle produces a vertical lift on the nail.

In many machines, two or more levers are connected, with the force arm of one being linked to the weight arm of another as in drawing No. 4. This increases the lifting force at the weight, along with keeping the length of the lever within compact limits.

This compounding can go on indefinitely and is found in many variations. One example is the platform scale, where a heavy load on the platform is balanced by a small weight on the scale beam. In the drawing, the weight arm of the upper lever becomes, through the vertical link, the force operating on the force arm of the lower lever.

If we look at the wheels of a ground-driven mowing machine, we find that the wheel rim, spokes and axle form a continuous lever as in drawing No. 5. The wheel rim transmits the force of the forward movement of the mower to the spokes, which are the force arms. The spokes are attached to the wheel hub, which is keyed to the axle. The center of the axle is the fulcrum, and the radius of the axle is the weight arm.

In the case of the mower, the weight arm (or axle radius) is extended by the addition of a gear, which is also keyed to the axle. The radius of the drive gear becomes the weight arm, while the teeth on the circumference pull the weight. In a mower, the weight is the system of intermediate gears and the pitman that causes the cutter bar knife to reciprocate and cut hay.

Making work easier

If the wheel is driven by the gear and axle, as in the case of a tractor drive wheel, the situation is reversed. Although the center of the axle is still the fulcrum, the spokes and attached wheel rim become the weight arm, while the radius of the axle and the gear become the force arm.

While it may seem that a lever allows a lot of work to be accomplished on the one side of a fulcrum, and a lot less on the other, the “Law of Machines” prevails. This law states that “the force multiplied by the distance it moves, equals the weight multiplied by the distance it moves.”

What that means, is that, while a pound of pressure on the force arm can be made to lift 10 or 100 times as many pounds on the weight arm by varying the relative lengths of these arms, the force arm then has to move 10 or 100 times as far as the weight arm. Thus the work done on one side of the fulcrum is exactly equal to that done on the other side, provided there is no friction involved.

Thanks to old Archimedes, we’ve learned to combine levers in many forms to build machines that make our work easier and our lives more enjoyable. FC

Sam Moore grew up on a farm in western Pennsylvania. He now lives in Salem, Ohio, and collects antique tractors, implements and related items. Contact Sam by email at

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