Simple machine
A simple machine is a mechanical device that changes the direction or the magnitude of a force. The Greek philosopher Archimedes, working around the 3rd century BC, captured the idea in a single boast. "Give me a place to stand on, and I will move the Earth," he said. In the original Greek, the line runs as a short, defiant promise. Archimedes was not bragging about strength. He was pointing at something stranger. With the right arrangement of a lever, there is no limit to how much a force can be amplified. That insight sits beneath six humble devices that Renaissance scientists eventually grouped together. How can a tool multiply force without breaking the rules of nature? Why will a screw turn under your hand but never turn itself? And how did six categories built from ancient Greek texts give way to a theory that counts machines by their joints? The answers begin with a single applied force pushing against a single load.
Renaissance scientists fixed the list at six: the lever, the wheel and axle, the pulley, the inclined plane, the wedge, and the screw. Each takes one applied force and uses it to do work against one load force. Mechanical advantage, also called leverage, is the name for what they buy you. It is the ratio of the output force to the applied force, and it can run greater than one or less than one. A force amplifier raises the output but shortens the distance the load travels. Push harder over a short stretch, and the load moves a long way with less force, or barely at all with great force. The bargain is always the same. Whatever you gain in force, you give back in distance. These six were once seen as the elementary building blocks from which every machine is assembled, a view that grew in the Renaissance as a neoclassical amplification of ancient Greek texts. By the late 1800s that picture had already started to crack.
Heron of Alexandria, who lived from about 10 to 75 AD, wrote a work called Mechanics that listed five mechanisms able to "set a load in motion": the lever, the windlass, the pulley, the wedge, and the screw. He described how to build them and what they were for. Later Greek philosophers had settled on a classic five, leaving out the inclined plane, and could calculate the ideal mechanical advantage of each. The Greeks' grasp stopped at statics, the balance of forces. They had no account of dynamics, no notion of the tradeoff between force and distance, and no concept of work. During the Renaissance, the mechanical powers, as the simple machines were then called, were studied for how far they could lift a load, not just how hard they could push. That shift gave rise to the new idea of mechanical work. In 1586 the Flemish engineer Simon Stevin derived the mechanical advantage of the inclined plane, and it joined the others on the list. The full dynamic theory arrived in 1600, when the Italian scientist Galileo Galilei published Le Mecaniche, On Mechanics. Galileo showed the underlying mathematical similarity of the machines as force amplifiers. He was the first to explain that a simple machine creates no energy and only transforms it. The classic rules of sliding friction had a stranger fate.
Leonardo da Vinci, who lived from 1452 to 1519, discovered the classic rules of sliding friction in machines. He never published them. They survived only as notes in his notebooks, resting on pre-Newtonian science, including the belief that friction was an ethereal fluid. The rules sat unread until Guillaume Amontons rediscovered them in 1699. Charles-Augustin de Coulomb developed them further in 1785. Friction matters because every real machine loses some input power to it as heat. The mechanical efficiency of a machine is the ratio of power out to power in, a measure of those frictional losses. In a machine with friction, the mechanical advantage always falls short of the velocity ratio by the factor of the efficiency. A real machine cannot move as large a load as an ideal one driven by the same input force. An ideal machine, by contrast, dissipates nothing through friction, wear, or deformation, so its power in equals its power out exactly. For such a machine, the mechanical advantage equals the velocity ratio and also the distance ratio, the ratio of input distance moved to output distance moved. Both can be read straight off the geometry, as with a lever, whose advantage equals the ratio of its lever arms. Friction does more than waste energy. In some machines, it changes whether they can move backward at all.
Turn a screw and it advances, turn it the other way and it retreats, but no amount of pushing on the screw or the nut will make either of them turn. That refusal has a name: self-locking. Many simple machines are the opposite. If the load force grows high enough relative to the input, the load does work on the input and drives the machine backward, a motion called overhauling. A lever loaded heavily enough will swing its input arm back against the input force. Self-locking machines never do this. Once the input force is removed, friction holds them motionless at whatever position they were left. The behavior shows up mainly where large areas of sliding contact meet: the screw, the inclined plane, and the wedge. On an inclined plane that is not too steep, with enough friction, a load pulled up will stay put when released rather than sliding down, whatever its weight. A wedge hammered into a block of wood with a sledge hammer forces the sides apart, yet no amount of compression from the wood walls will pop it back out. There is a sharp threshold for all of this. A machine is self-locking if and only if its efficiency falls below 50 percent. Whether it crosses that line depends on the coefficient of static friction between its parts and on the distance ratio, the ideal mechanical advantage. Make both high enough, and the machine locks itself.
A bicycle runs on simple machines stacked together: wheels, levers, and pulleys all live inside its mechanism. A machine built this way is a compound machine, formed from simple machines connected in series, the output force of one feeding the input of the next. A bench vise pairs a lever, its handle, with a screw. A simple gear train strings together several wheels and axles. The payoff compounds. The mechanical advantage of a compound machine equals the product of the mechanical advantages of the simple machines that form it. Efficiency works the same way, multiplying down the chain. Because each loss stacks on the last, a long series of imperfect machines bleeds power at every joint. This building-block view, powerful as it is, could not keep up with the machinery of the Industrial Revolution. The proliferation and sophistication of modern machine linkages outran the six tidy categories. Post-Renaissance authors compiled longer lists under names like basic machines, machine elements, and compound machines, to set them apart from the classical six. One man counted them in the hundreds.
Franz Reuleaux collected and studied over 800 elementary machines, and by the late 1800s he had identified hundreds of machine elements, which he called simple machines. The sheer number led him somewhere unexpected. A lever, a pulley, and a wheel and axle, he realized, are in essence the same device: a body rotating about a hinge. An inclined plane, a wedge, and a screw are likewise one thing: a block sliding on a flat surface. What mattered was not the device but the joint, the connection that provides movement. Modern machine theory took up that idea and now analyzes machines as kinematic chains built from elementary linkages called kinematic pairs. The bearings at the fulcrum of a lever, and those that let a wheel and axle or a pulley turn, are hinged joints. The flat surfaces of the inclined plane and wedge are sliding joints. The screw earns its own pair, the helical joint. From four joint types, the revolute, sliding, cam, and gear joints, plus cables and belts, a machine becomes an assembly of solid parts linking those joints. Two levers, or cranks, joined by a connecting link form a planar four-bar linkage. Add more links and the chain grows into a six-bar linkage, or extends in series into a robot. The design of such mechanisms, choosing the geometry that delivers the required movement and force, is called kinematic synthesis, and it reaches from the steam engine to the robot manipulator.
Common questions
What is a simple machine?
A simple machine is a mechanical device that changes the direction or magnitude of a force. It uses mechanical advantage, also called leverage, to multiply force, and the term usually refers to the six classical devices defined by Renaissance scientists.
What are the six simple machines?
The six classical simple machines are the lever, the wheel and axle, the pulley, the inclined plane, the wedge, and the screw. Renaissance scientists defined this set.
Who discovered the principle of mechanical advantage in the simple machine?
The Greek philosopher Archimedes originated the idea of a simple machine around the 3rd century BC and discovered the principle of mechanical advantage in the lever. His remark, "Give me a place to stand on, and I will move the Earth," expressed that there was no limit to the force amplification mechanical advantage could achieve.
Why is a screw a self-locking simple machine?
A screw is self-locking because friction between its large sliding surfaces prevents the load force from turning it backward. A machine is self-locking if and only if its efficiency is below 50 percent, which depends on both the static friction between parts and the ideal mechanical advantage.
What is the mechanical advantage of a compound machine?
The mechanical advantage of a compound machine equals the product of the mechanical advantages of the simple machines that form it. A compound machine connects simple machines in series, with the output force of one providing the input force to the next, as in a bench vise or a gear train.
How did Galileo and Simon Stevin advance the theory of simple machines?
In 1586 the Flemish engineer Simon Stevin derived the mechanical advantage of the inclined plane, adding it to the list. In 1600 the Italian scientist Galileo Galilei worked out the complete dynamic theory in Le Mecaniche, showing the machines' mathematical similarity as force amplifiers and explaining that they transform energy rather than create it.
How does modern machine theory describe simple machines?
Modern machine theory analyzes machines as kinematic chains composed of elementary linkages called kinematic pairs. Franz Reuleaux, who studied over 800 elementary machines, showed that levers, pulleys, and wheels and axles are bodies rotating about a hinge, while inclined planes, wedges, and screws are blocks sliding on a flat surface, making the joints the primary elements.
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