Simple machine: the story on HearLore

Simple machine

Archimedes of Syracuse declared that with a long enough lever and a place to stand, he could move the Earth. This bold statement, recorded by the later mathematician Pappus of Alexandria in the 4th century, was not merely a philosophical flourish but the first recorded articulation of mechanical advantage. Around the 3rd century BC, Archimedes studied the lever, pulley, and screw, discovering that force could be multiplied without limit if the distance from the fulcrum was increased sufficiently. His work laid the foundation for understanding how a small input force could generate a massive output force, a concept that would eventually allow humanity to move mountains, quite literally. While the Greeks understood the statics of these machines, the balance of forces, they lacked the concept of dynamics, which describes the tradeoff between force and distance or the concept of work. This gap in understanding would remain until the Renaissance, when engineers began to study how far a machine could lift a load, not just how much force it could apply.

Renaissance Mechanics

The dynamics of mechanical powers began to be studied from a new perspective during the Renaissance, shifting the focus from static balance to the actual work performed. In 1586, the Flemish engineer Simon Stevin derived the mechanical advantage of the inclined plane, adding it to the existing list of mechanisms that could set a load in motion. The complete dynamic theory of simple machines was finally worked out by the Italian scientist Galileo Galilei in 1600 in his treatise On Mechanics. Galileo demonstrated the underlying mathematical similarity of all the machines as force amplifiers and was the first to explain that simple machines do not create energy, only transform it. This insight was revolutionary because it established that a machine cannot do more work than it receives from the input force, a principle that holds true even when friction is ignored. The classic rules of sliding friction in machines were discovered by Leonardo da Vinci between 1452 and 1519, but his findings were unpublished and documented only in his notebooks, based on pre-Newtonian science that incorrectly believed friction was an ethereal fluid. These rules were not rediscovered until 1699 by Guillaume Amontons and further developed by Charles-Augustin de Coulomb in 1785.

The Six Classical Devices

Renaissance scientists defined the six classical simple machines that remain the standard building blocks of mechanics today: the lever, wheel and axle, pulley, inclined plane, wedge, and screw. Each of these devices uses a single applied force to do work against a single load force, changing either the direction or the magnitude of that force. A lever multiplies force by increasing the distance from the fulcrum, while a pulley changes the direction of the force to make lifting easier. The inclined plane allows a heavy load to be raised with less force over a longer distance, and the wedge functions as a moving inclined plane to split materials. The screw is essentially an inclined plane wrapped around a cylinder, converting rotational motion into linear force. Although these machines work differently mechanically, they function similarly in a mathematical sense, with the mechanical advantage calculated from their geometric dimensions. In an ideal simple machine that does not dissipate energy through friction, wear, or deformation, the power into the machine equals the power out, and the mechanical advantage is equal to the velocity ratio, which is the ratio of input velocity to output velocity.

Common questions

What did Archimedes of Syracuse say about moving the Earth with a lever?

Archimedes of Syracuse declared that with a long enough lever and a place to stand, he could move the Earth. This statement was recorded by the mathematician Pappus of Alexandria in the 4th century and represents the first recorded articulation of mechanical advantage. Archimedes studied the lever, pulley, and screw around the 3rd century BC to discover that force could be multiplied without limit if the distance from the fulcrum was increased sufficiently.

When did Galileo Galilei publish the complete dynamic theory of simple machines?

Galileo Galilei worked out the complete dynamic theory of simple machines in 1600 in his treatise On Mechanics. He demonstrated the underlying mathematical similarity of all machines as force amplifiers and explained that simple machines do not create energy, only transform it. This principle holds true even when friction is ignored and establishes that a machine cannot do more work than it receives from the input force.

Who discovered the classic rules of sliding friction in machines and when were they rediscovered?

Leonardo da Vinci discovered the classic rules of sliding friction in machines between 1452 and 1519, but his findings were unpublished and documented only in his notebooks. These rules were not rediscovered until 1699 by Guillaume Amontons and further developed by Charles-Augustin de Coulomb in 1785. Da Vinci based his work on pre-Newtonian science that incorrectly believed friction was an ethereal fluid.

What are the six classical simple machines defined by Renaissance scientists?

Renaissance scientists defined the six classical simple machines as the lever, wheel and axle, pulley, inclined plane, wedge, and screw. Each of these devices uses a single applied force to do work against a single load force, changing either the direction or the magnitude of that force. These machines function similarly in a mathematical sense with the mechanical advantage calculated from their geometric dimensions.

Under what condition is a machine considered self-locking or non-overhauling?

A machine will be self-locking if and only if its efficiency is below 50 percent, meaning the work dissipated in friction is greater than the work done by the load force moving it backwards even with no input force. Self-locking occurs mainly in machines with large areas of sliding contact between moving parts, such as the screw, inclined plane, and wedge. In these machines, no amount of load force can move it backwards if the frictional forces are high enough.

How is the mechanical advantage of a compound machine calculated?

The mechanical advantage of a compound machine is the ratio of the output force exerted by the last machine in the series divided by the input force applied to the first machine. Because the output force of each machine is the input of the next, the mechanical advantage is also given by the product of the mechanical advantages of the series of simple machines that form it. Similarly, the efficiency of a compound machine is also the product of the efficiencies of the series of simple machines that form it.