A simple machine is a
mechanical device
A machine is a physical system using power to apply forces and control movement to perform an action. The term is commonly applied to artificial devices, such as those employing engines or motors, but also to natural biological macromolecul ...
that changes the direction or magnitude of a
force.
In general, they can be defined as the simplest mechanisms that use
mechanical advantage
Mechanical advantage is a measure of the force amplification achieved by using a tool, mechanical device or machine system. The device trades off input forces against movement to obtain a desired amplification in the output force. The model for ...
(also called
leverage) to multiply force.
Usually the term refers to the six classical simple machines that were defined by
Renaissance
The Renaissance ( , ) , from , with the same meanings. is a period in European history
The history of Europe is traditionally divided into four time periods: prehistoric Europe (prior to about 800 BC), classical antiquity (800 BC to AD ...
scientists:
*
Lever
*
Wheel and axle
*
Pulley
*
Inclined plane
*
Wedge
A wedge is a triangular shaped tool, and is a portable inclined plane, and one of the six simple machines. It can be used to separate two objects or portions of an object, lift up an object, or hold an object in place. It functions by converti ...
*
Screw
A simple machine uses a single applied force to do
work
Work may refer to:
* Work (human activity), intentional activity people perform to support themselves, others, or the community
** Manual labour, physical work done by humans
** House work, housework, or homemaking
** Working animal, an animal t ...
against a single load force. Ignoring
friction losses, the work done on the load is equal to the work done by the applied force. The machine can increase the amount of the output force, at the cost of a proportional decrease in the distance moved by the load. The ratio of the output to the applied force is called the ''
mechanical advantage
Mechanical advantage is a measure of the force amplification achieved by using a tool, mechanical device or machine system. The device trades off input forces against movement to obtain a desired amplification in the output force. The model for ...
''.
Simple machines can be regarded as the elementary "building blocks" of which all more complicated
machines (sometimes called "compound machines"
) are composed.
For example, wheels, levers, and pulleys are all used in the mechanism of a
bicycle.
The mechanical advantage of a compound machine is just the product of the mechanical advantages of the simple machines of which it is composed.
Although they continue to be of great importance in mechanics and applied science, modern mechanics has moved beyond the view of the simple machines as the ultimate building blocks of which all
machines
A machine is a physical system using power to apply forces and control movement to perform an action. The term is commonly applied to artificial devices, such as those employing engines or motors, but also to natural biological macromolecul ...
are composed, which arose in the Renaissance as a
neoclassical amplification of
ancient Greek
Ancient Greek includes the forms of the Greek language used in ancient Greece and the ancient world from around 1500 BC to 300 BC. It is often roughly divided into the following periods: Mycenaean Greek (), Dark Ages (), the Archaic p ...
texts. The great variety and sophistication of modern machine linkages, which arose during the
Industrial Revolution
The Industrial Revolution was the transition to new manufacturing processes in Great Britain, continental Europe, and the United States, that occurred during the period from around 1760 to about 1820–1840. This transition included going f ...
, is inadequately described by these six simple categories. Various post-Renaissance authors have compiled expanded lists of "simple machines", often using terms like ''basic machines'',
''compound machines'',
or ''machine elements'' to distinguish them from the classical simple machines above. By the late 1800s,
Franz Reuleaux had identified hundreds of machine elements, calling them ''simple machines''.
Modern machine theory analyzes machines as
kinematic chains composed of elementary linkages called
kinematic pair
In classical mechanics, a kinematic pair is a connection between two physical objects that imposes constraints on their relative movement (kinematics). German engineer Franz Reuleaux introduced the kinematic pair as a new approach to the study ...
s.
History
The idea of a simple machine originated with the Greek philosopher
Archimedes around the 3rd century BC, who studied the
Archimedean simple machines: lever, pulley, and
screw.
He discovered the principle of
mechanical advantage
Mechanical advantage is a measure of the force amplification achieved by using a tool, mechanical device or machine system. The device trades off input forces against movement to obtain a desired amplification in the output force. The model for ...
in the lever. Archimedes' famous remark with regard to the lever: "Give me a place to stand on, and I will move the Earth," ( el, δῶς μοι πᾶ στῶ καὶ τὰν γᾶν κινάσω) expresses his realization that there was no limit to the amount of force amplification that could be achieved by using mechanical advantage. Later Greek philosophers defined the classic five simple machines (excluding the
inclined plane) and were able to calculate their (ideal) mechanical advantage.
For example,
Heron of Alexandria
Hero of Alexandria (; grc-gre, Ἥρων ὁ Ἀλεξανδρεύς, ''Heron ho Alexandreus'', also known as Heron of Alexandria ; 60 AD) was a Greek mathematician and engineer who was active in his native city of Alexandria, Roman Egypt. He i ...
(c. 10–75 AD) in his work ''Mechanics'' lists five mechanisms that can "set a load in motion":
lever,
windlass,
pulley,
wedge
A wedge is a triangular shaped tool, and is a portable inclined plane, and one of the six simple machines. It can be used to separate two objects or portions of an object, lift up an object, or hold an object in place. It functions by converti ...
, and
screw,
and describes their fabrication and uses. However the Greeks' understanding was limited to the
statics of simple machines (the balance of forces), and did not include
dynamics, the tradeoff between force and distance, or the concept of
work
Work may refer to:
* Work (human activity), intentional activity people perform to support themselves, others, or the community
** Manual labour, physical work done by humans
** House work, housework, or homemaking
** Working animal, an animal t ...
.
During the
Renaissance
The Renaissance ( , ) , from , with the same meanings. is a period in European history
The history of Europe is traditionally divided into four time periods: prehistoric Europe (prior to about 800 BC), classical antiquity (800 BC to AD ...
the dynamics of the ''mechanical powers'', as the simple machines were called, began to be studied from the standpoint of how far they could lift a load, in addition to the force they could apply, leading eventually to the new concept of mechanical work. In 1586 Flemish engineer
Simon Stevin
Simon Stevin (; 1548–1620), sometimes called Stevinus, was a Flemish mathematician, scientist and music theorist. He made various contributions in many areas of science and engineering, both theoretical and practical. He also translated vario ...
derived the mechanical advantage of the inclined plane, and it was included with the other simple machines. The complete dynamic theory of simple machines was worked out by Italian scientist
Galileo Galilei
Galileo di Vincenzo Bonaiuti de' Galilei (15 February 1564 – 8 January 1642) was an Italian astronomer, physicist and engineer, sometimes described as a polymath. Commonly referred to as Galileo, his name was pronounced (, ). He wa ...
in 1600 in (''On Mechanics''), in which he showed the underlying mathematical similarity of the machines as force amplifiers.
He was the first to explain that simple machines do not create
energy, only transform it.
The classic rules of sliding
friction in machines were discovered by
Leonardo da Vinci (1452–1519), but were unpublished and merely documented in his notebooks, and were based on pre-Newtonian science such as believing friction was an
ethereal fluid. They were rediscovered by
Guillaume Amontons
Guillaume Amontons (31 August 1663 – 11 October 1705) was a French scientific instrument inventor and physicist. He was one of the pioneers in studying the problem of friction, which is the resistance to motion when bodies make contact. He is ...
(1699) and were further developed by
Charles-Augustin de Coulomb
Charles-Augustin de Coulomb (; ; 14 June 1736 – 23 August 1806) was a French officer, engineer, and physicist. He is best known as the eponymous discoverer of what is now called Coulomb's law, the description of the electrostatic force of attra ...
(1785).
Ideal simple machine
If a simple machine does not dissipate energy through friction, wear or deformation, then energy is conserved and it is called an ideal simple machine. In this case, the power into the machine equals the power out, and the mechanical advantage can be calculated from its geometric dimensions.
Although each machine works differently mechanically, the way they function is similar mathematically. In each machine, a force
is applied to the device at one point, and it does
work
Work may refer to:
* Work (human activity), intentional activity people perform to support themselves, others, or the community
** Manual labour, physical work done by humans
** House work, housework, or homemaking
** Working animal, an animal t ...
moving a load
at another point.
Although some machines only change the direction of the force, such as a stationary pulley, most machines multiply the magnitude of the force by a factor, the
mechanical advantage
Mechanical advantage is a measure of the force amplification achieved by using a tool, mechanical device or machine system. The device trades off input forces against movement to obtain a desired amplification in the output force. The model for ...
that can be calculated from the machine's geometry and friction.
Simple machines do not contain a source of
energy,
so they cannot do more
work
Work may refer to:
* Work (human activity), intentional activity people perform to support themselves, others, or the community
** Manual labour, physical work done by humans
** House work, housework, or homemaking
** Working animal, an animal t ...
than they receive from the input force.
A simple machine with no
friction or
elasticity is called an ''ideal machine''.
Due to
conservation of energy, in an ideal simple machine, the power output (rate of energy output) at any time
is equal to the power input
The power output equals the velocity of the load
multiplied by the load force
. Similarly the power input from the applied force is equal to the velocity of the input point
multiplied by the applied force
. Therefore,
So the mechanical advantage of an ideal machine
is equal to the ''velocity ratio'', the ratio of input velocity to output velocity
The ''velocity ratio'' is also equal to the ratio of the distances covered in any given period of time
Therefore the mechanical advantage of an ideal machine is also equal to the ''distance ratio'', the ratio of input distance moved to output distance moved
This can be calculated from the geometry of the machine. For example, the mechanical advantage and distance ratio of the
lever is equal to the ratio of its
lever arm
In physics and mechanics, torque is the rotational equivalent of linear force. It is also referred to as the moment of force (also abbreviated to moment). It represents the capability of a force to produce change in the rotational motion of ...
s.
The mechanical advantage can be greater or less than one:
* If
, the output force is greater than the input, the machine acts as a force amplifier, but the distance moved by the load
is less than the distance moved by the input force
.
* If
, the output force is less than the input, but the distance moved by the load is greater than the distance moved by the input force.
In the
screw, which uses rotational motion, the input force should be replaced by the
torque, and the velocity by the
angular velocity the shaft is turned.
Friction and efficiency
All real machines have friction, which causes some of the input power to be dissipated as heat. If
is the power lost to friction, from conservation of energy
The
mechanical efficiency
In mechanical engineering, mechanical efficiency is a dimensionless number that measures the effectiveness of a mechanism or machine in transforming the power input to the device to power output. A machine is a mechanical linkage in which for ...
of a machine (where
) is defined as the ratio of power out to the power in, and is a measure of the frictional energy losses
As above, the power is equal to the product of force and velocity, so
Therefore,
So in non-ideal machines, the mechanical advantage is always less than the velocity ratio by the product with the efficiency
. So a machine that includes friction will not be able to move as large a load as a corresponding ideal machine using the same input force.
Compound machines
A ''compound machine'' is a
machine formed from a set of simple machines connected in series with the output force of one providing the input force to the next. For example, a
bench vise consists of a lever (the vise's handle) in series with a screw, and a simple
gear train
A gear train is a mechanical system formed by mounting gears on a frame so the teeth of the gears engage.
Gear teeth are designed to ensure the pitch circles of engaging gears roll on each other without slipping, providing a smooth transmission ...
consists of a number of
gear
A gear is a rotating circular machine part having cut teeth or, in the case of a cogwheel or gearwheel, inserted teeth (called ''cogs''), which mesh with another (compatible) toothed part to transmit (convert) torque and speed. The basic ...
s (
wheels and axles) connected in series.
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, that is
Because the output force of each machine is the input of the next,
, this mechanical advantage is also given by
Thus, the mechanical advantage of the compound machine is equal to 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
Self-locking machines
In many simple machines, if the load force
on the machine is high enough in relation to the input force
, the machine will move backwards, with the load force doing work on the input force.
So these machines can be used in either direction, with the driving force applied to either input point. For example, if the load force on a lever is high enough, the lever will move backwards, moving the input arm backwards against the input force. These are called ''reversible'', ''non-locking'' or ''overhauling'' machines, and the backward motion is called ''overhauling''.
However, in some machines, if the frictional forces are high enough, no amount of load force can move it backwards, even if the input force is zero. This is called a ''self-locking'', ''nonreversible'', or ''non-overhauling'' machine.
These machines can only be set in motion by a force at the input, and when the input force is removed will remain motionless, "locked" by friction at whatever position they were left.
Self-locking occurs mainly in those machines with large areas of sliding contact between moving parts: the
screw,
inclined plane, and
wedge
A wedge is a triangular shaped tool, and is a portable inclined plane, and one of the six simple machines. It can be used to separate two objects or portions of an object, lift up an object, or hold an object in place. It functions by converti ...
:
* The most common example is a screw. In most screws, applying torque to the shaft can cause it to turn, moving the shaft linearly to do work against a load, but no amount of axial load force against the shaft will cause it to turn backwards.
* In an inclined plane, a load can be pulled up the plane by a sideways input force, but if the plane is not too steep and there is enough friction between load and plane, when the input force is removed the load will remain motionless and will not slide down the plane, regardless of its weight.
* A wedge can be driven into a block of wood by force on the end, such as from hitting it with a sledge hammer, forcing the sides apart, but no amount of
compression
Compression may refer to:
Physical science
*Compression (physics), size reduction due to forces
*Compression member, a structural element such as a column
*Compressibility, susceptibility to compression
* Gas compression
*Compression ratio, of a ...
force from the wood walls will cause it to pop back out of the block.
A machine will be self-locking if and only if its efficiency
is below 50%:
Whether a machine is self-locking depends on both the friction forces (
coefficient of static friction) between its parts, and the distance ratio
(ideal mechanical advantage). If both the friction and ideal mechanical advantage are high enough, it will self-lock.
Proof
When a machine moves in the forward direction from point 1 to point 2, with the input force doing work on a load force, from conservation of energy
the input work
is equal to the sum of the work done on the load force
and the work lost to friction
If the efficiency is below 50%
From
When the machine moves backward from point 2 to point 1 with the load force doing work on the input force, the work lost to friction
is the same
So the output work is
Thus the machine self-locks, because the work dissipated in friction is greater than the work done by the load force moving it backwards even with no input force.
Modern machine theory
Machines are studied as mechanical systems consisting of
actuators and
mechanisms that transmit forces and movement, monitored by sensors and controllers. The components of actuators and mechanisms consist of links and joints that form kinematic chains.
Kinematic chains
Simple machines are elementary examples of
kinematic chains that are used to model
mechanical systems
A machine is a physical system using power to apply forces and control movement to perform an action. The term is commonly applied to artificial devices, such as those employing engines or motors, but also to natural biological macromolecul ...
ranging from the steam engine to robot manipulators. The bearings that form the fulcrum of a lever and that allow the wheel and axle and pulleys to rotate are examples of a
kinematic pair
In classical mechanics, a kinematic pair is a connection between two physical objects that imposes constraints on their relative movement (kinematics). German engineer Franz Reuleaux introduced the kinematic pair as a new approach to the study ...
called a hinged joint. Similarly, the flat surface of an inclined plane and wedge are examples of the kinematic pair called a sliding joint. The screw is usually identified as its own kinematic pair called a helical joint.
Two levers, or cranks, are combined into a planar
four-bar linkage
In the study of mechanisms, a four-bar linkage, also called a four-bar, is the simplest closed-chain movable linkage. It consists of four bodies, called ''bars'' or ''links'', connected in a loop by four joints. Generally, the joints are config ...
by attaching a link that connects the output of one crank to the input of another. Additional links can be attached to form a
six-bar linkage or in series to form a robot.
Classification of machines
The identification of simple machines arises from a desire for a systematic method to invent new machines. Therefore, an important concern is how simple machines are combined to make more complex machines. One approach is to attach simple machines in series to obtain compound machines.
However, a more successful strategy was identified by
Franz Reuleaux, who collected and studied over 800 elementary machines. He realized that a lever, pulley, and wheel and axle are in essence the same device: a body rotating about a hinge. Similarly, an inclined plane, wedge, and screw are a block sliding on a flat surface.
[Hartenberg, R.S. & J. Denavit (1964]
Kinematic synthesis of linkages
New York: McGraw-Hill, online link from Cornell University
Cornell University is a private statutory land-grant research university based in Ithaca, New York. It is a member of the Ivy League. Founded in 1865 by Ezra Cornell and Andrew Dickson White, Cornell was founded with the intention to tea ...
.
This realization shows that it is the joints, or the connections that provide movement, that are the primary elements of a machine. Starting with four types of joints, the
revolute joint,
sliding joint,
cam joint and
gear joint, and related connections such as cables and belts, it is possible to understand a machine as an assembly of solid parts that connect these joints.
Kinematic synthesis
The design of mechanisms to perform required movement and force transmission is known as
kinematic synthesis
In mechanical engineering, kinematic synthesis (also known as mechanism synthesis) determines the size and configuration of mechanisms that shape the flow of power through a mechanical system, or machine, to achieve a desired performance. The wo ...
. This is a collection of geometric techniques for the mechanical design of
linkages,
cam and follower mechanisms and
gears and gear trains.
See also
*
Linkage (mechanical)
A mechanical linkage is an assembly of systems connected to manage forces and movement. The movement of a body, or link, is studied using geometry so the link is considered to be rigid. The connections between links are modeled as providing i ...
*
Cam and follower mechanisms
*
Gears and gear trains
*
Mechanism (engineering)
*
Rolamite, the only elementary machine discovered in the 20th century
References
{{DEFAULTSORT:Simple Machine
Mechanical engineering