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Screw (simple machine)
Encyclopedia
A screw is a mechanism that converts rotational
motion to linear motion
, and a torque
(rotational force) to a linear force
. It is one of the six classical simple machine
s. The most common form consists of a cylindrical shaft with helical
grooves or ridges called threads
around the outside. The screw passes through a hole in another object or medium, with threads on the inside of the hole that mesh with the screw's threads. When the shaft of the screw is rotated relative to the stationary threads, the screw moves along its axis relative to the medium surrounding it; for example rotating a wood screw forces it into wood. In screw mechanisms, either the screw shaft can rotate through a threaded hole in a stationary object, or a threaded collar such as a nut
can rotate around a stationary screw shaft. Geometrically, a screw can be viewed as a narrow inclined plane
wrapped around a shaft.
Other mechanisms that use the same principle, also called screws, don't necessarily have a shaft or threads. For example, a corkscrew
is a helix-shaped rod with a sharp point, and an Archimedes' screw
is a water pump that uses a rotating helical chamber to move water uphill. The common principle of all screws is that a rotating helix
can cause linear motion.
A screw can amplify force; a small rotational force (torque
) on the shaft can exert a large axial force on a load. The smaller the pitch, the distance between the screw's threads, the greater the mechanical advantage
, the ratio of output to input force. Screws are widely used in threaded fastener
s to hold objects together, and in devices such as screw tops for containers, vise
s, screw jacks and screw press
es.
, and by the first century BC was used in the form of the screw press
and the Archimedes screw, but when it was invented is unknown. Greek philosopher Archytas of Tarrentum
(428 - 347 BC) was said by the Greeks to have invented the screw. The Greek philosopher Archimedes
is credited with inventing the Archimedes' screw water pump around 234 BC, although there is evidence it may have come from Egypt. Archimedes was first to study the screw as a machine, so he is sometimes considered the inventor of the screw. Greek philosophers defined the screw as one of the simple machine
s and could calculate its (ideal) mechanical advantage
. For example, Heron of Alexandria (52 CE) listed the screw as one of the five mechanisms that could "set a load in motion", defined it as an inclined plane
wrapped around a cylinder, and described its fabrication and use, including a tap
for cutting female screw threads.
Screw fasteners began to be used in the 15th century, in clocks, after screw-cutting lathe
s were developed. The screw was apparently applied to drilling and moving materials (besides water) around this time also, when images of auger
s and drills began to appear in European paintings. The complete dynamic theory of simple machines, including the screw, was worked out by Italian scientist Galileo Galilei
in 1600 in Le Meccaniche ("On Mechanics").
The fineness or coarseness of a screw's threads are defined by two closely related quantities:
In most screws, called "single start" screws, which have a single helical thread wrapped around them, the lead and pitch are equal. They only differ in "multiple start" screws, which have several intertwined threads. In these screws the lead is equal to the pitch multiplied by the number of starts. Multiple-start screws are used when a large linear motion for a given rotation is desired, for example in screw caps on bottles, and ball point pens.
direction. This is known as a right-handed (RH) thread, because it follows the right hand grip rule: when the fingers of the right hand are curled around the shaft in the direction of rotation, the thumb will point in the direction of motion of the shaft. Threads oriented in the opposite direction are known as left-handed (LH).
By common convention, right-handedness is the default handedness for screw threads. Therefore, most threaded parts and fasteners have right-handed threads. One explanation for why right-handed threads became standard is that for a right-handed person, tightening a right-handed screw with a screwdriver
is easier than tightening a left-handed screw, because it uses the stronger supinator muscle
of the arm rather than the weaker pronator
muscle. Since most people are right-handed, right-handed threads became standard on threaded fasteners. Left-handed screw threads are used in some machines and in these applications:
The screw propeller, although it shares the name screw, works on very different physical principles from the above types of screw, and the information in this article is not applicable to it.
a screw shaft moves when it is rotated through an angle of 
degrees is:
where
is the lead of the screw.
The distance ratio of a simple machine
is defined as the ratio of the distance the applied force moves to the distance the load moves. For a screw it is the ratio of the circular distance din a point on the edge of the shaft moves to the linear distance dout the shaft moves. If r is the radius of the shaft, in one turn a point on the screw's rim moves a distance of 2πr, while its shaft moves linearly by the lead distance l. So the distance ratio is
MA of a screw is defined as the ratio of axial output force Fout applied by the shaft on a load to the rotational force Fin applied to the rim of the shaft to turn it. For a screw with no friction
, (also called an ideal screw) the mechanical advantage is equal to the distance ratio:
It can be seen that the mechanical advantage of a screw depends on its lead,
. The smaller the distance between its threads, the larger the mechanical advantage, and the larger the force the screw can exert for a given applied force. However most actual screws have large amounts of friction and their machanical advantage is less than given by the above equation.
. Because of this, the input force required to turn a screw depends on how far from the shaft it is applied; the farther from the shaft, the less force is needed to turn it. The force on a screw is not usually applied at the rim as assumed above. It is often applied by some form of lever; for example a bolt is turned by a wrench
. The mechanical advantage in this case can be calculated by using the length of the lever arm for r in the above equation. This extraneous factor r can be removed from the above equation by writing it in terms of torque:
of only 15% - 20%, the rest of the work applied in turning them is lost to friction. When friction is included, the mechanical advantage is no longer equal to the distance ratio but also depends on the screw's efficiency. From conservation of energy
, the work Win done on the screw by the input force turning it is equal to the sum of the work done moving the load Wout, and the work dissipated as heat by friction
Wfric in the screw
The efficiency
η is a dimensionless number between 0 and 1 defined as the ratio of output work to input work
Work is defined as the force multiplied by the distance moved, so
and 
and therefore
or in terms of torque :
So the mechanical advantage of an actual screw is reduced from what it would be in an ideal, frictionless screw by the efficiency
. Because of their low efficiency, in powered machinery screws are not often used as linkages to transfer large amounts of power (except in lead screws) but are more often used in positioners that operate intermittently.
s which are "reciprocal" or "non locking" which means if the load force is great enough they will move backwards or "overhaul". Thus, the machine can be used in either direction. For example, in a lever
, if the force on the load end is too large it will move backwards, doing work on the applied force. Most screws are designed to be self-locking, and in the absence of torque on the shaft will stay at whatever position they are left. However, some screw mechanisms with a large enough pitch and good lubrication are not self-locking, and a very few, such as a push drill
, use the screw in the opposite direction, applying axial force to the shaft to turn the screw.
This self-locking property is one reason for the very large use of the screw in threaded fastener
s such as wood screws, sheet metal screws, stud
s and bolt
s. Tightening the fastener by turning it puts compression force on the materials or parts being fastened together, but no amount of force from the parts will cause the screw to untighten. This property is also the basis for the use of screws in screw top container lids, vise
s, C-clamp
s, and screw jacks. A heavy object can be raised by turning the jack shaft, but when the shaft is released it will stay at whatever height it is raised to.
A screw will be self locking if and only if its efficiency
is below 50%.
Whether a screw is self-locking depends on the pitch angle and the coefficient of friction of the threads; very well-lubricated, low friction threads with a large enough pitch may "overhaul".
Rotation
A rotation is a circular movement of an object around a center of rotation. A three-dimensional object rotates always around an imaginary line called a rotation axis. If the axis is within the body, and passes through its center of mass the body is said to rotate upon itself, or spin. A rotation...
motion to linear motion
Linear motion
Linear motion is motion along a straight line, and can therefore be described mathematically using only one spatial dimension. The linear motion can be of two types: uniform linear motion, with constant velocity or zero acceleration; non uniform linear motion, with variable velocity or non-zero...
, and a torque
Torque
Torque, moment or moment of force , is the tendency of a force to rotate an object about an axis, fulcrum, or pivot. Just as a force is a push or a pull, a torque can be thought of as a twist....
(rotational force) to a linear force
Force
In physics, a force is any influence that causes an object to undergo a change in speed, a change in direction, or a change in shape. In other words, a force is that which can cause an object with mass to change its velocity , i.e., to accelerate, or which can cause a flexible object to deform...
. It is one of the six classical simple machine
Simple machine
A simple machine is a mechanical device that changes the direction or magnitude of a force.In general, they can be defined as the simplest mechanisms that use mechanical advantage to multiply force. A simple machine uses a single applied force to do work against a single load force...
s. The most common form consists of a cylindrical shaft with helical
Helix
A helix is a type of smooth space curve, i.e. a curve in three-dimensional space. It has the property that the tangent line at any point makes a constant angle with a fixed line called the axis. Examples of helixes are coil springs and the handrails of spiral staircases. A "filled-in" helix – for...
grooves or ridges called threads
Screw thread
A screw thread, often shortened to thread, is a helical structure used to convert between rotational and linear movement or force. A screw thread is a ridge wrapped around a cylinder or cone in the form of a helix, with the former being called a straight thread and the latter called a tapered thread...
around the outside. The screw passes through a hole in another object or medium, with threads on the inside of the hole that mesh with the screw's threads. When the shaft of the screw is rotated relative to the stationary threads, the screw moves along its axis relative to the medium surrounding it; for example rotating a wood screw forces it into wood. In screw mechanisms, either the screw shaft can rotate through a threaded hole in a stationary object, or a threaded collar such as a nut
Nut (hardware)
A nut is a type of hardware fastener with a threaded hole. Nuts are almost always used opposite a mating bolt to fasten a stack of parts together. The two partners are kept together by a combination of their threads' friction, a slight stretch of the bolt, and compression of the parts...
can rotate around a stationary screw shaft. Geometrically, a screw can be viewed as a narrow inclined plane
Inclined plane
The inclined plane is one of the original six simple machines; as the name suggests, it is a flat surface whose endpoints are at different heights. By moving an object up an inclined plane rather than completely vertical, the amount of force required is reduced, at the expense of increasing the...
wrapped around a shaft.
Other mechanisms that use the same principle, also called screws, don't necessarily have a shaft or threads. For example, a corkscrew
Corkscrew
A corkscrew is a kitchen tool for drawing stopping corks from wine bottles. Generally, a corkscrew consists of a pointed metallic helix attached to a handle. The user grips the handle and screws the metal point into the cork, until the helix is firmly embedded, then a vertical pull on the...
is a helix-shaped rod with a sharp point, and an Archimedes' screw
Archimedes' screw
The Archimedes' screw, also called the Archimedean screw or screwpump, is a machine historically used for transferring water from a low-lying body of water into irrigation ditches...
is a water pump that uses a rotating helical chamber to move water uphill. The common principle of all screws is that a rotating helix
Helix
A helix is a type of smooth space curve, i.e. a curve in three-dimensional space. It has the property that the tangent line at any point makes a constant angle with a fixed line called the axis. Examples of helixes are coil springs and the handrails of spiral staircases. A "filled-in" helix – for...
can cause linear motion.
A screw can amplify force; a small rotational force (torque
Torque
Torque, moment or moment of force , is the tendency of a force to rotate an object about an axis, fulcrum, or pivot. Just as a force is a push or a pull, a torque can be thought of as a twist....
) on the shaft can exert a large axial force on a load. The smaller the pitch, the distance between the screw's threads, the greater the mechanical advantage
Mechanical advantage
Mechanical advantage is a measure of the force amplification achieved by using a tool, mechanical device or machine system. Ideally, the device preserves the input power and simply trades off forces against movement to obtain a desired amplification in the output force...
, the ratio of output to input force. Screws are widely used in threaded fastener
Threaded fastener
A threaded fastener is a discrete piece of hardware that has internal or external screw threads. They are usually used for the assembly of multiple parts and facilitate disassembly.The most common types are the screw and nut...
s to hold objects together, and in devices such as screw tops for containers, vise
Vise
Vise may refer to:* Miami Vise, a defunct AFL team* Vise , a mechanical screw apparatus* Vise , an architectural element* Venus In-Situ Explorer * The Vise, TV show* Visé, BelgiumPeople with the surname Vise:...
s, screw jacks and screw press
Screw press
A screw press is a type of machine press in which the ram is driven up and down by a screw. The screw shaft can be driven by a handle, or a wheel. It works by using a coarse screw to convert the rotation of the handle or drive-wheel into a small downward movement of greater force. The overhead...
es.
History
The screw was one of the last of the simple machines to be invented. It first appeared in ancient GreeceGreece
Greece , officially the Hellenic Republic , and historically Hellas or the Republic of Greece in English, is a country in southeastern Europe....
, and by the first century BC was used in the form of the screw press
Screw press
A screw press is a type of machine press in which the ram is driven up and down by a screw. The screw shaft can be driven by a handle, or a wheel. It works by using a coarse screw to convert the rotation of the handle or drive-wheel into a small downward movement of greater force. The overhead...
and the Archimedes screw, but when it was invented is unknown. Greek philosopher Archytas of Tarrentum
Archytas
Archytas was an Ancient Greek philosopher, mathematician, astronomer, statesman, and strategist. He was a scientist of the Pythagorean school and famous for being the reputed founder of mathematical mechanics, as well as a good friend of Plato....
(428 - 347 BC) was said by the Greeks to have invented the screw. The Greek philosopher Archimedes
Archimedes
Archimedes of Syracuse was a Greek mathematician, physicist, engineer, inventor, and astronomer. Although few details of his life are known, he is regarded as one of the leading scientists in classical antiquity. Among his advances in physics are the foundations of hydrostatics, statics and an...
is credited with inventing the Archimedes' screw water pump around 234 BC, although there is evidence it may have come from Egypt. Archimedes was first to study the screw as a machine, so he is sometimes considered the inventor of the screw. Greek philosophers defined the screw as one of the simple machine
Simple machine
A simple machine is a mechanical device that changes the direction or magnitude of a force.In general, they can be defined as the simplest mechanisms that use mechanical advantage to multiply force. A simple machine uses a single applied force to do work against a single load force...
s and could calculate its (ideal) mechanical advantage
Mechanical advantage
Mechanical advantage is a measure of the force amplification achieved by using a tool, mechanical device or machine system. Ideally, the device preserves the input power and simply trades off forces against movement to obtain a desired amplification in the output force...
. For example, Heron of Alexandria (52 CE) listed the screw as one of the five mechanisms that could "set a load in motion", defined it as an inclined plane
Inclined plane
The inclined plane is one of the original six simple machines; as the name suggests, it is a flat surface whose endpoints are at different heights. By moving an object up an inclined plane rather than completely vertical, the amount of force required is reduced, at the expense of increasing the...
wrapped around a cylinder, and described its fabrication and use, including a tap
Taps and dies
Taps and dies are cutting tools used to create screw threads, which is called threading. A tap is used to cut the female portion of the mating pair . A die is used to cut the male portion of the mating pair . The process of cutting threads using a tap is called tapping, whereas the process using a...
for cutting female screw threads.
Screw fasteners began to be used in the 15th century, in clocks, after screw-cutting lathe
Screw-cutting lathe
A screw-cutting lathe is a machine capable of cutting very accurate screw threads via single-point screw-cutting, which is the process of guiding the linear motion of the tool bit in a precisely known ratio to the rotating motion of the workpiece...
s were developed. The screw was apparently applied to drilling and moving materials (besides water) around this time also, when images of auger
Auger
An auger is a drilling device, or drill bit, that usually includes a rotating helical screw blade called a "flighting" to act as a screw conveyor to remove the drilled out material...
s and drills began to appear in European paintings. The complete dynamic theory of simple machines, including the screw, was worked out by Italian scientist Galileo Galilei
Galileo Galilei
Galileo Galilei , was an Italian physicist, mathematician, astronomer, and philosopher who played a major role in the Scientific Revolution. His achievements include improvements to the telescope and consequent astronomical observations and support for Copernicanism...
in 1600 in Le Meccaniche ("On Mechanics").
Lead and pitch
- The leadLead (engineering)Lead is the axial advance of a helix or screw during one complete turn The lead for a screw thread is the axial travel for a single revolution....
is defined as the linear distance the screw travels in one complete revolution (360°) of the shaft. The lead determines the mechanical advantageMechanical advantageMechanical advantage is a measure of the force amplification achieved by using a tool, mechanical device or machine system. Ideally, the device preserves the input power and simply trades off forces against movement to obtain a desired amplification in the output force...
of the screw; the smaller the lead, the higher the mechanical advantage. - The pitch is defined as the axial distance between the crests of adjacent threads.
In most screws, called "single start" screws, which have a single helical thread wrapped around them, the lead and pitch are equal. They only differ in "multiple start" screws, which have several intertwined threads. In these screws the lead is equal to the pitch multiplied by the number of starts. Multiple-start screws are used when a large linear motion for a given rotation is desired, for example in screw caps on bottles, and ball point pens.
Handedness
The helix of a screw's thread can twist in two possible directions, which is known as handedness. Most screw threads are oriented so that when seen from above, the screw shaft moves away from the viewer (the screw is tightened) when turned in a clockwiseClockwise
Circular motion can occur in two possible directions. A clockwise motion is one that proceeds in the same direction as a clock's hands: from the top to the right, then down and then to the left, and back to the top...
direction. This is known as a right-handed (RH) thread, because it follows the right hand grip rule: when the fingers of the right hand are curled around the shaft in the direction of rotation, the thumb will point in the direction of motion of the shaft. Threads oriented in the opposite direction are known as left-handed (LH).
By common convention, right-handedness is the default handedness for screw threads. Therefore, most threaded parts and fasteners have right-handed threads. One explanation for why right-handed threads became standard is that for a right-handed person, tightening a right-handed screw with a screwdriver
Screwdriver
A screwdriver is a tool for driving screws and often rotating other machine elements with the mating drive system. The screwdriver is made up of a head or tip, which engages with a screw, a mechanism to apply torque by rotating the tip, and some way to position and support the screwdriver...
is easier than tightening a left-handed screw, because it uses the stronger supinator muscle
Supinator muscle
In human anatomy, the supinator is a broad muscle in the posterior compartment of the forearm, curved around the upper third of the radius. Its function is to supinate the forearm.-Terminology:...
of the arm rather than the weaker pronator
Pronation
In anatomy, pronation is a rotational movement of the forearm at the radioulnar joint, or of the foot at the subtalar and talocalcaneonavicular joints. For the forearm, when standing in the anatomical position, pronation will move the palm of the hand from an anterior-facing position to a...
muscle. Since most people are right-handed, right-handed threads became standard on threaded fasteners. Left-handed screw threads are used in some machines and in these applications:
- Where the rotation of a shaft would cause a conventional right-handed nut to loosen rather than to tighten due to fretting induced precessionPrecession (mechanical)Precession is the process of a round part in a round hole rotating with respect to that hole because of clearance between them and a radial force on the part that changes direction. The direction of rotation of the inner part is opposite to the direction of rotation of the radial force. Fretting...
. Examples include:- The left hand pedalBicycle pedalA bicycle pedal is the part of a bicycle that the rider pushes with their foot to propel the bicycle. It provides the connection between the cyclist's foot or shoe and the crank allowing the leg to turn the bottom bracket spindle and propel the bicycle's wheels...
on a bicycleBicycleA bicycle, also known as a bike, pushbike or cycle, is a human-powered, pedal-driven, single-track vehicle, having two wheels attached to a frame, one behind the other. A person who rides a bicycle is called a cyclist, or bicyclist....
. - The left-hand screw holding a circular sawCircular sawThe circular saw is a machine using a toothed metal cutting disc or blade. The term is also loosely used for the blade itself. The blade is a tool for cutting wood or other materials and may be hand-held or table-mounted. It can also be used to make narrow slots...
blade or a bench grinderBench grinderA bench grinder is a type of benchtop grinding machine used to drive abrasive wheels. A pedestal grinder is a larger version of a bench grinder that is mounted on a pedestal, which is bolted to the floor...
wheel on.
- The left hand pedal
- In some devices that have threads on either end, like turnbuckleTurnbuckleA turnbuckle, stretching screw or bottlescrew is a device for adjusting the tension or length of ropes, cables, tie rods, and other tensioning systems. It normally consists of two threaded eyelets, one screwed into each end of a small metal frame, one with a left-hand thread and the other with a...
s and removable pipe segments. These parts have one right-handed and one left-handed thread so that turning the piece tightens or loosens both threads at the same time. - In some gas supply connections to prevent dangerous misconnections, for example in gas welding the flammable gas supply uses left-handed threads.
- To prevent the public from unscrewing them, for example left-handed light bulbs are used in some railway and subway stations.
- Coffin lids are traditionally held on with left-handed screws.
Uses
- Because of its self-locking property (see below) the screw is widely used in threaded fastenerThreaded fastenerA threaded fastener is a discrete piece of hardware that has internal or external screw threads. They are usually used for the assembly of multiple parts and facilitate disassembly.The most common types are the screw and nut...
s to hold objects or materials together: the wood screw, sheet metal screw, studStudStud may refer to:* Stud , an animal retained for breeding* Stud farm, a property where livestock are bred-Objects:* Cleat , a protrusion on the bottom of a shoe to provide extra grip...
, and boltBolt-Fasteners:*A cap screw, as used in a bolted joint*Screw, a cylindrical threaded fastener*Dead bolt, a kind of locking mechanism*Bolt , an anchor point used in rock climbing-Weaponry:*Bolt , a mechanism used in firearms...
and nutNut (hardware)A nut is a type of hardware fastener with a threaded hole. Nuts are almost always used opposite a mating bolt to fasten a stack of parts together. The two partners are kept together by a combination of their threads' friction, a slight stretch of the bolt, and compression of the parts...
. - The self-locking property is also key to the screw's use in a wide range of other applications, such as the corkscrewCorkscrewA corkscrew is a kitchen tool for drawing stopping corks from wine bottles. Generally, a corkscrew consists of a pointed metallic helix attached to a handle. The user grips the handle and screws the metal point into the cork, until the helix is firmly embedded, then a vertical pull on the...
, screw top container lid, threaded pipeThreaded pipeA threaded pipe is a pipe with screw-threaded ends for assembly.- Tapered threads :The threaded pipes used in some plumbing installations for the delivery of gases or fluids under pressure have a threaded section that is slightly conical . This is called a "tapered thread"...
joint, viseViseVise may refer to:* Miami Vise, a defunct AFL team* Vise , a mechanical screw apparatus* Vise , an architectural element* Venus In-Situ Explorer * The Vise, TV show* Visé, BelgiumPeople with the surname Vise:...
, C-clampC-clampA C-clamp is a type of clamp device typically used to hold a wood or metal workpiece, and are often used in, but are not limited to, carpentry and welding...
, and screw jack. - Screws are also used as linkages in machines to transfer power, in the worm gear, lead screw, ball screwBall screwA ball screw is a mechanical linear actuator that translates rotational motion to linear motion with little friction. A threaded shaft provides a helical raceway for ball bearings which act as a precision screw. As well as being able to apply or withstand high thrust loads, they can do so with...
, and roller screwRoller screwA roller screw, also known as a planetary roller screw or satellite roller screw, is a low-friction precision mechanical device for converting rotational motion to linear motion, or vice versa. Planetary roller screws are most commonly used as the actuator mechanism in electro-mechanical linear...
. Due to their low efficiency, screw linkages are seldom used to carry high power, but are more often employed in low power, intermittent uses such as positioning actuatorActuatorAn actuator is a type of motor for moving or controlling a mechanism or system. It is operated by a source of energy, usually in the form of an electric current, hydraulic fluid pressure or pneumatic pressure, and converts that energy into some kind of motion. An actuator is the mechanism by which...
s. - Rotating helical screw blades or chambers are used to move material in the Archimedes' screwArchimedes' screwThe Archimedes' screw, also called the Archimedean screw or screwpump, is a machine historically used for transferring water from a low-lying body of water into irrigation ditches...
, auger earth drillAugerAn auger is a drilling device, or drill bit, that usually includes a rotating helical screw blade called a "flighting" to act as a screw conveyor to remove the drilled out material...
, and screw conveyorScrew conveyorA screw conveyor or auger conveyor is a mechanism that uses a rotating helical screw blade, called a "flighting", usually within a tube, to move liquid or granular materials. They are used in many bulk handling industries...
. - The micrometerMicrometerA micrometer , sometimes known as a micrometer screw gauge, is a device incorporating a calibrated screw used widely for precise measurement of small distances in mechanical engineering and machining as well as most mechanical trades, along with other metrological instruments such as dial, vernier,...
uses a precision calibrated screw for measuring lengths with great accuracy.
The screw propeller, although it shares the name screw, works on very different physical principles from the above types of screw, and the information in this article is not applicable to it.
Distance moved
The linear distance a screw shaft moves when it is rotated through an angle of degrees is:where
is the lead of the screw.The distance ratio of a simple machine
Simple machine
A simple machine is a mechanical device that changes the direction or magnitude of a force.In general, they can be defined as the simplest mechanisms that use mechanical advantage to multiply force. A simple machine uses a single applied force to do work against a single load force...
is defined as the ratio of the distance the applied force moves to the distance the load moves. For a screw it is the ratio of the circular distance din a point on the edge of the shaft moves to the linear distance dout the shaft moves. If r is the radius of the shaft, in one turn a point on the screw's rim moves a distance of 2πr, while its shaft moves linearly by the lead distance l. So the distance ratio is
Frictionless mechanical advantage
The mechanical advantageMechanical advantage
Mechanical advantage is a measure of the force amplification achieved by using a tool, mechanical device or machine system. Ideally, the device preserves the input power and simply trades off forces against movement to obtain a desired amplification in the output force...
MA of a screw is defined as the ratio of axial output force Fout applied by the shaft on a load to the rotational force Fin applied to the rim of the shaft to turn it. For a screw with no friction
Friction
Friction is the force resisting the relative motion of solid surfaces, fluid layers, and/or material elements sliding against each other. There are several types of friction:...
, (also called an ideal screw) the mechanical advantage is equal to the distance ratio:
It can be seen that the mechanical advantage of a screw depends on its lead,
. The smaller the distance between its threads, the larger the mechanical advantage, and the larger the force the screw can exert for a given applied force. However most actual screws have large amounts of friction and their machanical advantage is less than given by the above equation.Torque form
The rotational force applied to the screw is actually a torqueTorque
Torque, moment or moment of force , is the tendency of a force to rotate an object about an axis, fulcrum, or pivot. Just as a force is a push or a pull, a torque can be thought of as a twist....
. Because of this, the input force required to turn a screw depends on how far from the shaft it is applied; the farther from the shaft, the less force is needed to turn it. The force on a screw is not usually applied at the rim as assumed above. It is often applied by some form of lever; for example a bolt is turned by a wrenchWrench
A wrench or spanner is a tool used to provide grip and mechanical advantage in applying torque to turn objects—usually rotary fasteners, such as nuts and bolts—or keep them from turning....
. The mechanical advantage in this case can be calculated by using the length of the lever arm for r in the above equation. This extraneous factor r can be removed from the above equation by writing it in terms of torque:
Actual mechanical advantage and efficiency
Because of the large area of sliding contact between the moving and stationary threads, screws typically have large frictional energy losses. Even well-lubricated jack screws have efficienciesMechanical efficiency
Mechanical efficiency measures the effectiveness of a machine in transforming the energy and power that is input to the device into an output force and movement...
of only 15% - 20%, the rest of the work applied in turning them is lost to friction. When friction is included, the mechanical advantage is no longer equal to the distance ratio but also depends on the screw's efficiency. From conservation of energy
Conservation of energy
The nineteenth century law of conservation of energy is a law of physics. It states that the total amount of energy in an isolated system remains constant over time. The total energy is said to be conserved over time...
, the work Win done on the screw by the input force turning it is equal to the sum of the work done moving the load Wout, and the work dissipated as heat by friction
Friction
Friction is the force resisting the relative motion of solid surfaces, fluid layers, and/or material elements sliding against each other. There are several types of friction:...
Wfric in the screw
The efficiency
Mechanical efficiency
Mechanical efficiency measures the effectiveness of a machine in transforming the energy and power that is input to the device into an output force and movement...
η is a dimensionless number between 0 and 1 defined as the ratio of output work to input work
Work is defined as the force multiplied by the distance moved, so
and and therefore or in terms of torque :So the mechanical advantage of an actual screw is reduced from what it would be in an ideal, frictionless screw by the efficiency
. Because of their low efficiency, in powered machinery screws are not often used as linkages to transfer large amounts of power (except in lead screws) but are more often used in positioners that operate intermittently.Self-locking property
The large frictional forces due to the large area of sliding contact between the threads cause most screws to be "self-locking", also called "non-reciprocal" or "non-overhauling". This means that applying a torque to the shaft will cause it to turn, but no amount of axial load force against the shaft will cause it to turn back the other way, even if the applied torque is zero. This is in contrast to some other simple machineSimple machine
A simple machine is a mechanical device that changes the direction or magnitude of a force.In general, they can be defined as the simplest mechanisms that use mechanical advantage to multiply force. A simple machine uses a single applied force to do work against a single load force...
s which are "reciprocal" or "non locking" which means if the load force is great enough they will move backwards or "overhaul". Thus, the machine can be used in either direction. For example, in a lever
Lever
In physics, a lever is a rigid object that is used with an appropriate fulcrum or pivot point to either multiply the mechanical force that can be applied to another object or resistance force , or multiply the distance and speed at which the opposite end of the rigid object travels.This leverage...
, if the force on the load end is too large it will move backwards, doing work on the applied force. Most screws are designed to be self-locking, and in the absence of torque on the shaft will stay at whatever position they are left. However, some screw mechanisms with a large enough pitch and good lubrication are not self-locking, and a very few, such as a push drill
Drill
A drill or drill motor is a tool fitted with a cutting tool attachment or driving tool attachment, usually a drill bit or driver bit, used for drilling holes in various materials or fastening various materials together with the use of fasteners. The attachment is gripped by a chuck at one end of...
, use the screw in the opposite direction, applying axial force to the shaft to turn the screw.
Threaded fastener
A threaded fastener is a discrete piece of hardware that has internal or external screw threads. They are usually used for the assembly of multiple parts and facilitate disassembly.The most common types are the screw and nut...
s such as wood screws, sheet metal screws, stud
Stud
Stud may refer to:* Stud , an animal retained for breeding* Stud farm, a property where livestock are bred-Objects:* Cleat , a protrusion on the bottom of a shoe to provide extra grip...
s and bolt
Bolt
-Fasteners:*A cap screw, as used in a bolted joint*Screw, a cylindrical threaded fastener*Dead bolt, a kind of locking mechanism*Bolt , an anchor point used in rock climbing-Weaponry:*Bolt , a mechanism used in firearms...
s. Tightening the fastener by turning it puts compression force on the materials or parts being fastened together, but no amount of force from the parts will cause the screw to untighten. This property is also the basis for the use of screws in screw top container lids, vise
Vise
Vise may refer to:* Miami Vise, a defunct AFL team* Vise , a mechanical screw apparatus* Vise , an architectural element* Venus In-Situ Explorer * The Vise, TV show* Visé, BelgiumPeople with the surname Vise:...
s, C-clamp
C-clamp
A C-clamp is a type of clamp device typically used to hold a wood or metal workpiece, and are often used in, but are not limited to, carpentry and welding...
s, and screw jacks. A heavy object can be raised by turning the jack shaft, but when the shaft is released it will stay at whatever height it is raised to.
A screw will be self locking if and only if its efficiency
is below 50%.Whether a screw is self-locking depends on the pitch angle and the coefficient of friction of the threads; very well-lubricated, low friction threads with a large enough pitch may "overhaul".