Torsion spring - AbsoluteAstronomy.com

A torsion spring is a spring

Spring (device)

A spring is an elastic object used to store mechanical energy. Springs are usually made out of spring steel. Small springs can be wound from pre-hardened stock, while larger ones are made from annealed steel and hardened after fabrication...

that works by torsion

Torsion (mechanics)

In solid mechanics, torsion is the twisting of an object due to an applied torque. In sections perpendicular to the torque axis, the resultant shear stress in this section is perpendicular to the radius....

or twisting; that is, a flexible elastic

Elasticity (physics)

In physics, elasticity is the physical property of a material that returns to its original shape after the stress that made it deform or distort is removed. The relative amount of deformation is called the strain....

object that stores mechanical energy

Mechanical energy

In physics, mechanical energy is the sum of potential energy and kinetic energy present in the components of a mechanical system. It is the energy associated with the motion and position of an object. The law of conservation of energy states that in an isolated system that is only subject to...

when it is twisted. The amount of force (actually 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....

) it exerts is proportional to the amount it is twisted. There are two types. A torsion bar is a straight bar of metal or rubber that is subjected to twisting (shear stress

Shear stress

A shear stress, denoted \tau\, , is defined as the component of stress coplanar with a material cross section. Shear stress arises from the force vector component parallel to the cross section...

) about its axis by torque applied at its ends. A more delicate form used in sensitive instruments, called a torsion fiber consists of a fiber

Fiber

Fiber is a class of materials that are continuous filaments or are in discrete elongated pieces, similar to lengths of thread.They are very important in the biology of both plants and animals, for holding tissues together....

of silk, glass, or quartz

Fused quartz

Fused quartz and fused silica are types of glass containing primarily silica in amorphous form. They are manufactured using several different processes...

under tension, that is twisted about its axis. The other type, a helical torsion spring, is a metal rod or wire in the shape of a 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...

(coil) that is subjected to twisting about the axis of the coil by sideways forces (bending moment

Bending Moment

A bending moment exists in a structural element when a moment is applied to the element so that the element bends. Moments and torques are measured as a force multiplied by a distance so they have as unit newton-metres , or pound-foot or foot-pound...

s) applied to its ends, twisting the coil tighter. This terminology can be confusing because in a helical torsion spring the forces acting on the wire are actually bending stresses, not torsional (shear) stresses.

Torsion coefficient

As long as they are not twisted beyond their elastic limit, torsion springs obey an angular form of Hooke's law

Hooke's law

In mechanics, and physics, Hooke's law of elasticity is an approximation that states that the extension of a spring is in direct proportion with the load applied to it. Many materials obey this law as long as the load does not exceed the material's elastic limit. Materials for which Hooke's law...

where

is the torque exerted by the spring in newton-meters, and

is the angle of twist from its equilibrium position in radian

Radian

Radian is the ratio between the length of an arc and its radius. The radian is the standard unit of angular measure, used in many areas of mathematics. The unit was formerly a SI supplementary unit, but this category was abolished in 1995 and the radian is now considered a SI derived unit...

is a constant with units of newton-meters / radian, variously called the spring's torsion coefficient, torsion elastic modulus, rate, or just spring constant, equal to the torque required to twist the spring through an angle of 1 radian. It is analogous to the spring constant of a linear spring. The negative sign indicates that the direction of the torque is opposite to the direction of twist.

The energy U, in joule

Joule

The joule ; symbol J) is a derived unit of energy or work in the International System of Units. It is equal to the energy expended in applying a force of one newton through a distance of one metre , or in passing an electric current of one ampere through a resistance of one ohm for one second...

s, stored in a torsion spring is:

Uses

Some familiar examples of uses are the strong helical torsion springs that operate clothespins and traditional springloaded-bar type mousetrap

Mousetrap

A mousetrap is a specialized type of animal trap designed primarily to catch mice; however, it may also trap other small animals. Mousetraps are usually set in an indoor location where there is a suspected infestation of rodents. There are various types of mousetrap, each with its own advantages...

s. Other uses are in the large coiled torsion springs used to counter-balance the weight of garage door

Garage door

A garage door is a large door on a garage that can either be opened manually or by a garage door opener. Garage doors are necessarily large to allow passage of automobiles and/or trucks.-Description:...

s, and a similar system is used to assist in opening the trunk (boot) cover

Decklid

The decklid is the cover over the trunk/boot of motor vehicles that allows access to the main storage or luggage compartment...

on some sedans. Small coiled torsion springs are often used to operate pop-up doors found on small consumer goods like digital camera

Digital camera

A digital camera is a camera that takes video or still photographs, or both, digitally by recording images via an electronic image sensor. It is the main device used in the field of digital photography...

s and compact disc

Compact Disc

The Compact Disc is an optical disc used to store digital data. It was originally developed to store and playback sound recordings exclusively, but later expanded to encompass data storage , write-once audio and data storage , rewritable media , Video Compact Discs , Super Video Compact Discs ,...

players. Other more specific uses:

Torsion bar suspension has been used in vehicle suspension
Suspension (vehicle)
Suspension is the term given to the system of springs, shock absorbers and linkages that connects a vehicle to its wheels. Suspension systems serve a dual purpose — contributing to the car's roadholding/handling and braking for good active safety and driving pleasure, and keeping vehicle occupants...

at least from the time of the 1934 Citroen Traction Avant
Citroën Traction Avant
The Citroën Traction Avant is an automobile which was produced by the French manufacturer Citroën from 1934 to 1957. About 760,000 units were produced.-Impact on the world:...

. The Volkswagen Beetle
Volkswagen Beetle
The Volkswagen Type 1, widely known as the Volkswagen Beetle or Volkswagen Bug, is an economy car produced by the German auto maker Volkswagen from 1938 until 2003...

and Porsche 911
Porsche 911
The Porsche 911 is a luxury 2-door sports coupe made by Porsche AG of Stuttgart, Germany. It has a distinctive design, rear-engined and with independent rear suspension, an evolution of the swing axle on the Porsche 356. The engine was also air-cooled until the introduction of the Type 996 in 1998...

are probably the most famous examples, but it has also been the dominant heavy armored vehicle suspension since World War II, and is now common in SUVs.

The sway bar
Sway bar
A sway bar or anti-roll bar or stabilizer bar is a part of an automobile suspension that helps reduce the roll of a vehicle that is induced by cornering or road irregularities. It connects opposite wheels together through short lever arms linked by a torsion spring...

used in many vehicle suspension
Suspension (vehicle)
Suspension is the term given to the system of springs, shock absorbers and linkages that connects a vehicle to its wheels. Suspension systems serve a dual purpose — contributing to the car's roadholding/handling and braking for good active safety and driving pleasure, and keeping vehicle occupants...

systems also uses the torsion spring principle.

The torsion pendulum used in torsion pendulum clock
Torsion pendulum clock
A torsion pendulum clock, or torsion clock, is a mechanical clock which keeps time with a mechanism called a torsion pendulum. This is a weighted disk or wheel, often a decorative wheel with 3 or 4 chrome balls on ornate spokes, suspended by a thin wire or ribbon called a torsion spring...

s is a wheel-shaped weight suspended from its center by a wire torsion spring. The weight rotates about the axis of the spring, twisting it, instead of swinging like an ordinary pendulum
Pendulum
A pendulum is a weight suspended from a pivot so that it can swing freely. When a pendulum is displaced from its resting equilibrium position, it is subject to a restoring force due to gravity that will accelerate it back toward the equilibrium position...

. The force of the spring reverses the direction of rotation, so the wheel oscillates back and forth, driven at the top by the clock's gears.

The torsion catapult
Catapult
A catapult is a device used to throw or hurl a projectile a great distance without the aid of explosive devices—particularly various types of ancient and medieval siege engines. Although the catapult has been used since ancient times, it has proven to be one of the most effective mechanisms during...

or mangonel
Mangonel
A mangonel was a type of catapult or siege engine used in the medieval period to throw projectiles at a castle's walls. The exact meaning of the term is debatable, and several possibilities have been suggested. Mangonel may also be indirectly referring to the 'mangon' a French hard stone found in...

is a medieval siege engine
Siege engine
A siege engine is a device that is designed to break or circumvent city walls and other fortifications in siege warfare. Some have been operated close to the fortifications, while others have been used to attack from a distance. From antiquity, siege engines were constructed largely of wood and...

invented by the ancient Greeks. It uses a torsion spring consisting of twisted ropes to swing an arm that throws a heavy missile at the enemy with great force.

The balance spring
Balance spring
A balance spring, or hairspring, is a part used in mechanical timepieces. The balance spring, attached to the balance wheel, controls the speed at which the wheels of the timepiece turn, and thus the rate of movement of the hands...

or hairspring in mechanical watch
Watch
A watch is a small timepiece, typically worn either on the wrist or attached on a chain and carried in a pocket, with wristwatches being the most common type of watch used today. They evolved in the 17th century from spring powered clocks, which appeared in the 15th century. The first watches were...

es is a fine spiral-shaped torsion spring that pushes the balance wheel
Balance wheel
The balance wheel is the timekeeping device used in mechanical watches and some clocks, analogous to the pendulum in a pendulum clock. It is a weighted wheel that rotates back and forth, being returned toward its center position by a spiral spring, the balance spring or hairspring...

back toward its center position as it rotates back and forth. The balance wheel and spring function similarly to the torsion pendulum above in keeping time for the watch.

The D'Arsonval movement used in mechanical pointer-type meters to measure electrical current is a type of torsion balance (see below). A coil of wire attached to the pointer twists in a magnetic field against the resistance of a torsion spring. Hooke's law ensures that the angle of the pointer is proportional to the current.

A DMD or digital micromirror device
Digital micromirror device
A digital micromirror device, or DMD, is an optical semiconductor that is the core of DLP projection technology, and was invented by Dr. Larry Hornbeck and Dr. William E. "Ed" Nelson of Texas Instruments in 1987....

chip is at the heart of many video projectors. It uses hundreds of thousands of tiny mirrors on tiny torsion springs fabricated on a silicon surface to reflect light onto the screen, forming the image.

Torsion balance

The torsion balance, also called torsion pendulum, is a scientific apparatus for measuring very weak forces, usually credited to Charles-Augustin de Coulomb

Charles-Augustin de Coulomb

Charles-Augustin de Coulomb was a French physicist. He is best known for developing Coulomb's law, the definition of the electrostatic force of attraction and repulsion. The [SI unit] of charge, the coulomb, was named after him....

, who invented it in 1777, but independently invented by John Michell

John Michell

John Michell was an English natural philosopher and geologist whose work spanned a wide range of subjects from astronomy to geology, optics, and gravitation. He was both a theorist and an experimenter....

sometime before 1783. Its most well-known uses were by Coulomb to measure the electrostatic force between charges to establish Coulomb's Law

Coulomb's law

Coulomb's law or Coulomb's inverse-square law, is a law of physics describing the electrostatic interaction between electrically charged particles. It was first published in 1785 by French physicist Charles Augustin de Coulomb and was essential to the development of the theory of electromagnetism...

, and by Henry Cavendish

Henry Cavendish

Henry Cavendish FRS was a British scientist noted for his discovery of hydrogen or what he called "inflammable air". He described the density of inflammable air, which formed water on combustion, in a 1766 paper "On Factitious Airs". Antoine Lavoisier later reproduced Cavendish's experiment and...

in 1798 in the Cavendish experiment

Cavendish experiment

The Cavendish experiment, performed in 1797–98 by British scientist Henry Cavendish was the first experiment to measure the force of gravity between masses in the laboratory, and the first to yield accurate values for the gravitational constant. Because of the unit conventions then in use,...

to measure the gravitational force between two masses to calculate the density of the Earth, leading later to a value for the gravitational constant

Gravitational constant

The gravitational constant, denoted G, is an empirical physical constant involved in the calculation of the gravitational attraction between objects with mass. It appears in Newton's law of universal gravitation and in Einstein's theory of general relativity. It is also known as the universal...

.

The torsion balance consists of a bar suspended from its middle by a thin fiber. The fiber acts as a very weak torsion spring. If an unknown force is applied at right angles to the ends of the bar, the bar will rotate, twisting the fiber, until it reaches an equilibrium where the twisting force or torque of the fiber balances the applied force. Then the magnitude of the force is proportional to the angle of the bar. The sensitivity of the instrument comes from the weak spring constant of the fiber, so a very weak force causes a large rotation of the bar.

In Coulomb's experiment, the torsion balance was an insulating rod with a metal-coated ball attached to one end, suspended by a silk thread. The ball was charged with a known charge of static electricity, and a second charged ball of the same polarity was brought near it. The two charged balls repelled one another, twisting the fiber through a certain angle, which could be read from a scale on the instrument. By knowing how much force it took to twist the fiber through a given angle, Coulomb was able to calculate the force between the balls. Determining the force for different charges and different separations between the balls, he showed that it followed an inverse-square proportionality law, now known as Coulomb's law

Coulomb's law

.

To measure the unknown force, the spring constant of the torsion fiber must first be known. This is difficult to measure directly because of the smallness of the force. Cavendish accomplished this by a method widely used since: measuring the resonant vibration period

Resonance

In physics, resonance is the tendency of a system to oscillate at a greater amplitude at some frequencies than at others. These are known as the system's resonant frequencies...

of the balance. If the free balance is twisted and released, it will oscillate slowly clockwise and counterclockwise as a harmonic oscillator

Harmonic oscillator

In classical mechanics, a harmonic oscillator is a system that, when displaced from its equilibrium position, experiences a restoring force, F, proportional to the displacement, x: \vec F = -k \vec x \, where k is a positive constant....

, at a frequency that depends on the moment of inertia of the beam and the elasticity of the fiber. Since the inertia of the beam can be found from its mass, the spring constant can be calculated.

Coulomb first developed the theory of torsion fibers and the torsion balance in his 1785 memoir, Recherches theoriques et experimentales sur la force de torsion et sur l'elasticite des fils de metal &c. This led to its use in other scientific instruments, such as galvanometer

Galvanometer

A galvanometer is a type of ammeter: an instrument for detecting and measuring electric current. It is an analog electromechanical transducer that produces a rotary deflection of some type of pointer in response to electric current flowing through its coil in a magnetic field. .Galvanometers were...

s, and the Nichols radiometer

Nichols radiometer

A Nichols radiometer was the apparatus used by Ernest Fox Nichols and Gordon Ferrie Hull in 1901 for the measurement of radiation pressure. It consisted of a pair of small silvered glass mirrors suspended in the manner of a torsion balance by a fine quartz fibre within an enclosure in which the air...

which measured the radiation pressure

Radiation pressure

Radiation pressure is the pressure exerted upon any surface exposed to electromagnetic radiation. If absorbed, the pressure is the power flux density divided by the speed of light...

of light. In the early 1900s gravitational torsion balances were used in petroleum prospecting. Today torsion balances are still used in physics experiments. In 1987, gravity researcher A.H. Cook wrote:

The most important advance in experiments on gravitation and other delicate measurements was the introduction of the torsion balance by Michell and its use by Cavendish. It has been the basis of all the most significant experiments on gravitation ever since.

Torsional harmonic oscillators

For definition of terms see end of section

Torsion balances, torsion pendulums and balance wheels are examples of torsional harmonic oscillators that can oscillate with a rotational motion about the axis of the torsion spring, clockwise and counterclockwise, in harmonic motion

Simple harmonic motion

Simple harmonic motion can serve as a mathematical model of a variety of motions, such as the oscillation of a spring. Additionally, other phenomena can be approximated by simple harmonic motion, including the motion of a simple pendulum and molecular vibration....

. Their behavior is analogous to translational spring-mass oscillators (see Harmonic oscillator#Equivalent systems). The general equation of motion is:

If the damping is small,

, as is the case with torsion pendulums and balance wheels, the frequency of vibration is very near the natural resonant frequency

Mechanical resonance

Mechanical resonance is the tendency of a mechanical system to absorb more energy when the frequency of its oscillations matches the system's natural frequency of vibration than it does at other frequencies...

of the system:

The general solution in the case of no drive force (

), called the transient solution, is:

where:

Applications

The balance wheel of a mechanical watch is a harmonic oscillator whose resonant frequency

sets the rate of the watch. The resonant frequency is regulated, first coarsely by adjusting

with weight screws set radially into the rim of the wheel, and then more finely by adjusting

with a regulating lever that changes the length of the balance spring.

In a torsion balance the drive torque is constant and equal to the unknown force to be measured

, times the moment arm of the balance beam

, so

. When the oscillatory motion of the balance dies out, the deflection will be proportional to the force:

To determine

it is necessary to find the torsion spring constant

. If the damping is low, this can be obtained by measuring the natural resonant frequency of the balance, since the moment of inertia of the balance can usually be calculated from its geometry, so:

In measuring instruments, such as the D'Arsonval ammeter movement, it is often desired that the oscillatory motion die out quickly so the steady state result can be read off. This is accomplished by adding damping to the system, often by attaching a vane that rotates in a fluid such as air or water (this is why magnetic compasses are filled with fluid). The value of damping that causes the oscillatory motion to settle quickest is called the critical damping

Damping

In physics, damping is any effect that tends to reduce the amplitude of oscillations in an oscillatory system, particularly the harmonic oscillator.In mechanics, friction is one such damping effect...

Definition of terms
Term	Unit	Definition
	radians	Angle of deflection from rest position
		Moment of inertia
		Rotational friction (damping)
		Coefficient of torsion spring
		Drive torque
	Hz	Undamped (or natural) resonant frequency
		Undamped resonant frequency in radians
	Hz	Damped resonant frequency
		Damped resonant frequency in radians
		Reciprocal of damping time constant
	rad	Phase angle of oscillation
	m	Distance from axis to where force is applied

External links

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