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A torsion spring is a
spring Spring(s) may refer to: Common uses * Spring (season), a season of the year * Spring (device), a mechanical device that stores energy * Spring (hydrology), a natural source of water * Spring (mathematics), a geometric surface in the shape of a h ...
that works by twisting its end along its axis; that is, a flexible
elastic Elastic is a word often used to describe or identify certain types of elastomer, elastic used in garments or stretchable fabrics. Elastic may also refer to: Alternative name * Rubber band, ring-shaped band of rubber used to hold objects togethe ...
object that stores mechanical energy when it is twisted. When it is twisted, it exerts a
torque 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 th ...
in the opposite direction, proportional to the amount (angle) it is twisted. There are various types: *A torsion bar is a straight bar of metal or rubber that is subjected to twisting (
shear stress Shear stress, often denoted by ( Greek: tau), is the component of stress coplanar with a material cross section. It arises from the shear force, the component of force vector parallel to the material cross section. '' Normal stress'', on ...
) 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 or fibre (from la, fibra, links=no) is a natural or artificial substance that is significantly longer than it is wide. Fibers are often used in the manufacture of other materials. The strongest engineering materials often incorporate ...
of silk, glass, or
quartz Quartz is a hard, crystalline mineral composed of silica ( silicon dioxide). The atoms are linked in a continuous framework of SiO4 silicon-oxygen tetrahedra, with each oxygen being shared between two tetrahedra, giving an overall chemical f ...
under tension, that is twisted about its axis. *A helical torsion spring, is a metal rod or wire in the shape of a helix (coil) that is subjected to twisting about the axis of the coil by sideways forces ( bending moments) applied to its ends, twisting the coil tighter. *Clocks use a spiral wound torsion spring (a form of helical torsion spring where the coils are around each other instead of piled up) sometimes called a "clock spring" or colloquially called a mainspring. Those types of torsion springs are also used for attic stairs, clutches,
typewriter A typewriter is a mechanical or electromechanical machine for typing characters. Typically, a typewriter has an array of keys, and each one causes a different single character to be produced on paper by striking an inked ribbon selectivel ...
s and other devices that need near constant torque for large angles or even multiple revolutions.


Torsion, bending

Torsion bars and torsion fibers do work by torsion. However, the terminology can be confusing because in helical torsion spring (including clock spring), the forces acting on the wire are actually
bending In applied mechanics, bending (also known as flexure) characterizes the behavior of a slender structural element subjected to an external load applied perpendicularly to a longitudinal axis of the element. The structural element is assumed to ...
stresses, not torsional (shear) stresses. A helical torsion spring actually works by torsion when it is bent (not twisted). We will use the word "torsion" in the following for a torsion spring according to the definition given above, whether the material it is made of actually works by torsion or by bending.


Torsion coefficient

As long as they are not twisted beyond their
elastic limit In materials science and engineering, the yield point is the point on a stress-strain curve that indicates the limit of elastic behavior and the beginning of plastic behavior. Below the yield point, a material will deform elastically and wi ...
, torsion springs obey an angular form of
Hooke's law In physics, Hooke's law is an empirical law which states that the force () needed to extend or compress a spring by some distance () scales linearly with respect to that distance—that is, where is a constant factor characteristic of t ...
: : \tau = -\kappa\theta\, where \tau\, is the torque exerted by the spring in newton-meters, and \theta\, is the angle of twist from its equilibrium position in
radian The radian, denoted by the symbol rad, is the unit of angle in the International System of Units (SI) and is the standard unit of angular measure used in many areas of mathematics. The unit was formerly an SI supplementary unit (before that ...
s. \kappa\, 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 change in torque required to twist the spring through an angle of 1 radian. The torsion constant may be calculated from the geometry and various material properties. 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 The joule ( , ; symbol: J) is the unit of energy in the International System of Units (SI). It is equal to the amount of work done when a force of 1 newton displaces a mass through a distance of 1 metre in the direction of the force appli ...
s, stored in a torsion spring is: : U = \frac\kappa\theta^2


Uses

Some familiar examples of uses are the strong, helical torsion springs that operate
clothespin A clothespin (US English), or clothes peg (UK English) is a fastener used to hang up clothes for drying, usually on a clothes line. Clothespins come in many different designs. Design During the 1700s laundry was hung on bushes, limbs or lin ...
s and traditional spring-loaded-bar type
mousetrap A mousetrap is a specialized type of animal trap designed primarily to catch and, usually, kill mice. Mousetraps are usually set in an indoor location where there is a suspected infestation of rodents. Larger traps are designed to catch other s ...
s. Other uses are in the large, coiled torsion springs used to counterbalance the weight of garage doors, and a similar system is used to assist in opening the trunk (boot) cover on some sedans. Small, coiled torsion springs are often used to operate pop-up doors found on small consumer goods like
digital camera A digital camera is a camera that captures photographs in digital memory. Most cameras produced today are digital, largely replacing those that capture images on photographic film. Digital cameras are now widely incorporated into mobile devices ...
s and
compact disc The compact disc (CD) is a digital optical disc data storage format that was co-developed by Philips and Sony to store and play digital audio recordings. In August 1982, the first compact disc was manufactured. It was then released in O ...
players. Other more specific uses: *A ''
torsion bar suspension A torsion bar suspension, also known as a torsion spring suspension, is any vehicle suspension that uses a torsion bar as its main weight-bearing spring. One end of a long metal bar is attached firmly to the vehicle chassis; the opposite end term ...
'' is a thick, steel torsion-bar spring attached to the body of a vehicle at one end and to a lever arm which attaches to the axle of the wheel at the other. It absorbs road shocks as the wheel goes over bumps and rough road surfaces, cushioning the ride for the passengers. Torsion-bar suspensions are used in many modern cars and trucks, as well as military vehicles. *The ''
sway bar An anti-roll bar (roll bar, anti-sway bar, sway bar, stabilizer bar) is a part of many automobile suspensions that helps reduce the body roll of a vehicle during fast cornering or over road irregularities. It connects opposite (left/right) whee ...
'' used in many
vehicle suspension Suspension is the system of tires, tire air, springs, shock absorbers and linkages that connects a vehicle to its wheels and allows relative motion between the two. Suspension systems must support both road holding/ handling and ride ...
systems also uses the torsion spring principle. *The ''torsion pendulum'' used in torsion pendulum clocks 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 A pendulum is a weight suspended from a pivot so that it can swing freely. When a pendulum is displaced sideways from its resting, equilibrium position, it is subject to a restoring force due to gravity that will accelerate it back toward th ...
. 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. *Torsion springs consisting of twisted ropes or
sinew A tendon or sinew is a tough, high-tensile-strength band of dense fibrous connective tissue that connects muscle to bone. It is able to transmit the mechanical forces of muscle contraction to the skeletal system without sacrificing its ability ...
, were used to store
potential energy In physics, potential energy is the energy held by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors. Common types of potential energy include the gravitational potenti ...
to power several types of ancient weapons; including the Greek
ballista The ballista (Latin, from Greek βαλλίστρα ''ballistra'' and that from βάλλω ''ballō'', "throw"), plural ballistae, sometimes called bolt thrower, was an ancient missile weapon that launched either bolts or stones at a distant ...
and the Roman scorpio and catapults like the
onager The onager (; ''Equus hemionus'' ), A new species called the kiang (''E. kiang''), a Tibetan relative, was previously considered to be a subspecies of the onager as ''E. hemionus kiang'', but recent molecular studies indicate it to be a distinct ...
. *The ''
balance spring A balance spring, or hairspring, is a spring attached to the balance wheel in mechanical timepieces. It causes the balance wheel to oscillate with a resonant frequency when the timepiece is running, which controls the speed at which the wheels of ...
'' or hairspring in mechanical
watch A watch is a portable timepiece intended to be carried or worn by a person. It is designed to keep a consistent movement despite the motions caused by the person's activities. A wristwatch is designed to be worn around the wrist, attached ...
es is a fine, spiral-shaped torsion spring that pushes the
balance wheel A balance wheel, or balance, is the timekeeping device used in mechanical watches and small 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 ...
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 electric 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 chip is at the heart of many
video projectors A video projector is an image projector that receives a video signal and projects the corresponding image on a projection screen using a lens system. Video projectors use a very bright ultra-high-performance lamp (a special mercury arc lamp), X ...
. 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. * Badge tether


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 (; ; 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 ...
, who invented it in 1777, but independently invented by
John Michell John Michell (; 25 December 1724 – 21 April 1793) was an English natural philosopher and clergyman who provided pioneering insights into a wide range of scientific fields including astronomy, geology, optics, and gravitation. Considered ...
sometime before 1783. Its most well-known uses were by Coulomb to measure the
electrostatic force Coulomb's inverse-square law, or simply Coulomb's law, is an experimental law of physics that quantifies the amount of force between two stationary, electrically charged particles. The electric force between charged bodies at rest is convention ...
between charges to establish
Coulomb's Law Coulomb's inverse-square law, or simply Coulomb's law, is an experimental law of physics that quantifies the amount of force between two stationary, electrically charged particles. The electric force between charged bodies at rest is convention ...
, and by
Henry Cavendish Henry Cavendish ( ; 10 October 1731 – 24 February 1810) was an English natural philosopher and scientist who was an important experimental and theoretical chemist and physicist. He is noted for his discovery of hydrogen, which he termed "infl ...
in 1798 in the
Cavendish experiment The Cavendish experiment, performed in 1797–1798 by English 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 con ...
to measure the gravitational force between two masses to calculate the density of the Earth, leading later to a value for the
gravitational constant The gravitational constant (also known as the universal gravitational constant, the Newtonian constant of gravitation, or the Cavendish gravitational constant), denoted by the capital letter , is an empirical physical constant involved in ...
. 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 inverse-square law, or simply Coulomb's law, is an experimental law of physics that quantifies the amount of force between two stationary, electrically charged particles. The electric force between charged bodies at rest is convention ...
. To measure the unknown force, the
spring constant In physics, Hooke's law is an empirical law which states that the force () needed to extend or compress a spring by some distance () scales linearly with respect to that distance—that is, where is a constant factor characteristic of th ...
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 of the balance. If the free balance is twisted and released, it will oscillate slowly clockwise and counterclockwise as a
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 const ...
, at a frequency that depends on the
moment of inertia The moment of inertia, otherwise known as the mass moment of inertia, angular mass, second moment of mass, or most accurately, rotational inertia, of a rigid body is a quantity that determines the torque needed for a desired angular accele ...
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 A galvanometer is an electromechanical measuring instrument for electric current. Early galvanometers were uncalibrated, but improved versions, called ammeters, were calibrated and could measure the flow of current more precisely. A galvan ...
s, and the Nichols radiometer which measured the
radiation pressure Radiation pressure is the mechanical pressure exerted upon any surface due to the exchange of momentum between the object and the electromagnetic field. This includes the momentum of light or electromagnetic radiation of any wavelength that is a ...
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

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. Their behavior is analogous to translational spring-mass oscillators (see Harmonic oscillator Equivalent systems). The general
differential equation In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, ...
of motion is: :I\frac + C\frac + \kappa\theta = \tau(t) If the
damping Damping is an influence within or upon an oscillatory system that has the effect of reducing or preventing its oscillation. In physical systems, damping is produced by processes that dissipate the energy stored in the oscillation. Examples i ...
is small, C \ll \sqrt\,, as is the case with torsion pendulums and balance wheels, the frequency of vibration is very near the natural resonant frequency of the system: :f_n = \frac = \frac\sqrt\, Therefore, the period is represented by: :T_n = \frac = \frac = 2\pi \sqrt\, The general solution in the case of no drive force (\tau = 0\,), called the transient solution, is: :\theta = Ae^ \cos\, where: ::\alpha = C/2I\, ::\omega = \sqrt = \sqrt\,


Applications

The balance wheel of a mechanical watch is a harmonic oscillator whose resonant frequency f_n\, sets the rate of the watch. The resonant frequency is regulated, first coarsely by adjusting I\, with weight screws set radially into the rim of the wheel, and then more finely by adjusting \kappa\, 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 F\,, times the moment arm of the balance beam L\,, so \tau(t) = FL\,. When the oscillatory motion of the balance dies out, the deflection will be proportional to the force: :\theta = FL/\kappa\, To determine F\, it is necessary to find the torsion spring constant \kappa\,. 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: :\kappa = (2\pi f_n)^2 I\, 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 dampingC_c\,: :C_c = 2 \sqrt\,


See also

*
Beam (structure) A beam is a structural element that primarily resists loads applied laterally to the beam's axis (an element designed to carry primarily axial load would be a strut or column). Its mode of deflection is primarily by bending. The loads applied ...
* Slinky, helical toy spring


References


Bibliography

* . Detailed account of Coulomb's experiment. * . Shows pictures of the Coulomb torsion balance, and describes Coulomb's contributions to torsion technology. * . Describes the Nichols radiometer. * . Description of how torsion balances were used in petroleum prospecting, with pictures of a 1902 instrument. *


External links


Torsion balance interactive java tutorial
link broken] * ttps://web.archive.org/web/20100718003115/http://www.mssu.edu/seg-vm/pict0349.html How torsion balances were used in petroleum prospecting(web archive link)
Mechanics of torsion springs
Web archive link, accessed December 8, 2016.
Solved mechanics problems involving springs (springs in series and in parallel)Milestones in the History of Springs
{{Automotive handling Articles containing video clips Pendulums Springs (mechanical) Torque