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A spring is an
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. In everyday use the term often refers to coil springs, but there are many different spring designs. Modern springs are typically manufactured from spring steel, although some non-metallic objects like the bow are also springs. When a conventional spring, without stiffness variability features, is compressed or stretched from its resting position, it exerts an opposing
force In physics, a force is an influence that can change the motion of an object. A force can cause an object with mass to change its velocity (e.g. moving from a state of rest), i.e., to accelerate. Force can also be described intuitively as a ...
approximately proportional to its change in length (this approximation breaks down for larger deflections). The ''rate'' or ''spring constant'' of a spring is the change in the force it exerts, divided by the change in
deflection Deflection or deflexion may refer to: Board games * Deflection (chess), a tactic that forces an opposing chess piece to leave a square * Khet (game), formerly ''Deflexion'', an Egyptian-themed chess-like game using lasers Mechanics * Deflection ...
of the spring. That is, it is the
gradient In vector calculus, the gradient of a scalar-valued differentiable function of several variables is the vector field (or vector-valued function) \nabla f whose value at a point p is the "direction and rate of fastest increase". If the gr ...
of the force versus deflection curve. An
extension Extension, extend or extended may refer to: Mathematics Logic or set theory * Axiom of extensionality * Extensible cardinal * Extension (model theory) * Extension (predicate logic), the set of tuples of values that satisfy the predicate * Ext ...
or compression spring's rate is expressed in units of force divided by distance, for example or N/m or lbf/in. A torsion spring is a spring that works by twisting; when it is twisted about its axis by an angle, it produces 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 ...
proportional to the angle. A torsion spring's rate is in units of torque divided by angle, such as
N·m The newton-metre (also newton metre or newton meter; symbol N⋅m or N m) is the unit of torque (also called ) in the International System of Units (SI). One newton-metre is equal to the torque resulting from a force of one newton app ...
/ rad or ft·lbf/degree. The inverse of spring rate is compliance, that is: if a spring has a rate of 10 N/mm, it has a compliance of 0.1 mm/N. The stiffness (or rate) of springs in parallel is additive, as is the compliance of springs in series. Springs are made from a variety of elastic materials, the most common being spring steel. Small springs can be wound from pre-hardened stock, while larger ones are made from annealed steel and hardened after fabrication. Some
non-ferrous metal In metallurgy, non-ferrous metals are metals or alloys that do not contain iron ( allotropes of iron, ferrite, and so on) in appreciable amounts. Generally more costly than ferrous metals, non-ferrous metals are used because of desirable prop ...
s are also used including phosphor bronze and
titanium Titanium is a chemical element with the symbol Ti and atomic number 22. Found in nature only as an oxide, it can be reduced to produce a lustrous transition metal with a silver color, low density, and high strength, resistant to corrosion i ...
for parts requiring corrosion resistance and beryllium copper for springs carrying electrical current (because of its low electrical resistance).


History

Simple non-coiled springs were used throughout human history, e.g. the bow (and arrow). In the Bronze Age more sophisticated spring devices were used, as shown by the spread of
tweezers Tweezers are small hand tools used for grasping objects too small to be easily handled with the human fingers. Tweezers are thumb-driven forceps most likely derived from tongs used to grab or hold hot objects since the dawn of recorded histo ...
in many cultures.
Ctesibius of Alexandria Ctesibius or Ktesibios or Tesibius ( grc-gre, Κτησίβιος; fl. 285–222 BC) was a Greek inventor and mathematician in Alexandria, Ptolemaic Egypt. He wrote the first treatises on the science of compressed air and its uses in pumps (a ...
developed a method for making
bronze Bronze is an alloy consisting primarily of copper, commonly with about 12–12.5% tin and often with the addition of other metals (including aluminium, manganese, nickel, or zinc) and sometimes non-metals, such as phosphorus, or metalloids suc ...
with spring-like characteristics by producing an alloy of bronze with an increased proportion of tin, and then hardening it by hammering after it was cast. Coiled springs appeared early in the 15th century, in door locks. The first spring powered-clocks appeared in that century and evolved into the first large watches by the 16th century. In 1676 British physicist Robert Hooke postulated
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 ...
, which states that the force a spring exerts is proportional to its extension.


Types

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Classification

Springs can be classified depending on how the load force is applied to them: ; Tension/extension spring: The spring is designed to operate with a tension load, so the spring stretches as the load is applied to it. ; Compression spring: Designed to operate with a compression load, so the spring gets shorter as the load is applied to it. ; Torsion spring: Unlike the above types in which the load is an axial force, the load applied to a torsion spring is 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 ...
or twisting force, and the end of the spring rotates through an angle as the load is applied. ; Constant spring: Supported load remains the same throughout deflection cycle ; Variable spring: Resistance of the coil to load varies during compression ; Variable stiffness spring: Resistance of the coil to load can be dynamically varied for example by the control system, some types of these springs also vary their length thereby providing actuation capability as well They can also be classified based on their shape: ; Flat spring: Made of a flat spring steel. ; Machined spring: Manufactured by machining bar stock with a lathe and/or milling operation rather than a coiling operation. Since it is machined, the spring may incorporate features in addition to the elastic element. Machined springs can be made in the typical load cases of compression/extension, torsion, etc. ; Serpentine spring: A zig-zag of thick wire, often used in modern upholstery/furniture. ; Garter spring: A coiled steel spring that is connected at each end to create a circular shape.


Common types

The most common types of spring are: ; Cantilever spring: A flat spring fixed only at one end like a
cantilever A cantilever is a rigid structural element that extends horizontally and is supported at only one end. Typically it extends from a flat vertical surface such as a wall, to which it must be firmly attached. Like other structural elements, a cant ...
, while the free-hanging end takes the load. ; Coil spring: Also known as a helical spring. A spring (made by winding a wire around a cylinder) is of two types: * ''Tension'' or ''extension springs'' are designed to become longer under load. Their turns (loops) are normally touching in the unloaded position, and they have a hook, eye or some other means of attachment at each end. * ''Compression springs'' are designed to become shorter when loaded. Their turns (loops) are not touching in the unloaded position, and they need no attachment points. * ''Hollow tubing springs'' can be either extension springs or compression springs. Hollow tubing is filled with oil and the means of changing hydrostatic pressure inside the tubing such as a membrane or miniature piston etc. to harden or relax the spring, much like it happens with water pressure inside a garden hose. Alternatively tubing's cross-section is chosen of a shape that it changes its area when tubing is subjected to torsional deformation: change of the cross-section area translates into change of tubing's inside volume and the flow of oil in/out of the spring that can be controlled by valve thereby controlling stiffness. There are many other designs of springs of hollow tubing which can change stiffness with any desired frequency, change stiffness by a multiple or move like a linear actuator in addition to its spring qualities. ; Arc spring: A pre-curved or arc-shaped helical compression spring, which is able to transmit a torque around an axis. ;
Volute spring A volute spring, also known as a conical spring, is a compression spring in the form of a cone (somewhat like the classical volute decorative architectural ornament). Under compression, the coils slide past each other, thus enabling the spring to ...
: A compression coil spring in the form of a cone so that under compression the coils are not forced against each other, thus permitting longer travel. ; Balance spring: Also known as a hairspring. A delicate spiral spring used in
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, galvanometers, and places where electricity must be carried to partially rotating devices such as steering wheels without hindering the rotation. ; Leaf spring: A flat spring used in vehicle suspensions, electrical switches, and bows. ; V-spring: Used in antique
firearm A firearm is any type of gun designed to be readily carried and used by an individual. The term is legally defined further in different countries (see Legal definitions). The first firearms originated in 10th-century China, when bamboo tubes ...
mechanisms such as the wheellock,
flintlock Flintlock is a general term for any firearm that uses a flint-striking ignition mechanism, the first of which appeared in Western Europe in the early 16th century. The term may also apply to a particular form of the mechanism itself, also know ...
and percussion cap locks. Also door-lock spring, as used in antique door latch mechanisms.


Other types

Other types include: ;
Belleville washer A Belleville washer, also known as a coned-disc spring, conical spring washer, disc spring, Belleville spring or cupped spring washer, is a conical shell which can be loaded along its axis either statically or dynamically. A Belleville washer is ...
: A disc shaped spring commonly used to apply tension to a bolt (and also in the initiation mechanism of pressure-activated landmines) ; Constant-force spring: A tightly rolled ribbon that exerts a nearly constant force as it is unrolled ; Gas spring: A volume of compressed gas. ; Ideal Spring: A notional spring used in physics: it has no weight, mass, or damping losses. The force exerted by the spring is proportional to the distance the spring is stretched or compressed from its relaxed position. ; Mainspring: A spiral ribbon shaped spring used as a power store of
clockwork Clockwork refers to the inner workings of either mechanical devices called clocks and watches (where it is also called the movement) or other mechanisms that work similarly, using a series of gears driven by a spring or weight. A clockwork mech ...
mechanisms:
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,
clock A clock or a timepiece is a device used to measure and indicate time. The clock is one of the oldest human inventions, meeting the need to measure intervals of time shorter than the natural units such as the day, the lunar month and ...
s, music boxes, windup toys, and
mechanically powered flashlight A mechanically powered flashlight is a flashlight that is powered by electricity generated by the muscle power of the user, so it does not need replacement of batteries, or recharging from an electrical source. There are several types which use ...
s ; Negator spring: A thin metal band slightly concave in cross-section. When coiled it adopts a flat cross-section but when unrolled it returns to its former curve, thus producing a constant force throughout the displacement and ''negating'' any tendency to re-wind. The most common application is the retracting steel tape rule. ; Progressive rate coil springs: A coil spring with a variable rate, usually achieved by having unequal distance between turns so that as the spring is compressed one or more coils rests against its neighbour. ; Rubber band: A tension spring where energy is stored by stretching the material. ; Spring
washer Washer most commonly refers to: *Washer (hardware), a thin usually disc-shaped plate with a hole in the middle typically used with a bolt or nut *Washing machine, for cleaning clothes Washer may also refer to: *Dishwasher, a machine for cleani ...
: Used to apply a constant tensile force along the axis of a
fastener A fastener (US English) or fastening (UK English) is a hardware device that mechanically joins or affixes two or more objects together. In general, fasteners are used to create non-permanent joints; that is, joints that can be removed or disman ...
. ; Torsion spring: Any spring designed to be twisted rather than compressed or extended. Used in
torsion bar 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 termi ...
vehicle suspension systems. ; Wave spring: Any of many wave shaped springs, washers, and expanders, including linear springs, all of which are generally made with flat wire or discs that are '' marcelled'' according to industrial terms, usually by die-stamping, into a wavy regular pattern resulting in curvilinear lobes. Round wire wave springs exist as well. Types include wave washer, single turn wave spring, multi-turn wave spring, linear wave spring, marcel expander, interlaced wave spring, and nested wave spring.


Physics


Hooke's law

As long as not stretched or compressed 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 ...
, most springs obey Hooke's law, which states that the force with which the spring pushes back is linearly proportional to the distance from its equilibrium length: : F=-kx, \ where : ''x'' is the displacement vector – the distance and direction the spring is deformed from its equilibrium length. : ''F'' is the resulting force vector – the magnitude and direction of the restoring force the spring exerts : ''k'' is the rate, spring constant or force constant of the spring, a constant that depends on the spring's material and construction. The negative sign indicates that the force the spring exerts is in the opposite direction from its displacement Coil springs and other common springs typically obey Hooke's law. There are useful springs that don't: springs based on beam bending can for example produce forces that vary
nonlinear In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and many oth ...
ly with displacement. If made with constant pitch (wire thickness), conical springs have a variable rate. However, a conical spring can be made to have a constant rate by creating the spring with a variable pitch. A larger pitch in the larger-diameter coils and a smaller pitch in the smaller-diameter coils forces the spring to collapse or extend all the coils at the same rate when deformed.


Simple harmonic motion

Since force is equal to mass, ''m'', times acceleration, ''a'', the force equation for a spring obeying Hooke's law looks like: :F = m a \quad \Rightarrow \quad -k x = m a. \, The mass of the spring is small in comparison to the mass of the attached mass and is ignored. Since acceleration is simply the second
derivative In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value). Derivatives are a fundamental tool of calculus. ...
of x with respect to time, : - k x = m \frac. \, This is a second order linear
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, ...
for the displacement x as a function of time. Rearranging: :\frac + \frac x = 0, \, the solution of which is the sum of a sine and cosine: : x(t) = A \sin \left(t \sqrt \right) + B \cos \left(t \sqrt \right). \, A and B are arbitrary constants that may be found by considering the initial displacement and velocity of the mass. The graph of this function with B = 0 (zero initial position with some positive initial velocity) is displayed in the image on the right.


Energy dynamics

In simple harmonic motion of a spring-mass system, energy will fluctuate between
kinetic energy In physics, the kinetic energy of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acce ...
and
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 ...
, but the total energy of the system remains the same. A spring that obeys
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 ...
with spring constant ''k'' will have a total system energy ''E'' of: E = \left (\frac \right )kA^2 Here, A is the
amplitude The amplitude of a periodic variable is a measure of its change in a single period (such as time or spatial period). The amplitude of a non-periodic signal is its magnitude compared with a reference value. There are various definitions of am ...
of the wave-like motion that is produced by the oscillating behavior of the spring. The potential energy ''U'' of such a system can be determined through the spring constant ''k'' and its displacement ''x'': U = \left (\frac \right )kx^2 The
kinetic energy In physics, the kinetic energy of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acce ...
''K'' of an object in simple harmonic motion can be found using the mass of the attached object ''m'' and the
velocity Velocity is the directional speed of an object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time (e.g. northbound). Velocity i ...
at which the object oscillates ''v'': K = \left (\frac \right )mv^2 Since there is no energy loss in such a system, energy is always conserved and thus: E = K + U


Frequency & period

The
angular frequency In physics, angular frequency "''ω''" (also referred to by the terms angular speed, circular frequency, orbital frequency, radian frequency, and pulsatance) is a scalar measure of rotation rate. It refers to the angular displacement per unit ti ...
ω of an object in simple harmonic motion, given in radians per second, is found using the spring constant ''k'' and the mass of the oscillating object ''m':'' \omega=\sqrt The period ''T'', the amount of time for the spring-mass system to complete one full cycle, of such harmonic motion is given by: T = \frac=2\pi\sqrt The
frequency Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is eq ...
''f'', the number of oscillations per unit time, of something in simple harmonic motion is found by taking the inverse of the period: f = \frac = \frac = \frac\sqrt


Theory

In classical physics, a spring can be seen as a device that stores
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 ...
, specifically elastic potential energy, by straining the bonds between the
atom Every atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of neutrons. Only the most common variety of hydrogen has no neutrons. Every solid, liquid, gas, a ...
s of an
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 ...
material. Hooke's law of elasticity states that the extension of an elastic rod (its distended length minus its relaxed length) is linearly proportional to its tension, the
force In physics, a force is an influence that can change the motion of an object. A force can cause an object with mass to change its velocity (e.g. moving from a state of rest), i.e., to accelerate. Force can also be described intuitively as a ...
used to stretch it. Similarly, the contraction (negative extension) is proportional to the compression (negative tension). This law actually holds only approximately, and only when the deformation (extension or contraction) is small compared to the rod's overall length. For deformations beyond the
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 ...
, atomic bonds get broken or rearranged, and a spring may snap, buckle, or permanently deform. Many materials have no clearly defined elastic limit, and Hooke's law can not be meaningfully applied to these materials. Moreover, for the superelastic materials, the linear relationship between force and displacement is appropriate only in the low-strain region. Hooke's law is a mathematical consequence of the fact that the potential energy of the rod is a minimum when it has its relaxed length. Any
smooth function In mathematical analysis, the smoothness of a function is a property measured by the number of continuous derivatives it has over some domain, called ''differentiability class''. At the very minimum, a function could be considered smooth if ...
of one variable approximates a
quadratic function In mathematics, a quadratic polynomial is a polynomial of degree two in one or more variables. A quadratic function is the polynomial function defined by a quadratic polynomial. Before 20th century, the distinction was unclear between a polynomia ...
when examined near enough to its minimum point as can be seen by examining the
Taylor series In mathematics, the Taylor series or Taylor expansion of a function is an infinite sum of terms that are expressed in terms of the function's derivatives at a single point. For most common functions, the function and the sum of its Taylor ser ...
. Therefore, the force – which is the derivative of energy with respect to displacement – approximates a linear function. Force of fully compressed spring : F_ = \frac \ where : E –
Young's modulus Young's modulus E, the Young modulus, or the modulus of elasticity in tension or compression (i.e., negative tension), is a mechanical property that measures the tensile or compressive stiffness of a solid material when the force is applied ...
: d – spring wire diameter : L – free length of spring : n – number of active windings : \nuPoisson ratio : D – spring outer diameter


Zero-length springs

"Zero-length spring" is a term for a specially designed coil spring that would exert zero force if it had zero length; if there were no constraint due to the finite wire diameter of such a helical spring, it would have zero length in the unstretched condition. That is, in a line graph of the spring's force versus its length, the line passes through the origin. Obviously a coil spring cannot contract to zero length, because at some point the coils touch each other and the spring can't shorten any more. Zero length springs are made by manufacturing a coil spring with built-in tension (A twist is introduced into the wire as it is coiled during manufacture; this works because a coiled spring "unwinds" as it stretches), so if it ''could'' contract further, the equilibrium point of the spring, the point at which its restoring force is zero, occurs at a length of zero. In practice, zero length springs are made by combining a "negative length" spring, made with even more tension so its equilibrium point would be at a "negative" length, with a piece of inelastic material of the proper length so the zero force point would occur at zero length. A zero length spring can be attached to a mass on a hinged boom in such a way that the force on the mass is almost exactly balanced by the vertical component of the force from the spring, whatever the position of the boom. This creates a horizontal "pendulum" with very long oscillation period. Long-period pendulums enable seismometers to sense the slowest waves from earthquakes. The
LaCoste Lacoste S.A. is a French company, founded in 1933 by tennis player René Lacoste, and entrepreneur Mangkha. It sells clothing, footwear, sportswear, eyewear, leather goods, perfume, towels and watches. The company can be recognised by its ...
suspension with zero-length springs is also used in gravimeters because it is very sensitive to changes in gravity. Springs for closing doors are often made to have roughly zero length, so that they exert force even when the door is almost closed, so they can hold it closed firmly.


Uses

* Airsoft gun *
Aerospace Aerospace is a term used to collectively refer to the atmosphere and outer space. Aerospace activity is very diverse, with a multitude of commercial, industrial and military applications. Aerospace engineering consists of aeronautics and ast ...
*
Buckling spring A buckling spring is a type of keyswitch mechanism, popularized by IBM's keyboards for the PC, PC/AT, 5250/3270 terminals, PS/2, and other systems. It was used by IBM's Model F keyboards (for instance the AT keyboard), and the more common ...
keyboards * Educational *
Firearms A firearm is any type of gun designed to be readily carried and used by an individual. The term is legally defined further in different countries (see Legal definitions). The first firearms originated in 10th-century China, when bamboo tubes ...
* Forward or aft spring, a method of mooring a vessel to a shore fixture * Industrial Equipment *
Jewelry Jewellery ( UK) or jewelry ( U.S.) consists of decorative items worn for personal adornment, such as brooches, rings, necklaces, earrings, pendants, bracelets, and cufflinks. Jewellery may be attached to the body or the clothes. From a w ...
: Clasp mechanisms. * Lock mechanisms: Key-recognition and for coordinating the movements of various parts of the lock. * Spring mattresses *
Medical Devices A medical device is any device intended to be used for medical purposes. Significant potential for hazards are inherent when using a device for medical purposes and thus medical devices must be proved safe and effective with reasonable assura ...
* Mini Drill * Pens * Pogo Stick * Pop-open devices:
CD players A CD player is an electronic device that plays audio compact discs, which are a digital optical disc data storage format. CD players were first sold to consumers in 1982. CDs typically contain recordings of audio material such as music or au ...
,
Tape recorder An audio tape recorder, also known as a tape deck, tape player or tape machine or simply a tape recorder, is a sound recording and reproduction device that records and plays back sounds usually using magnetic tape for storage. In its present ...
s, Toasters, etc. * Reverberation in electronic organs * Slinky * Spring reverb * Spring shoes * Switchblades: Folding or sliding knives with a spring-loaded opening mechanism. * Toy * Trampoline *
Upholstery Upholstery is the work of providing furniture, especially seats, with padding, springs, webbing, and fabric or leather covers. The word also refers to the materials used to upholster something. ''Upholstery'' comes from the Middle English ...
: Upholstery coil springs *
Vehicle A vehicle (from la, vehiculum) is a machine that transports people or cargo. Vehicles include wagons, bicycles, motor vehicles (motorcycles, cars, trucks, buses, mobility scooters for disabled people), railed vehicles (trains, trams), ...
s: Vehicle suspension, Leaf springs *
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: Balance springs and in mechanical timepieces, mainsprings for winding mechanical timepieces, and spring-loaded bars for attaching the bands and the clasps.


See also

* Shock absorber * Slinky, helical spring toy *
Volute spring A volute spring, also known as a conical spring, is a compression spring in the form of a cone (somewhat like the classical volute decorative architectural ornament). Under compression, the coils slide past each other, thus enabling the spring to ...


References


Further reading

* Sclater, Neil. (2011). "Spring and screw devices and mechanisms." ''Mechanisms and Mechanical Devices Sourcebook.'' 5th ed. New York: McGraw Hill. pp. 279–299. . Drawings and designs of various spring and screw mechanisms. * Parmley, Robert. (2000). "Section 16: Springs." ''Illustrated Sourcebook of Mechanical Components.'' New York: McGraw Hill. Drawings, designs and discussion of various springs and spring mechanisms. * Warden, Tim. (2021). “Bundy 2 Alto Saxophone.” This saxophone is known for having the strongest tensioned needle springs in existence.


External links

* * *
Springs with Dynamically Variable Stiffness (patent)

Smart Springs and their Combinations (patent)
{{DEFAULTSORT:Spring (Device)