Escapement

An escapement is a mechanical linkage in mechanical watches and clocks that gives impulses to the timekeeping element and periodically releases the gear train to move forward, advancing the clock's hands. The impulse action transfers energy to the clock's timekeeping element (usually a pendulum or balance wheel) to replace the energy lost to friction during its cycle and keep the timekeeper oscillating. The escapement is driven by force from a coiled spring or a suspended weight, transmitted through the timepiece's gear train. Each swing of the pendulum or balance wheel releases a tooth of the escapement's escape wheel, allowing the clock's gear train to advance or "escape" by a fixed amount. This regular periodic advancement moves the clock's hands forward at a steady rate. At the same time, the tooth gives the timekeeping element a push, before another tooth catches on the escapement's pallet, returning the escapement to its "locked" state. The sudden stopping of the escapement's tooth is what generates the characteristic "ticking" sound heard in operating mechanical clocks and watches.

The first mechanical escapement, the verge escapement, was invented in medieval Europe during the 13th century and was the crucial innovation that led to the development of the mechanical clock. The design of the escapement has a large effect on a timepiece's accuracy, and improvements in escapement design drove improvements in time measurement during the era of mechanical timekeeping from the 13th through the 19th century.

Escapements are also used in other mechanisms besides timepieces. Manual typewriters used escapements to step the carriage as each letter (or space) was typed.

History

The invention of the escapement was an important step in the history of technology, as it made the all-mechanical clock possible.^{: p.514-515} The first all-mechanical escapement, the verge escapement, was invented in 13th-century Europe. It allowed timekeeping methods to move from continuous processes such as the flow of water in water clocks, to repetitive oscillatory processes such as the swing of pendulums, enabling more accurate timekeeping. Oscillating timekeepers are the controlling devices in all modern clocks.

Liquid-driven escapements

The earliest liquid-driven escapement was described by the Greek engineer Philo of Byzantium in the 3rd century BC in chapter 31 of his technical treatise Pneumatics, as part of a washstand. A counterweighted spoon, supplied by a water tank, tips over in a basin when full, releasing a spherical piece of pumice in the process. Once the spoon has emptied, it is pulled up again by the counterweight, closing the door on the pumice by the tightening string. Remarkably, Philo's comment that "its construction is similar to that of clocks" indicates that such escapement mechanisms were already integrated in ancient water clocks.

In China, the Tang dynasty Buddhist monk Yi Xing, along with government official Liang Lingzan, made in 723 (or 725) AD the escapement for the workings of a water-powered armillary sphere and clock drive, which was the world's first clockwork escapement. Song dynasty horologists Zhang Sixun and Su Song duly applied escapement devices for their astronomical clock towers in the 10th century, where water flowed into a container on a pivot. However, the technology later stagnated and retrogressed. According to historian Derek J. de Solla Price, the Chinese escapement spread west and was the source of Western escapement technology.

According to Ahmad Y. Hassan, a mercury escapement described in a Spanish document for Alfonso X in 1277 can be traced to earlier Arabic sources.^{[unreliable source?]} Knowledge of these mercury escapements may have spread through Europe with translations of Arabic and Spanish texts.

However, none of these were true mechanical escapements, since they still depended on the flow of liquid through a hole to measure time. In these designs, a container tipped over each time it filled up, thus advancing the clock's wheels each time an equal quantity of water was measured out. The time between releases depended on the rate of flow, as do all liquid clocks. The rate of flow of a liquid through a hole varies with temperature and viscosity changes and decreases with pressure as the level of liquid in the source container drops. The development of mechanical clocks depended on the invention of an escapement which would allow a clock's movement to be controlled by an oscillating weight, which would stay constant.

Mechanical escapements

The first mechanical escapement, the verge escapement, was used in a bell-ringing apparatus called an alarum for several centuries before it was adapted to clocks. Some sources claim that French architect Villard de Honnecourt invented the first escapement in 1237, citing a drawing of a rope linkage to turn a statue of an angel to follow the sun, found in his notebooks; however, the consensus is that this was not an escapement.

Astronomer Robertus Anglicus wrote in 1271 that clockmakers were trying to invent an escapement, but had not yet been successful. Records in financial transactions for the construction of clocks point to the late 13th century as the most likely date for when tower clock mechanisms transitioned from water clocks to mechanical escapements.^: 103-104 Most sources agree that mechanical escapement clocks existed by 1300.

However, the earliest available description of an escapement was not a verge escapement, but a variation called a strob escapement. Described in Richard of Wallingford's 1327 manuscript Tractatus Horologii Astronomici on the clock that he built at the Abbey of St. Albans, this escapement consisted of a pair of escape wheels on the same axle, with alternating radial teeth. The verge rod was suspended between them, with a short crosspiece that rotated first in one direction and then the other as the staggered teeth pushed past.^: 103-104 Although no other example is known, it is possible that this was the first clock escapement design.^: 103-104

The verge became the standard escapement used in all other early clocks and watches, and remained the only known escapement for 400 years. Its performance was limited by friction and recoil, but most importantly, the early balance wheels used in verge escapements, known as the foliot, lacked a balance spring and thus had no natural "beat", severely limiting their timekeeping accuracy.^{: p.514-515 : 124-125}

A great leap in the accuracy of escapements happened after 1657, due to the invention of the pendulum and the addition of the balance spring to the balance wheel,^: 124-125 which made the timekeepers in both clocks and watches harmonic oscillators. The resulting improvement in timekeeping accuracy enabled greater focus on the accuracy of the escapement. The next two centuries, the "golden age" of mechanical horology, saw the invention of over 300 escapement designs, although only about ten of these were ever widely used in clocks and watches.

The invention of the crystal oscillator and the quartz clock in the 1920s, which became the most accurate clock by the 1930s, shifted technological research in timekeeping to electronic methods, and escapement design ceased to play a role in advancing timekeeping precision.

Reliability

The reliability of an escapement depends on the quality of workmanship and the level of maintenance given. A poorly constructed or poorly maintained escapement will cause problems. The escapement must accurately convert the oscillations of the pendulum or balance wheel into rotation of the clock or watch gear train, and it must deliver enough energy to the pendulum or balance wheel to maintain its oscillation.

In many escapements, the unlocking of the escapement involves sliding motion; for example, in the animation shown above, the pallets of the anchor slide against the escapement wheel teeth as the pendulum swings. The pallets are often made of very hard materials such as polished stone (for example, artificial ruby), but even so, they normally require lubrication. Since lubricating oil degrades over time due to evaporation, dust, and oxidation, periodic re-lubrication is needed. If this is not done, the timepiece may work unreliably or stop altogether, and the escapement components may be subjected to rapid wear. The increased reliability of modern watches is due primarily to the higher-quality oils used for lubrication. Lubricant lifetimes can be greater than five years in a high-quality watch.

Some escapements avoid sliding friction, such as the grasshopper escapement of John Harrison in the 18th century. These designs may avoid the need for lubrication in the escapement (though it does not obviate the requirement for lubrication of other parts of the gear train).

Accuracy

The accuracy of a mechanical clock is dependent on the accuracy of the timing device. If this is a pendulum, then the pendulum's period of swing determines the accuracy. If the pendulum rod is made of metal, it will expand and contract with heat, lengthening or shortening the pendulum; this changes the time taken for a swing. Special alloys are used in expensive pendulum-based clocks to minimize this distortion. The degrees of arc in which a pendulum may swing varies; highly accurate pendulum-based clocks have very small arcs in order to minimize the circular error.

Pendulum-based clocks can achieve outstanding accuracy. Even into the 20th century, pendulum-based clocks were reference timepieces in laboratories.

Escapements play a big part in accuracy as well. The precise point in the pendulum's travel at which impulse is supplied will affect how closely to time the pendulum will swing. Ideally, the impulse should be evenly distributed on either side of the lowest point of the pendulum's swing. This is called "being in beat." This is because pushing a pendulum when it is moving towards mid-swing makes it gain, whereas pushing it while it is moving away from mid-swing makes it lose. If the impulse is evenly distributed then it gives energy to the pendulum without changing the time of its swing.

The pendulum's period depends slightly on the size of the swing. If the amplitude changes from 4° to 3°, the period of the pendulum will decrease by about 0.013 percent, which translates into a gain of about 12 seconds per day. This is caused by the restoring force on the pendulum being circular not linear; thus, the period of the pendulum is only approximately linear in the regime of the small angle approximation. To be time-independent, the path must be cycloidal. To minimize the effect with amplitude, pendulum swings are kept as small as possible.

As a rule, whatever the method of impulse, the action of the escapement should have the smallest effect on the oscillator that can be achieved. This effect, which all escapements have to a larger or smaller degree, is known as the escapement error.

Any escapement with sliding friction will need lubrication, but as this deteriorates the friction will increase, and, perhaps, insufficient power will be transferred to the timing device. If the timing device is a pendulum, the increased frictional forces will decrease the Q factor, increasing the resonance band, and decreasing its precision. For spring-driven clocks, the impulse force applied by the spring changes as the spring is unwound, following Hooke's law. For gravity-driven clocks, the impulse force also increases as the driving weight falls and more chain suspends the weight from the gear train; in practice, however, this effect is only seen in large public clocks, and it can be avoided by a closed-loop chain.

Watches and smaller clocks do not use pendulums as the timing device. Instead, they use a balance spring: a fine spring connected to a metal balance wheel that oscillates (rotates back and forth). Most modern mechanical watches have a working frequency of 3–4 Hz (oscillations per second) or 6–8 beats per second (21,600–28,800 beats per hour; bph). Faster or slower speeds are used in some watches (33,600 bph, or 19,800 bph). The working frequency depends on the balance spring's stiffness (spring constant); to keep time, the stiffness should not vary with temperature. Consequently, balance springs use sophisticated alloys; in this area, watchmaking is still advancing. As with the pendulum, the escapement must provide a small kick each cycle to keep the balance wheel oscillating. Also, the same lubrication problem occurs over time; the watch will lose accuracy (typically it will speed up) when the escapement lubrication starts to fail.^{[citation needed]}

Pocket watches were the predecessor of modern wristwatches. Pocket watches, being in the pocket, were usually in a vertical orientation. Gravity causes some loss of accuracy as it magnifies over time any lack of symmetry in the weight of the balance. The tourbillon was invented to minimize this: the balance and spring are put in a cage that rotates (typically but not necessarily, once a minute), smoothing gravitational distortions. This very clever and sophisticated clockwork is a prized complication in wristwatches, even though the natural movement of the wearer tends to smooth gravitational influences anyway.

The most accurate commercially produced mechanical clock was the electromechanical Shortt-Synchronome free pendulum clock invented by W. H. Shortt in 1921, which had an uncertainty of about 1 second per year. The most accurate mechanical clock to date is probably the electromechanical Littlemore Clock, built by noted archaeologist E. T. Hall in the 1990s. In Hall's paper, he reports an uncertainty of 3 parts in 10⁹ measured over 100 days (an uncertainty of about 0.02 seconds over that period). Both of these clocks are electromechanical clocks: they use a pendulum as the timekeeping element, but electrical power rather than a mechanical gear train to supply energy to the pendulum.

Theory of escapements

Resonance

The timekeeping element in mechanical clocks and watches, the pendulum or balance wheel, is in physics called a harmonic oscillator (resonator).^: 515 It consists of a mass which is returned to its equilibrium position by a restoring force proportional to its displacement. Its advantage for timekeeping is that it oscillates preferentially at a specific resonant frequency ${\displaystyle f}$ or period independent of the width (amplitude) of swing, dependent only on its physical characteristics, and resists oscillating at other rates.^: 37 The resonant frequency is determined by the moment of inertia of the resonator and the restoring force: in balance wheels the elasticity of the hairspring, in pendulums gravitational force.^: 516-517

Feedback oscillator

The escapement is a feedback control device, the drive force is triggered each time the resonator reaches a specific point in its cycle. The resonator (pendulum or balance wheel) and escapement together form a mechanical feedback oscillator, analogous to the electronic oscillator circuit in a quartz watch.^: 39 It is driven by the continuous force (torque) of the timepiece's mainspring or weights, transmitted through the wheel train. The job of the escapement is to apply this force in short pushes (impulses) to the pendulum or balance wheel to maintain its oscillating motion, so it doesn't stop, with minimal disturbance to the period.

Escapements are challenging to understand because they are bidirectional devices: energy (impulses) to keep the oscillator going passes through the escapement from the wheel train to the oscillator, but timing signals, the locking and release of the escape wheel, which control how fast the wheel train and clock hands advance, pass in the opposite direction from the oscillator to the wheel train.

Q factor

The interaction of the escapement with the oscillator inevitably disturbs its natural swing, changing the period slightly. In precision clocks and watches this is often the major cause of inaccuracy. The escapement must interact with the oscillator to perform two functions each swing: when triggered at a certain point in the oscillator's swing it releases the clock's wheels to move forward a fixed amount, and applies an impulse force to the oscillator to replace the small amount of energy lost to friction each cycle.

How much error the escapement impulses cause depends on the oscillator's resonance curve. This curve is not infinitely "sharp". It has a small natural frequency range around its resonant frequency called the resonance width ${\displaystyle W}$.^: 43–44 In operation the actual frequency of the oscillator can vary randomly within this range in response to variations in the impulse of the escapement, but outside this frequency range the oscillator does not work at all.^: 47

The measure of the possible accuracy of a harmonic oscillator as a timekeeper is a dimensionless parameter called the Q factor,^: 41 which is equal to the resonant frequency ${\displaystyle f}$ divided by the resonance width

${\displaystyle Q={f \over W}}$

The larger the ${\displaystyle Q}$ factor, the smaller the resonance width as a fraction of the resonant frequency so the more precisely the oscillator regulates the rate of the timepiece.

The ${\displaystyle Q}$ factor depends on how much friction the oscillator has, how many swings it makes before it runs down when it is swinging freely.^: 44–45 The less friction the higher the ${\displaystyle Q}$. The ${\displaystyle Q}$ is equal to 2π times the ratio of the stored energy in the pendulum or balance wheel to the energy lost to friction during each cycle, which is equal to the energy added by the escapement impulse each cycle. So the larger the ${\displaystyle Q}$ is, the smaller the energy loss, the smaller the impulse that has to be applied each cycle to keep it oscillating, and the smaller the disturbance to the oscillator's natural motion.^: 44–45 The ${\displaystyle Q}$ of balance wheels is around 300, that of pendulums is 10³ - 10⁵, while that of quartz crystals in quartz clocks is 10⁵ - 10⁶. This explains why balance wheels are generally less accurate timekeepers than pendulums, which are less accurate than quartz clocks.

Isochronism

If the impulse applied by the escapement could be identical and applied at the identical point each cycle, the response of the oscillator would be identical and its period would be constant, and the escapement would not cause any inaccuracy. However this is not possible. There are unavoidable small variations in the drive force applied to the escapement in all timepieces, due to causes such as the mainspring running down, variations in lubrication viscosity with temperature, lubrication drying up, accumulation of dirt and corrosion, changes in friction due to wear, thermal expansion of parts with temperature changes, and "positional error" in watches: changing friction when the watch is turned and the weight of gear wheel arbors presses against bearing surfaces.

Therefore the goal of escapement design is to apply the impulse in a way that minimizes the change in period with changes in drive force. This is called isochronism. No escapement is completely isochronous, but the less a change in drive force disturbs the oscillator, the more accurate the timepiece can be.

Even if the escapement operation were perfectly isochronous, the pendulum or balance wheel itself inevitably has small inherent departures from isochronism, caused by failure of the restoring force to be exactly proportional to amplitude. In balance wheels this is due to small nonlinearities in the balance spring. In pendulums this is due to circular error, a small increase in the period of swing with amplitude.

The Airy condition

In 1826 George Biddell Airy showed that for maximum isochronism the best place in its cycle to apply the impulse to a harmonic oscillator is at its equilibrium position; in a pendulum at the bottom of its swing, and in a balance wheel as it passes through its center rest position, where the restoring force of the spring is zero. In contrast, applying an impulse force to the oscillator at the extremes of its swing causes maximum disturbance to its motion. Airy proved that, if driven by an impulse symmetrical about its equilibrium point, an ideal harmonic oscillator is isochronous; its period is independent of its drive force and amplitude of swing. The best escapements such as the deadbeat and the lever approximate this condition.

Detachment

Since the force of the escapement on the oscillator is the source of error in precision timepieces, in general the more the oscillator is left undisturbed to swing freely during its cycle by the escapement, the more accurate it can be. Escapements are classified by how much of the oscillator's cycle the escapement exerts force (impulse) on it:

• In "frictional" escapements, like the verge and anchor escapement, the escape wheel teeth are pushing on the oscillator throughout its cycle, by sliding friction on the pallets. This disturbs the oscillator, so these are less accurate.^: 144
• In "frictional-rest" escapements, like the duplex, cylinder, and deadbeat escapement, the oscillator is only impulsed during part of its cycle, but the escapement makes sliding frictional contact with the oscillator during the rest of the cycle.^: 655 These can be more accurate, depending on the amount of friction.
• In "detached" escapements, such as the Riefler, lever and chronometer escapement, the escapement linkage does not contact the oscillator except during the impulse period in the center of its swing, so these are among the most accurate escapements.^: 114

A major source of inaccuracy is friction between the sliding parts of the escapement; the escape wheel tooth sliding as it pushes on the pallet. In precision timepieces the pallet surfaces are made of jewels, principally synthetic sapphire, whose ultrahard surfaces have only 10-20% of the coefficient of friction of metal on metal. The surfaces are lubricated to reduce friction further. In the most accurate escapements, such as the detent escapement, the duplex escapement, and the coaxial escapement, the escape wheel tooth moves almost parallel to the pallet during impulse, reducing the friction, and do not require lubrication.

Mechanical escapements

Since 1658 when the introduction of the pendulum and balance spring made accurate timepieces possible, it has been estimated that more than three hundred different mechanical escapements have been devised, but only about 10 have seen widespread use. These are described below. In the 20th century, electric timekeeping methods replaced mechanical clocks and watches, so escapement design became a little-known curiosity.

Verge escapement

Verge escapement showing crown wheel (c), verge rod (v), and pallets (p,q). Orientation is shown for use with a pendulum. When used with a foliot, the wheel and rod are vertical.

Verge and foliot of De Vick clock, built 1379, Paris