The balance wheel appeared with the first mechanical clocks, in 14th century Europe, but it seems unknown exactly when or where it was first used. It is an improved version of the foliot, a primitive inertial timekeeper consisting of a straight bar with weights on the ends. The foliot weights could be slid in or out on the bar, to adjust the rate of the clock. The first clocks in northern Europe used foliots, while those in southern Europe used balance wheels. As clocks were made smaller, first as bracket clocks and lantern clocks and then as the first large watches after 1500, balance wheels began to be used in place of foliots. Since more of its weight is located on the rim away from the axis, a balance wheel could have a larger moment of inertia than a foliot of the same size, and keep better time. The wheel shape also had less air resistance, and its geometry partly compensated for thermal expansion error due to temperature changes.
These early balance wheels were crude timekeepers because they lacked the other essential element: the balance spring. Early balance wheels rotated freely in each direction until the escapement pushed it back the other way. This made the timekeeping strongly dependent on the driving force, so the watch slowed down as the mainspring unwound. A way forward opened when it was noticed that springy hog bristle curbs, added to limit the rotation of the wheel, increased its accuracy. Robert Hooke first applied a metal spring to the balance in 1658 and Jean de Hautefeuille and Christian Huygens improved it to its present spiral form in 1674 The addition of the spring made the balance wheel a harmonic oscillator, the basis of every modern clock, with a natural resonance frequency or ‘beat’ resistant to changes in the drive force or friction. This crucial innovation greatly increased the accuracy of watches, from several hours per day to perhaps 10 minutes per day, changing them from expensive novelties into useful timekeepers.
A simpler solution was devised around 1765 by Pierre Le Roy, and improved by John Arnold, and Thomas Earnshaw: the Earnshaw or compensating balance wheel. The key was to make the balance wheel change size with temperature. If the balance could be made to shrink in diameter as it got warmer, the smaller moment of inertia would make it rotate faster, like a spinning ice skater that pulls in her arms. The faster balance would take less time to oscillate back and forth, compensating for the slowing caused by the weaker spring.
To accomplish this, the outer rim of the balance was made of a ‘sandwich’ of two metals; a layer of steel on the inside fused to a layer of brass on the outside. Strips of this bimetallic construction bend toward the steel side when they are warmed, because the thermal expansion of brass is greater than steel. The rim was cut open at two points next to the spokes of the wheel, so it resembled an S-shape (see figure) with two circular bimetallic ‘arms’. Indeed, these wheels are sometimes referred to as "Z - balances". A temperature increase makes the arms bend inward toward the center of the wheel, and the shift of mass inward makes the balance spin faster, cancelling out the slowing due to the spring. The amount of compensation is adjusted by moveable weights on the arms. Marine chronometers with this type of balance had errors of only 3 - 4 seconds per day over a wide temperature range. By the 1870s compensated balances began to be used in watches.
The standard Earnshaw compensation balance dramatically reduced error due to temperature variations, but it didn't eliminate it. As first described by J. G. Ulrich, a compensated balance adjusted to keep correct time at a given low and high temperature will be a few seconds per day fast at intermediate temperatures. The reason is that the moment of inertia of the balance varies as the square of the radius of the compensation arms, and thus of the temperature. But the elasticity of the spring varies linearly with temperature.
To mitigate this problem, chronometer makers adopted various 'auxiliary compensation' schemes, which reduced error below 1 second per day. Most of the chronometers that came in first in the annual Greenwich Observatory trials between 1850 and 1914 were auxiliary compensation designs. Auxiliary compensation was never used in watches because of its complexity.
The bimetallic compensated balance wheel was made obsolete in the early 1900s by advances in metallurgy. Charles Edouard Guillaume won a Nobel prize for the 1896 invention of Invar, a nickel steel alloy with very low thermal expansion, and Elinvar (from El asticité invar iable) an alloy whose elasticity is unchanged over a wide temperature range, for balance springs. A solid Invar balance with a spring of Elinvar was largely unaffected by temperature, so it replaced the difficult-to-adjust bimetallic balance. This led to a series of improved low temperature coefficient alloys for balances and springs.
Until the 1980s balance wheels were used in chronometers, bank vault time locks, alarm clocks, kitchen timers, stopwatches, and time fuzes for bombs, but quartz technology has taken over these applications, and the main remaining use is in quality watches.
Modern (2007) watch balance wheels are usually made of Glucydur, a low thermal expansion alloy of beryllium, copper and iron, with springs of a low thermal coefficient of elasticity alloy such as Nivarox. The two alloys are matched so their residual temperature responses cancel out, resulting in even lower temperature error. The wheels are smooth, to reduce air friction. Instead of weight screws to adjust the poise, they are computer-poised at the factory, using a laser to burn a precise pit in the rim to make them balanced. Balances rotate about 1½ turns in each direction. The rate of the balance is adjusted with the regulator, a lever with a narrow slit on the end through which the balance spring passes. Moving the lever slides the slit up and down the balance spring, changing its effective length, and thus the resonant vibration rate of the balance. Since the regulator interferes with the spring’s action, chronometers and some precision watches have ‘free sprung’ balances with no regulator, such as the Gyromax. Their rate is adjusted by weight screws on the balance rim. A balance’s vibration rate is measured in beats (ticks) per hour, or BPH. The length of a beat is one swing of the balance wheel, between reversals of direction, so there are two beats in a complete cycle. Balances in precision watches are designed with faster beats, because they are less affected by motions of the wrist. Watches made prior to the 1970s usually had a rate of 18,000 BPH (5 beats per second). Current watches have beats of 21,600, 28,800, and a few have 36,000 BPH (10 beats per second). During WW2, Elgin produced a very precise stopwatch that ran at 40 beats per second (144,000 BPH), earning it the nickname 'Jitterbug'. The precision of the best balance wheel watches on the wrist is around a few seconds per day. The most accurate balance wheel timepieces made were marine chronometers, which by World War 2 had achieved accuracies of 0.1 second per day.