The Origin and Evolution of the Anchor Clock Escapement (II)
Temperature Compensation
As timepieces became more accurate, the effects of changes in temperature on timekeeping became more noticeable. In 1721, George Graham invented the mercury pendulum, which used a vessel with mercury instead of a pendulum bob. The quantity of mercury in the vessel could be adjusted such that the expansion of mercury offset the lengthening of the pendulum upon warming, thereby maintaining a constant center of gravity for a wide range of temperatures. A weight-driven clock with a Graham escapement and a mercury pendulum could achieve accuracy to within a few seconds per day!
In 1726, John Harrison (1693-1776) is believed to have invented the gridiron pendulum. This pendulum had a set of nine alternating brass and steel rods, framed together and adjusted so that the temperature effect on one metal offset the temperature effect on the other. Both the mercury and the gridiron pendula were based on the same principle of thermal expansion of metals.
The Grasshopper Escapement
No one can write about horology without mentioning the most brilliant horologist of all time. John Harrison devoted almost his entire life to solving the problem of measuring longitude, in pursuit of a £20,000 prize offered by the British Government in 1714. Harrison built four clocks, the first three of which were not suitable for use at sea, although they performed well on land. His first clock was tested at sea, but the motion of the ship affected the timekeeping of the clock.
These clocks had an entirely different escapement, not related to the anchor escapements, called the grasshopper escapement because of its action. Its limbs are fixed in a position that is offset from the pendulum (see Fig. 7), and they are free to rotate about their axes, appearing to jump in and out of the escape wheel teeth. While engaged with the teeth, they rotate with the escape wheel and with no sliding action until they are released, so there is virtually no friction in this escapement.
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Figure 7: Grasshopper Escapement.
When the pallets are released, the counterweight at the other end of each pallet causes the pallets to jump up. The vertical shaft in Fig. 7 is the upper portion of the pendulum. The grasshopper escapement has rarely been used because of the complexity and fragility of the design. I do not consider the grasshopper escapement to be related to the anchor escapements because it does not really have an anchor, despite having two limbs. The structure of the grasshopper escapement is sufficiently different and unique to merit placing it in a class of its own. The main characteristics of Harrison’s designs were the prevention of rust, the reduction of friction, and elimination of the need for lubrication by use of a self-lubricating and oil-rich woods, lignum vitae in particular. Harrison also attempted to compensate for temperature by using a bimetallic strip to counteract the effects of temperature on the hairspring. If the temperature became warmer, for example, the hairspring would become slightly longer, and the bimetallic strip would displace the end of the hairspring away from the regulating pins by a similar amount.
Harrison won the Longitude Prize with his fourth timepiece, which was actually a very large watch he had built to his own specifications. What is particularly noteworthy about this watch is that it had a verge escapement with a balance wheel, demonstrating that very accurate timekeeping was actually possible with this escapement. The balance wheel had a hairspring with an attachment at the outer end that compensated for temperature. The pallets on the verge were made of highly polished rubies to minimize friction. The gear train had a remontoire between the third and fourth wheels. The remontoire consisted of a secondary spring and a lever that served to provide approximately constant force to the escapement, despite the varying torque of the mainspring as it unwound. One reason why this watch was able to perform well despite turbulence at sea was because of its hairspring. The hairspring provided the main restoring force to the balance wheel by storing its kinetic energy as elastic energy and restoring the energy to the balance wheel when it changed direction of rotation. Another reason was frequency. By designing a watch that oscillated more quickly, the watch was less affected by the motion of the ship because resonance was avoided.
The Pinwheel Escapement
The first notable descendant of the Graham escapement was the pinwheel escapement, invented by Lepaute in 1753. The main objective of this design was to reduce the angle of swing of the pendulum. The pinwheel escapement was used in a few of the finest clocks, which were called jewelers’ regulators. However, this design is not superior to the Graham escapement. If both escapements were designed on the same geometric principles (so that the angles of their respective impulse faces were the same), the amplitude of pendulum swing would also be the same, thereby failing to reduce the circular error in the motion of the pendulum. The pinwheel escapement has the disadvantage of being particularly difficult to make because of the pallets: they must be nearly perfect or the escapement would not work at all! The clearances are so small that any sizable error would result in binding of the parts. The pallets are also asymmetrical, with one pallet located farther from its axis of rotation than the other. This design places the pallets next to each other, rather than on opposite sides of the escape wheel. As can be seen in Fig. 8, the escape wheel rotates clockwise and the upper entry pallet is closer to the pallets’ axis of rotation than the lower exit pallet. In contrast, the pallets in a Graham escapement are symmetric.
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Figure 8: Pinwheel Escapement.
The most efficient anchor escapements are the Graham and pinwheel escapements. The tooth or pin of the escape wheel slides across the impulse face, transferring energy from the escape wheel to the pallet and thus to the pendulum. Since the force vectors of the tooth and pallet are designed to be at right angles, the maximum achievable efficiency of these escapements is actually less than 50%. The sliding surfaces require lubrication because of friction.
The Detached Lever Escapement in Watches
Thomas Mudge (1717-1794) invented a new escapement for watches around 1750. He appears to have adapted the Graham escapement for use in a pocket watch, creating what became known as the detached lever escapement. The vast majority of all watches made since then (hundreds of millions of watches) were based on Mudge’s design. Whereas the pallets and the balance wheel of the verge escapement were attached and interdependent, they were detached and independent of one another in the detached lever escapement. This means that the balance wheel could oscillate back and forth freely and independently of the pallets, interacting with the pallets only near the midpoint of its oscillations. The pallet assembly has three arms, one for each of the two pallets and a third arm with a slot in the end, called a fork. The balance wheel has a pin under it that enters the slot in the fork as it goes by. The pin unlocks the pallets, and energy is transferred from the escape wheel to the pin. The pallet releases the escape wheel, and the pin exits the fork. The pin continues to rotate with the balance wheel until it changes direction and returns to engage the fork again. The balance wheel is free to rotate up to about 300º before the pin strikes the fork on the other side.
The balance wheels of most watches are set up to rotate between 180º and 270º in each direction. The balance wheel’s pin interacts with the pallet fork in about 16º, less than 10% of the total oscillation. The balance wheel is no longer restricted to rotating by only about 100º, enabling the watchmaker to make increased use of the elastic property of the hairspring for improved timekeeping. Since the balance wheel has much greater amplitude of oscillation, a longer hairspring is required, like the one shown in Fig. 4. Harrison’s watch would have been even more accurate if it had been equipped with a detached lever instead of a verge escapement!
Mudge’s watch included a safety pin to prevent the pallet fork from moving over to the wrong side of the balance wheel while the balance wheel rotated. If the pallet fork were on the wrong side of the balance wheel, the balance wheel’s pin would not engage with it correctly to unlock the pallets and receive energy from the escape wheel. However, this design did not include a means for preventing the fork from accidentally rubbing against the side of the balance wheel shaft (the part known to horologists as the roller table), interrupting the freedom of rotation of the balance wheel.
Notice that a fourth arm with a weight, shown with a circle in Fig. 9, was added for poise. The pallet assembly is poised when the weight of the parts is evenly distributed about the axis of rotation, so that the assembly is not heavier on one side than the other. The weight of the corresponding parts of the pallet assembly needs to be equally distributed for symmetric behavior. The word poised is used instead of balanced to avoid confusion with another part, the balance wheel (which, by the way, should also be poised).
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Figure 9: Detached Lever.
The most important advantage of detached lever escapements in watches, including the English lever, the Swiss lever, and the pin-pallet escapements, is that these watches were essentially self-starting. If the movement of the balance wheel was interrupted for any reason and the watch stopped, a slight movement of the watch in the pocket or on the wrist would start the watch ticking again.
The English Lever Watch Escapement
Other watchmakers did not adopt Mudge’s design until about 1820. Technology was slow to change, and the verge escapement was still widely used in watches until about 1840. Around 1820, a new design, based on Mudge’s detached lever escapement, emerged in the English Midlands. This new design, now called the English lever, slowly gained popularity until the verge escapement was phased out around 1840.
The English lever incorporated a major improvement over Mudge’s design. To keep the fork away from the balance wheel until the pin returns to engage the fork, force is necessary to prevent the fork from rotating, keeping it in its desired place. Whereas Graham’s pallets had curved locking faces to prevent recoil, the English lever had flat locking faces that leaned forward by about 15º to allow the escape wheel to rotate forward by about 1º during lock (see Fig. 10). When the pin (known to horologists as the roller jewel) on the balance wheel engages the fork to unlock the pallet, the escape wheel must be pushed in the opposite direction (backward), requiring a little extra force to unlock. This extra force is known as draw. You could say that this force serves to draw the fork away from the balance wheel between engagements. Draw is critical in watch design to ensure consistent timekeeping, although it was not included in the early lever designs.
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Figure 10: English Lever.
The English lever escapement was used until the end of watch production in England, around 1900. This end was caused by less expensive imports from the United States and Switzerland, and by the failure of English watchmakers to adapt to changing technologies and markets.
The Swiss Lever
There are two major differences between the Swiss lever and the English lever. As shown in Fig. 11, the axes of rotation of the escape wheel, the pallets, and the balance wheel all lie on a straight line. This design feature makes it much easier to fabricate this escapement so that it is symmetric. It is desirable to make the design of the pallets as symmetrical as possible so that the energy the balance wheel receives from the pallet fork would be of the same magnitude for both directions. If there were asymmetry, the balance wheel would rotate more in one direction than the other, which would make the timekeeping inconsistent, particularly if there were a change in the amplitude of oscillation of the balance wheel, contributing to isochronal error. In theory, the period should be the same for all amplitudes. In reality, the period decreases slightly as the amplitude increases, causing the watch to gain time. This difference is called isochronal error: iso meaning "same" and chronos meaning "time." Isochronal error of balance wheels should not be confused with the circular error of pendula, caused by gravitational forces. Gravitational forces do not affect a properly designed balance wheel.
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Figure 11: Swiss Lever.
Fig. 12 shows the second major difference between the Swiss and the English lever escapements. The teeth of the escape wheel in the English lever are pointed. The escape wheel in the Swiss lever, called the club-tooth escape wheel, has a slope added to the end of each tooth for added strength and to reduce drop. The ruby pallets are slightly narrower because of this design change, so that the impulse faces of the pallets are shorter. Each escape tooth has an impulse face as well, however, making the total length of impulse face equal to the sum of both the pallet’s impulse face and the tooth’s impulse face. A reduction in drop increases the transfer of energy from the escape wheel to the balance wheel for every revolution of the escape wheel. The Swiss lever escapement is therefore more efficient. The pallet assembly is as light as possible and is not poised, relying on draw to keep the fork away from the balance wheel. A very small number of high-grade watches do have poised forks, however.
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Figure 12: Club-Tooth Escape Wheel.
The Swiss lever design appeared between 1860 and 1870. It has been used in virtually all Swiss, American, and Japanese watches of quality produced since then (probably several hundred million watches), and it is still being produced today.
The Pin Pallet Escapement
The pin pallet escapement is another detached lever. It differs from the others in that the lock, draw, and impulse are all designed into the teeth of the escape wheel rather than the pallets. The pallets consist of small steel pins, as shown in Fig. 13.
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Figure 13: Pin Pallet Escapement.
The lowest grade pocket watches, such as the dollar watches, and the cheapest clocks, especially alarm clocks, had pin pallet escapements. Again, probably several hundred million timepieces were produced with several variations of this escapement. Some cheap mechanical alarm clocks are still being made with pin pallet escapements, using plastic escape wheels and steel pins in plastic pallet assemblies. Escapements with plastic parts should never be lubricated because the lubricants may react with the plastic. Besides, plastics are said to be self-lubricating.
The Brocot Escapement
The Brocot escapement, invented by Achille Brocot (1817-1878) in Paris around 1860, is a pin pallet escapement that was designed for use with pendulum clocks. The teeth of the escape wheel do not have draw designed into the locking faces since they follow the radial lines from the escape wheel’s axis of rotation, rather than appearing to lean forward (see Fig. 14). The impulse face is designed into the pallets rather than the escape teeth, which are pointed. The pin pallets consist of larger steel pins in the form of a half circle. Some ornamental clocks have Brocot escapements with ruby pins.
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Figure 14: Brocot Escapement.
A well-adjusted Brocot escapement has no recoil, so it is much more efficient than a recoil escapement. The impulse surfaces of the pin pallets are curved, however, which means that the direction of the force vector, acting to push the pallet, changes as the escape tooth slides across the impulse face. This escapement is therefore about 20% less efficient than a similarly proportioned Graham escapement, which has straight impulse faces. To design a similarly proportioned Brocot escapement, simply place Brocot pallets over the tips of Graham pallets, as shown in Fig. 15.
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Figure 15: Brocot pallets over Graham pallets.
This comparison clarifies the similarity between the Brocot and Graham escapements. The escape wheel of the Brocot escapement should have perpendicular teeth rather than teeth that appear to lean forward, as in the Graham escapement.
Other Escapements
Estimates are that several hundred different escapements were designed in the 18th and 19th centuries. Most were minor variations of the anchor escapements discussed above. There is, however, a different family of escapements that should be mentioned briefly here. The cylinder, duplex, and chronometer watch escapements differ in that they have no anchors and no pallets. The balance wheel receives energy directly from the escape wheel teeth.
By far the most important of these three escapements is the chronometer. The escape tooth provides energy to the balance wheel while the tooth and the balance wheel’s roller jewel roll together, in the same way the teeth in the gear train roll together. The direction of the tooth’s and the roller jewel’s force vectors is therefore the same at the midpoint of their engagement, so the efficiency of the energy transfer is near 100%. Since there is very little friction in this design, no lubrication of the escapement is required, an advantage for improved timekeeping.
High-grade marine chronometers, based on the chronometer escapement, have served for over 200 years at sea and are still being used for ship navigation. Their use has more recently decreased because of the new satellite navigation systems.
Conclusions
The influence of the anchor escapements on horology is enormous. As many as 90% of all pendulum clocks, produced since about 1660, have had anchor escapements of the recoil type. Although there are dozens of different styles, the design principles are essentially the same. Mechanical clocks with recoil escapements are still made today. Almost all finer clocks have been equipped with Graham escapements.
All timepieces with anchor escapements can be seen as having three sets of components. There is the driving component, consisting of a gear train with a source of potential energy (gravitational energy with a weight or elastic energy with a mainspring). There is the controlling component, consisting of an anchor and an oscillator, which interacts with the driving component and allows the energy in the driving component to be expended in a controlled manner. The energy is used to repel the oscillator (the pendulum, balance wheel, or foliot) from its center of oscillation (or its rest position). The driving component serves to replace energy in the oscillator, energy lost due to friction. The third component is the restoring component.
The restoring component consists primarily of an elastic spring (suspension spring or hairspring) that stores kinetic energy from the moving oscillator. The spring causes the oscillator to decelerate until it stops, and then uses the potential energy to accelerate the oscillator in the opposite direction (restoring the oscillator to its center of oscillation). Other restoring components include energy from the escapement, caused by recoil, and gravitation potential energy.
These three components interact to simulate simple harmonic motion as closely and as predictably as possible, with the objective of measuring the passage of time. The passage of time is shown by the rate of descent of the weight or by indicators (the hour, minute, and second hands) mounted onto the shafts of the gears.
The modern watch industry, after being overwhelmed by quartz technology, now produces mechanical watches to serve primarily a luxury market. All new mechanical watches, with a few extremely rare exceptions, have Swiss lever escapements. Modern methods of production have made it possible to mass-produce these accurate (to within a few seconds per day) and reliable watches with little need for manual adjustment. The Swiss lever design evolved with the development of industrial machinery since the Industrial Revolution and has recently been optimized with the application of computer technology and computer-aided design programs.
Finally, as mentioned in the Introduction, an escapement mechanism is a speed regulator that uses feedback to obtain precision operation despite imperfect components. Detailed analysis of this regulator, from mechanical and control engineering points of view, is incomplete. My hope is that this history of the origin and evolution of the anchor escapement will motivate continued research into the dynamics and operation of these fascinating, ubiquitous, and useful devices.
References
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Escapements in Motion