There are all sorts of resonances around us, in the world, in our culture, and in our technology. A tidal resonance causes the 55 foot tides in the Bay of Fundy. Mechanical and acoustical resonances and their control are at the center of practically every musical instrument that ever existed. Even our voices and speech are based on controlling the resonances in our throat and mouth. Technology is also a heavy user of resonance. All clocks, radios, televisions, and gps navigating systems use electronic resonators at their very core. Doctors use magnetic resonance imaging or MRI to sense the resonances in atomic nuclei to map the insides of their patients. In spite of the great diversity of resonators, they all share many common properties. In this blog, we will delve into their various aspects. It is hoped that this will serve both the students and professionals who would like to understand more about resonators. I hope all will enjoy the animations.

Origins of Newton's laws of motion

History of mechanical clocks with animations
Understanding a mechanical clock with animations
includes pendulum, balance wheel, and quartz clocks

## Saturday, March 19, 2011

### Balance wheel clocks

 previous: the pendulum clock up: home next: John Harrison, conclusion

## History of Mechanical Clocks with Animations

 Figure 4.1. Common balance wheel escapement. Mouse over the figure to see it in action. The red arrow shows the torque applied to the large gear on the bottom right by the drive spring (also called a "mainspring". It is not shown in the illustration). This type of escapement is the heart of a watch or chronometer. A typical balance wheel is 1 to 2 cm in diameter and undergoes oscillating rotations, about one per second, depending on the watch design. The outer tip of the hairspring is attached to the frame of the watch movement and provides the restoring force for the balance wheel resonance. The pointed toothed escapement wheel is driven by the drive spring via a chain of gears (only partially shown) which applies a constant torque to it in the direction indicated. The escapement lever pivots back and forth and is responsible for allowing the escapement wheel to progress only one tooth for each oscillation of the balance wheel and also responsible for giving the balance wheel a nudge each time to keep it oscillating. The tips of the escapement lever cause the audible ticking of the watch as they slide off the teeth of the escapement wheel. The rim of the balance wheel consists of two bimetal strips that warp outwards and inwards with temperature changes to correct for the expansion of metals and change in the spring constant of the hairspring. Screws around the perimeter are added for their weight to adjust the oscillation period and adjust the temperature compensation. In this figure, we have exaggerated the size of the escapement lever to show its function more clearly.

### 1.5 Balance wheel clocks

In 1675, a mere 19 years after he made the first pendulum clock, Christiaan Huygens again triumphed and made the first balance wheel clock. In the centuries to follow, this type of clock movement became common in the form of the pocket watch. The balance wheel resonator consists of two parts: the balance wheel, and the hairspring (also called a balance spring). The wheel is mounted on a small axle and fine bearing so as to allow it to turn back and forth almost without friction. The hairspring is a fine (i.e. very thin) wire bent in a spiral shape and attached at one end to the balance wheel and at the other end to the watch frame. The hairspring has the function of providing a restoring force, to make the balance wheel able to oscillate on its axis back and forth, the function that gravity does in the pendulum. See Wikipedia for more on balance springs and the period of a balance wheel resonator.

The balance wheel's motion is even more intriguing to observe than the pendulum's motion, ever rotating and reversing with the spiral spring decreasing and increasing in diameter. Like the pendulum, the period of this resonator depends almost entirely on fixed properties, in this case the geometry of the wheel and the spring, and very weakly on the state of lubrication of the parts or the tension in the power spring

Huygens used a verge escapement (see Figure 4.2), however verge escapements were seldom used by the watchmakers of later periods. Figure 4.1 shows one of the more commonly used escapement mechanisms for a pocket watch. Note that it is similar to that in the pendulum, with the addition of one more part, the detached escapement lever.

Figure 4.2. Huygen's balance wheel with verge escapement. Wikipedia.

Figure 4.3. Modern balance wheel in a pocket watch. The balance wheel is nestled in a support structure. It has a ruby bearing. Visible also is a gear. Wikipedia.

Figure 4.2. Typical pocket watch opened up to show balance wheel. The rest of the mechanism, the gears, power spring, and escapement mechanism, are mostly hidden from view. On top of the balance wheel, one sees the speed adjustment lever that can slightly shorten or elongate the active length of the hair spring and slightly change the period of the balance wheel to correct for the watch being too slow or too fast. Morguefile.com.

This additional part allows the successful operation of the balance wheel over a wide range of swing amplitudes, typically 100 degree amplitudes, and still actuate the escapement properly. The verge escapement was not so tolerant. The modern escapement is also more compact, fitting into the same plane as the balance wheel and gears. The larger swings allows a pocket watch to maintain its accuracy even when the watch is being moved around and twisted as is common for a watch in a person's pocket or on their wrist. Figure 4.1 shows the action. Note that similar to in the pendulum clocks, the escapement mechanism here does two functions: it allows the escape wheel to rotate only one tooth per cycle of the balance wheel and secondly, it gives the balance wheel a nudge each cycle to keep it going.

When compared to the pendulum clock, the balance wheel clock has two advantages. First it can be made smaller. Because whereas a pendulum needs to be a reasonable length, perhaps a half foot (15 cm) or more, to have a reasonable cycle time, the balance wheel can be made tiny and still have this same reasonable cycle time. Secondly (and more importantly), while the pendulum must be vertical, the balance wheel can operate in any orientation. The balance wheel clock is also less susceptible to errors due to motion of the whole clock. These features make it suitable for use as a pocket watch which needs to be small, work in any orientation, and be fairly insensitive to motion. Like the pendulum, balance wheels can be temperature compensated and also adjusted in speed.

A complete balance wheel clockworks is very similar to the previously discussed pendulum clocks (see Fig. 3.8 in the previous page). After the replacement of a pendulum with a balance wheel, the next most obvious difference reflects the usage: most balance wheel clocks are used as wrist watches or pocket watches. This means that everything is scaled down,i.e. smaller gears, hands, and other parts. Also, the power source is different. Hanging weights wouldn't work to power a wrist watch or pocket watch. Instead, a wound up mainspring is used.

Morguefile.com.

#### Clockmaking - an early high tech industry

For the next couple of centuries, the technology of watches and clocks was the high tech industry of the times and the watch makers were the high tech professionals of that industry. Almost ahead of their time, clock and watch makers developed the technology to make incredibly tiny, extremely precise parts out of precious and semiprecious material. There was constant rivalry as to whose escapement and whose product was the most accurate, most convenient, longest lived, best decorated and so on. To improve the lifetime of their products, watchmakers armored up more and more of the rubbing parts with the high tech ceramic of the day, little pieces of sapphire, ruby, garnet, or other semiprecious stones, called "jewels" in the language of the clockmakers.

Morguefile.com.

That coupled with the widespread use of gold and lavish decorations, made many of the watches of the day, true works of art and marvels of technology. Similar to expensive automobiles in this century, pocket watches became popular among the very rich and in fact the gold pocket watch was taken as an emblem of a wealthy man. We will next follow the pursuits of one very important man in the development of these clocks.

 previous: the pendulum clock up: home next: John Harrison, conclusion