How Pendulum Clocks Workby Marshall Brain

Have you ever looked inside a grandfather clock or a small mechanical alarm

clock, seen all the gears and springs and thought, "Wow -- that's

complicated!"? While clocks normally are fairly complicated, they do not have

to be confusing or mysterious. In fact, as you learn how a clock works, you

can see how clock designers faced and solved a number of interesting

problems to create accurate timekeeping devices. In this article, we'll help you

understand what makes clocks tick, so the next time you look inside one you

can make sense of what's happening.

Let's get started by taking a look at the different parts of a pendulum clock.

Pendulum Parts

Pendulum clocks have been used to keep time since 1656, and they have not

changed dramatically since then. Pendulum clocks were the first clocks made

to have any sort of accuracy. When you look at a pendulum clock from the

outside, you notice several different parts that are important to the mechanism

of all pendulum clocks:

There is the face of the clock, with its hour and minute hand (and sometimes

even a "moon phase" dial).

There are one or more weights (or, if the clock is more modern, a keyhole

used to wind a spring inside the clock -- we will stick with weight-driven clocks

in this article).

And, of course, there is the pendulum itself.

In most wall clocks that use a pendulum, the pendulum swings once per

second. In small cuckoo clocks the pendulum might swing twice a second. In

large grandfather clocks, the pendulum swings once every two seconds. So,

how do these parts work together to keep the clock ticking and the time

accurate? Let's take a look at the weight, first.

A Weighty Subject

The idea behind the weight is to act as an energy storage device so that the

clock can run for relatively long periods of time unattended. When you "wind"

a weight-driven clock, you pull on a cord that lifts the weight. That gives the

weight "potential energy" in the Earth's gravitational field. As we will see in a

moment, the clock uses that potential energy as the weight falls to drive the

clock's mechanism.

So let's say that we wanted to use a falling weight to create the simplest

possible clock -- a clock that has just a second hand on it. We want the

second hand on this simple clock to work like a normal second hand on any

clock, making one complete revolution every 60 seconds. We might try to do

that, as shown in the figure on the right, simply by attaching the weight's cord

to a drum and then attaching a second hand to the drum as well. This, of

course, would not work. In this simple mechanism, releasing the weight would

cause it to fall as fast as it could, spinning the drum at about 1,000 rpm until

the weight clattered on the floor.

Still, it's headed in the right direction. Let's say we put some kind

of frictiondevice on the drum -- some sort of brake pad or something that

would slow the drum down. This might work. We would certainly be able to

devise some scheme based on friction to get the second hand to make

approximately one revolution per minute. But it would only be approximate. As

the temperature and the humidity in the air changed, the friction in the device

would change. Thus our second hand would not keep very good time.

So, back in the 1600s, people who wanted to create accurate clocks were

trying to solve the problem of how to cause the second hand to make exactly

one revolution per minute. The Dutch astronomerChristiaan Huygens is

credited with first suggesting the use of a pendulum. Pendulums are useful

because they have an extremely interesting property: The period (the amount

of time it takes for a pendulum to go back and forth once) of a pendulum's

swing is related only to the length of the pendulum and the force of gravity.

Since gravity is constant at any given spot on the planet, the only thing that

affects the period of a pendulum is the length of the pendulum. The amount

of weight does not matter. Nor does the length of the arc that the pendulum

swings through. Only the length of the pendulum matters. If you're not

convinced, try the experiment on the following page!

Experiment Time

As we stated on the previous page, the only thing affecting the period of a

pendulum is the length of that pendulum. You can prove this fact to yourself

by performing the following experiment. For this experiment you will need:

A weight

A string

A table

A watch with a second hand (or a numeric seconds display on a digital watch)

For the weight you can use anything. In a pinch, a coffee mug or a book will

do -- it doesn't really matter. Tie the string to the weight. Then suspend your

pendulum over the edge of the table so that the length of the pendulum is

about 2 feet, as shown here:

Now pull the weight back about a foot and let your pendulum start swinging.

Time it for 30 or 60 seconds and count how many times it swings back and

forth. Remember that number. Now stop the pendulum and restart it, but this

time pull it back only 6 inches initially so it is swinging through a much smaller

arc. Count the number of swings again through the same 30- or 60-second

time period. What you will find is that the number you get is the same as the

first number you counted. In other words, the angle of the arc through which

the pendulum swings does not affect the pendulum's period. Only the length

of the pendulum's string matters. If you play around with the length of your

pendulum you will find that you can adjust it so that it swings back and forth

exactly 60 times in one minute.

(Note: If you want to be exactly accurate about the pendulum period, see this

interesting article.)

Once someone noticed this fact about pendulums, it was realized that you

could use the phenomenon to create an accurate clock. The figure below

shows how you can create a clock's escapement using a pendulum.

In an escapement there is a gear with teeth of some special shape. There is

also a pendulum, and attached to the pendulum is some sort of device to

engage the teeth of the gear. The basic idea that is being demonstrated in the

figure is that, for each swing of the pendulum back and forth, one tooth of the

gear is allowed to "escape."

For example, if the pendulum is swinging toward the left and passes through

the center position as shown in the figure on the right, then as the pendulum

continues toward the left the left-hand stop attached to the pendulum will

release its tooth. The gear will then advance one-half tooth's-width forward

and hit the right-hand stop. In advancing forward and running into the stop, the

gear will make a sound... "tick" or "tock" being the most common. That is

where the ticking sound of a clock or watch comes from!

One thing to keep in mind is that pendulums will not swing forever. Therefore,

one additional job of the escapement gear is to impart just enough energy into

the pendulum to overcome friction and allow it to keep swinging. To

accomplish this task, the anchor (the name given to the gizmo attached to the

pendulum to release the escapement gear one tooth at a time) and the teeth

on the escapement gear are specially shaped. The gear's teeth escape

properly, and the pendulum is given a nudge in the right direction by the

anchor each time through a swing. The nudge is the boost of energy that the

pendulum needs to overcome friction, so it keeps swinging.

So, let's say that you create an escapement. If you gave the escapement gear

60 teeth and attached this gear directly to the weight drum we discussed

above, and if you then used a pendulum with a period of one second, you

would have successfully created a clock in which the second hand turns at the

rate of one revolution per minute. By adjusting the pendulum's length very

carefully we could create a clock with very high accuracy.

However, while accurate, this clock would have two problems that would make

it less-than-useful:

1. Most people want a clock to have hour and minute hands as well.

2. You would have to wind the clock about every 20 minutes. Because the drum

makes one revolution every minute, the weight would unwind to the floor very

quickly. Most people would not like a clock that had to be rewound every 20

minutes!

So, what does it take to solve the winding problem? Read on...

Gearing Up!

The problem of having to rewind every 20 minutes is easy to solve. As

discussed in How Gear Ratios Work, you can create a high-ratio gear train

that causes the drum to make perhaps one turn every six to 12 hours. This

would give you a clock that you only had to rewind once a week or so. The

gear ratio between the weight drum and the escapement gear might be

something like 500:1, as shown in the diagram below:

In this diagram the escapement gear has 120 teeth, the pendulum has a

period of half a second and the second hand is connected directly to the

escapement gear. Each gear in the weight's gear train has an 8:1 ratio, so the

full train's ratio is 492:1.

You can see that if you let the escapement gear itself drive another gear train

with a ratio of 60:1, then you can attach the minute hand to the last gear in

that train. A final train with a ratio of 12:1 would handle the hour hand. Presto!

You have a clock.

Now this clock is nice, but it has two problems:

1. The hour, minute and second hands are on different axes. That problem is

generally solved by using tubular shafts on the gears and then arranging the

gear trains so that the gears driving the hour, minute and second hands share

the same axis. The tubular gear shafts are aligned one inside the other. Look

closely at any clock face and you can see this arrangement.

2. Because all of these gears are connected directly together, there is no

easy way to rewind or set the clock. That is often handled by having a gear

that can be slipped out of the train. When you pull on the stem of a wristwatch

to set the watch, that is essentially what you are doing. In the figure above,

you might imagine temporarily removing the small black gear to either wind or

set the clock.

You can see that, even though all the gears in a clock make it look

complicated, what a pendulum clock is doing is really pretty simple. There are

five basic parts:

Weight or spring - This provides the energy to turn the hands of the clock.

Weight gear train - A high-ratio gear train gears the weight drum way up so

that you don't have to rewind the clock very often.

Escapement - Made up of the pendulum, the anchor and the escapement

gear, the escapement precisely regulates the speed at which the weight's

energy is released.

Hand gear train - The train gears things down so the minute and hour hands

turn at the right rates.

Setting mechanism - This somehow disengages, slips or ratchets the gear

train so the clock can be rewound and set.

Once you understand these pieces, clocks are a piece of cake!

Q & A

Here's a set of questions from readers:

Watches obviously do not use pendulums, so how do they keep time? A

pendulum is one periodic mechanical system with a precise period. There are

other mechanical systems that have the same feature. For example, a weight

bouncing on a spring has a precise period. Another example is a wheel with a

spring on its axle. In this case, the spring causes the wheel to rotate back and

forth on its axis. Most mechanical watches use the wheel/spring arrangement.

What is the difference between a weight-driven and a spring-driven

clock? Nothing, really. Both a weight and a spring store energy. In a spring-

driven clock you wind the spring and it unwinds into the same sort of gear train

found on a weight-driven clock.

What can you do to make a clock more accurate? There is an excellent

book entitled "Longitude: The True Story of a Lone Genius Who Solved the

Greatest Scientific Problem of His Time", by Dava Sobel, that discusses the

creation of extremely accurate mechanical clocks to find a ship's longitude.

Creating accurate mechanical clocks that can live on a ship (unlike a

pendulum clock...) was a real challenge!

How does the moon phase dial on a grandfather clock work? The moon

phase dial works just like the hands of the clock do. The minute hand on a

clock moves at the rate of one revolution every hour. The hour hand moves at

one revolution every 12 hours. The moon phase dial moves at a rate of one

revolution every 56 days or so. The moon's cycle is 28 days, and the moon

phase dial generally has two moons painted on it.

For more information on pendulums, timekeeping and related topics, check

out the links on the next page.

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How Quartz Watches Workby Douglas Dwyer

During the 1970s, the "quartz watch" burst onto the scene as the newest high-

tech gadget. Initially, these watches had red LED displays and they cost

around $500 in the United States. Since then, the quartz watch has evolved

so that either an LCD or a traditional mechanical (hour and minute hand)

movement displays the time, and the price has fallen dramatically. It is not

uncommon to find quartz watches given away for free in boxes of cereal!

Have you ever wondered why it is called a quartzwatch? Or why quartz

watches are so much more accurate than wind-up watches? In this edition

ofHowStuffWorks, you will learn all about the amazing electronic

phenomenon called the quartz crystal and how it forms the heart of a quartz

watch!

Before Quartz

The wind-up watch is an amazing piece of technology itself! It is part of a

continuous research-and-development effort that started at the end of the 14th

Century. Over the years, different innovations made wind-up watches smaller,

thinner, more reliable, more accurate and even self-winding!

The components that you find in today's wind-up watches have been around

for centuries:

A spring to provide the power

Some sort of oscillating mass to provide a timebase

Two or more hands

An enumerated dial on the face of the watch

Gears to slow down from the ticking rate of the oscillating mass and connect

the mass and spring to the hands on the dial

See How Pendulum Clocks Work for a description of these different parts.

By the end of the 1960s, the Bulova watch company made the first step away

from the oscillating balance wheel -- it used a transistor oscillator that

maintained a tuning fork. This watch hummed at some hundreds of hertz (Hz,

cycles per second) rather than ticking! Cogs and wheels still converted the

mechanical movement of the tuning fork to movement of the hands, but two

major steps had been taken:

1. The replacement of the balance wheel and spring with a single-material

resonator: the tuning fork

2. The replacement of the wind-up main spring with a battery

A watch-making company in the late 1960s was bound to look for the next

step -- a technology that would give even better time keeping than the tuning

fork. Integrated circuits were very new at the time, but the price was

dropping rapidly and the number of transistors was growing. LEDs were also

new on the scene. There were still a couple of problems to be solved: finding

a new timing element and designing an integrated circuit that would use very

little power to allow the watch to run on a tiny internal battery.

The Quartz Crystal

There was no problem with the choice of a timing element. The quartz crystal

is possibly thousands of times better for timing than the tuning fork, and quartz

crystals had been around for many years. Only the type and the frequency of

the crystal needed to be chosen. The difficulty was in the selection of the

integrated circuit technology that would function at sufficiently low power.

Quartz crystals have been in regular use for many years to give an accurate

frequency for all radiotransmitters, radio receivers and computers. Their

accuracy comes from an amazing set of coincidences: Quartz -- which

is silicon dioxide like most sand -- is unaffected by most solvents and

remains crystalline to hundreds of degrees Fahrenheit. The property that

makes it an electronic miracle is the fact that, when compressed or bent, it

generates a charge or voltage on its surface. This is a fairly common

phenomenon called the Piezoelectric effect. In the same way, if a voltage is

applied, quartz will bend or change its shape very slightly.

If a bell were shaped by grinding a single crystal of quartz, it would ring for

minutes after being tapped. Almost no energy is lost in the material. A quartz

bell -- if shaped in the right direction to the crystalline axis -- will have an

oscillating voltage on its surface, and the rate of oscillation is unaffected by

temperature. If the surface voltage on the crystal is picked off with plated

electrodes and amplified by a transistor or integrated circuit, it can be re-

applied to the bell to keep it ringing.

A quartz bell could be made, but it is not the best shape because too much

energy is coupled to the air. The best shapes are a straight bar or a disk. A

bar has the advantage of keeping the same frequency provided the ratio of

length to width remains the same. A quartz bar can be tiny and oscillate at a

relatively low frequency -- 32 kilohertz (KHz) is usually chosen for watches not

only for size, but also because the circuits that divide down from the crystal

frequency to the few pulses per second for the display need more power for

higher frequencies. Power was a big problem for early watches, and the Swiss

spent millions trying to bring forward integrated-circuit technology to divide

down from the 1 to 2 MHz the more stable disk crystals generate.

Modern quartz watches now use a low-frequency bar or tuning-fork-shaped

crystal. Often, these crystals are made from thin sheets of quartz plated like

an integrated circuit and etched chemically to shape. The major difference

between good and indifferent time keeping is the initial frequency accuracy

and the precision of the angle of cut of the quartz sheet with respect to the

crystalline axis. The amount of contamination that is allowed to get through

the encapsulation to the crystal surface inside the watch can also affect the

accuracy.

The electronics of the watch initially amplifies noise at the crystal frequency.

This builds or regenerates intooscillation -- it starts the crystal ringing. The

output of the watch crystal oscillator is then converted to pulses suitable for

the digital circuits. These divide the crystal's frequency down and then

translate it into the proper format for the display. (See How Digital Clocks

Work for a detailed discussion of dividers and display drivers.) Or, in a quartz

watch with hands, the dividers create one-second pulses that drive a

tinyelectric motor, and this motor is connected to standard gears to drive the

hands.

For more information, check out the links on the next page.

How Digital Clocks Workby Marshall Brain

Chances are that in your bedroom you have a digital clock beside your bed.

Have you ever looked at it in the morning and wondered how it works?

In this article, you're going to learn exactly how a digital clock (or wristwatch)

works. In fact, you're even going to learn how to build your own!

To understand how a digital clock works, you have to get inside and see

what's going on. So let's get started!

Launch VideoThe Basics

If you have read How Pendulum Clocks Work, you know that all clocks

(regardless of technology) have a few required components:

A source of power to run the clock In a pendulum clock, the weights or the

springs handle this role.

An accurate timebase that acts as the clock's heartbeat In a pendulum

clock, the pendulum and escapement handle this role.

A way to gear down the timebase to extract different components of

time (hours, minutes, seconds) In a pendulum clock, gears serve this role.

A way to display the time In a pendulum clock, the hands and face serve

this role.

A digital clock is no different. It simply handles these functions electronically

rather than mechanically. So in a digital clock, there is an electrical power

supply (either a battery or 120-volt AC power from the wall). There is an

electronic timebase that "ticks" at some known and accurate rate. There is an

electronic "gearing mechanism" of some sort -- generally a digital clock

handles gearing with a component called a "counter." And there is a display,

usually either LEDs (light emitting diodes) or an LCD (liquid crystal display).

High-Level View

Here is a quick overview of the components of a digital clock at a high level.

At the heart of the clock there is a piece that can generate an accurate 60-

hertz (Hz, oscillations per second) signal. There are two ways to generate this

signal:

1. The signal can be extracted from the 60-Hz oscillations in a normal power

line. Many clocks that get their power from a wall socket use this technique

because it is cheap and easy. The 60-Hz signal on the power line is

reasonably accurate for this purpose.

2. The signal can be generated using a crystal oscillator. Obviously, any

battery-operated clock or wristwatch will use this technique instead. It takes

more parts, but is generally much more accurate.

The 60-Hz signal is divided down using a counter. When building your own

clock, a typical TTL part to use is a 7490 decade counter. This part can be

configured to divide by any number between 2 and 10, and generates a binary

number as output. So you take your 60-Hz time base, divide it by 10, divide it

by 6 and now you have a 1-Hz (1 oscillation per second) signal. This 1-Hz

signal is perfect for driving the "second hand" portion of the display. So far, the

clock looks like this in a block diagram:

To actually see the seconds, then the output of the counters needs to drive a

display. The two counters producebinary numbers. The divide-by-10 counter

is producing a 0-1-2-3-4-5-6-7-8-9 sequence on its outputs, while the divide-

by-6 counter is producing a 0-1-2-3-4-5 sequence on its outputs. We want to

display these binary numbers on something called a 7-segment display. A 7-

segment display has seven bars on it, and by turning on different bars you can

display different numbers:

To convert a binary number between 0 and 9 to the appropriate signals to

drive a 7-segment display, you use a (appropriately named) "binary number to

7-segment display converter." This chip looks at the binary number coming in

and turns on the appropriate bars in the 7-segment LED to display that

number. If we are displaying the seconds, then the seconds part of our clock

looks like this:

The output from this stage oscillates at a frequency of one-cycle-per-minute.

You can imagine that the minutes section of the clock looks exactly the same.

Finally, the hours section looks almost the same except that the divide-by-6

counter is replaced by a divide-by-2 counter.

Now there are two details left to figure out if you are building a real clock:

The clock as designed here does not understand that at 12:59:59 it is

supposed to cycle back to 1:00. That is a messy little problem, and there are a

couple of ways to solve it. One technique involves creating a little bit of logic

that can detect the number 13 and reset the hour section back to 1 (not zero).

Another technique involves using an adder. For our purposes, it is easier to

deal in military time, because military time includes a zero hour.

We need a way to set the clock. Typically this is handled by gating higher-

than-normal frequencies into the minutes section. For example, most clocks

have "fast" and "slow" set buttons. When you press the "fast" button, the 60-

Hz signal is driven straight into the minutes counter. When you press the

"slow" button, a 1-Hz signal is driven into the minutes section. There are other

possible techniques, but this one is the most common.

Now let's see what we have to do to build a real clock!

Building Your Own Digital Clock

The best way to understand the different components of a digital clock and

how they work together is to actually walk through the steps of building your

own clock. Here we will build just the "seconds" part of the clock, but you can

easily extend things to build a complete clock with hours, minutes and

seconds. To understand these steps, you will need to have read How Boolean

Logic Works and How Electronic Gates Work. In particular, the electronic

gates article introduces you to TTL chips, breadboards and power supplies. If

you have already played around with gates as described in that article, then

the description here will make a lot more sense.

The first thing we need is a power supply. We built one in the electronic

gates article. That time, we used a standard wall transformer that produced

DC (direct current) power and then regulated it to 5 volts using a 7805. For our

clock, we want to do things slightly differently because we are going to extract

our 60-Hz timebase from the power line. That means that we want

an AC rather than a DC transformer, and we will use a part called a bridge

rectifier to convert the AC to DC. Therefore, we need the following parts for

our power supply:

12-volt AC transformer (Jameco part #115602)

Bridge rectifier (Jameco part #103018)

7805 5-volt regulator (TO-220 case) (Jameco part #51262)

Two 470-microfarad electrolytic capacitors (Jameco part #93817)

5.1-volt zener diode (Jameco part #36097)

1-K-ohm resistor (Jameco part #29663)            

A few notes on the parts used:

The difference between the AC transformer we are using here and the DC

transformer we used in the article on gates is that the AC transformer

preserves the 60-Hz sine wave found in 120-volt household current. If you

want to use your volt-ohm meter to measure the voltage of an AC transformer,

be sure you use an AC voltage range rather than a DC range.

We use the bridge rectifier to convert the AC to DC. One of the terminals on

the rectifier will be marked with a "+" -- from that you can find the minus and

AC inputs. There is no polarity to an AC transformer, so it does not matter

which transformer lead you connect to which AC lead of the rectifier.

The 7805 and capacitors are wired just like they were in the electronic

gates article.

The resistor and the zener diode extract a 60-Hz signal from the

transformer's sine wave. A diode is a one-way valve for electrons. A zener

diode is also a one-way valve, but it also passes electrons in the other

direction if they are above a certain voltage. The zener diode therefore turns a

10-volt sine wave into a clipped wave oscillating between 0 and 5 volts. This is

perfect for clocking the TTL counters. The 1-K-ohm resistor makes sure that

the current to the zener diode is limited so we do not burn out the diode. The

diode will have a band painted on one end -- this band should be the end

connected to the resistor.

Circuit Diagram

Here's a circuit diagram for the power supply and time base.

As we saw in the article onelectronic gates, the power supply is the most

difficult part!

To create the rest of the clock you will need:

At least four 7490 or 74LS90 chips

At least two 7447 or 74LS47 binary-to-7-segment converters

At least 20 resistors for the LEDs in the 7-segment displays (330 ohms would

be fine.)

Some normal LEDs

At least two common-anode (CA) 7-segment LED displays (Jameco part #

17208 is typical.)

Breadboards, wire, etc. (See this page for a complete list.)

The number of chips, resistors and LEDs you need depends on how many

digits you are interested in implementing. Here we will discuss only seconds,

so the "at least" numbers are correct.

7490 Pinout

Let's look at the 7490 briefly to see how it works.

The 7490 is a decade counter, meaning it is able to count from 0 to 9

cyclically, and that is its natural mode. That is, QA, QB, QC and QD are 4 bits

in a binary number, and these pins cycle through 0 to 9, like this:

QD QC QB QA

0 0 0 0

0 0 0 1

0 0 1 0

0 0 1 1

0 1 0 0

0 1 0 1

0 1 1 0

0 1 1 1

1 0 0 0

1 0 0 1

You can also set the chip up to count up to other maximum numbers and then

return to zero. You "set it up" by changing the wiring of the R01, R02, R91 and

R92 lines. If both R01 and R02 are 1 (5 volts) and either R91 or R92 are 0

(ground), then the chip will reset QA, QB, QC and QD to 0. If both R91 and

R92 are 1 (5 volts), then the count on QA, QB, QC and QD goes to 1001 (5).

So:

To create a divide-by-10 counter, you first connect pin 5 to +5 volts and pin

10 to ground to power the chip. Then you connect pin 12 to pin 1 and ground

pins 2, 3, 6, and 7. You run the input clock signal (from the timebase or a

previous counter) in on pin 14. The output appears on QA, QB, QC and QD.

Use the output on pin 11 to connect to the next stage.

To create a divide-by-6 counter, you first connect pin 5 to +5 volts and pin 10

to ground to power the chip. Then you connect pin 12 to pin 1 and ground pins

6 and 7. Connect pin 2 to pin 9 and pin 3 to pin 8. Run the input clock signal

(from the timebase or a previous counter) in on pin 14. The output appears on

QA, QB and QC. Use pin 8 to connect to the next stage.