# For Clock

## Accuracy

The timekeeping elements in all modern clocks, which include pendulums, balance wheels, tuning forks, the quartz crystals used in quartz watches, and even the vibrating atoms in atomic clocks, are called harmonic oscillators. The reason harmonic oscillators are used in clocks is that they vibrate or oscillate at a specific resonant frequency (period) which is dependent on their construction, and resist oscillating at other rates. However the resonant frequency is not infinitely 'sharp'. Around the resonant frequency there is a narrow natural band of frequencies (or periods), called the resonance width or bandwidth, that the harmonic oscillator will oscillate at.[1] [2] The actual frequency of the oscillator in a clock may vary randomly within this bandwidth in response to disturbances, but at frequencies outside this band, the oscillator, and the clock, will not function at all.

#### Q factor

The measure of a harmonic oscillator's resistance to disturbances to its oscillation period is a dimensionless parameter called the Q factor equal to the resonant frequency divided by the resonance width.[2][3] The higher the Q, the smaller the resonance width, and the more constant the frequency or period of the oscillator for a given disturbance.[4] The reciprocal of the Q is roughly proportional to the limiting accuracy achievable by a harmonic oscillator as a time standard.[5]

The Q is related to how long it takes for the natural oscillations of an oscillator to die out due to friction. High quality oscillators, that "ring" for a long time after being set in motion, have high Q and keep better time. The Q can be measured by counting the number of oscillations it takes for the amplitude of the oscillator's vibrations to decay to 1/e = 36.8% of its initial amplitude, and multiplying by 2π.

As an example, in a pendulum clock, the pendulum must receive pushes from the clock's movement to keep it swinging, to replace the energy the pendulum loses to friction. These pushes, applied by a mechanism called the escapement, are the main source of disturbance to the pendulum's motion. The Q is equal to 2π times the energy stored in the pendulum, divided by the energy lost to friction during each oscillation period, which is the same as the energy added by the escapement each period. It can be seen that the smaller the fraction of the pendulum's energy that is lost to friction, the less energy needs to be added, the less the disturbance from the escapement, the more 'independent' the pendulum is of the clock's mechanism, and the more constant its period is.

The Q of an oscillator generally increases, other things being equal, with an increase in resonant frequency, or a decrease in dissipative forces like drag and friction.

Type of oscillator Frequency Q Peak accuracy
(Typical accuracy)
Water clock nonoscillating 15 min / day
1 hour / day
0.25-1 Hz 15 min / day
1 hour / day
Balance wheel 2-5 Hz 300 0.1 sec / day
0.3 sec / day
Pendulum 0.5-2 Hz 10000- 4 sec / year
10 sec / month
Torsion pendulum 0.05-0.125 Hz escapement  ?
4 min / month
Tuning fork 360 Hz  ?
2 sec / day
Quartz crystal 32 KHz - 5 MHz 105 - 106 1 sec / 2000 yrs[6]
15 sec / month
Cesium atomic clock 9.192 GHz 109 1 sec / 2*109 yrs
1 sec / 2,000,000 yrs

#### Higher accuracy

Slow mechanical oscillators like pendulums and balance wheels have a low enough Q that the disturbance caused by the impulses to keep them moving is often the limiting factor on their timekeeping accuracy. Therefore the design of the mechanism that provides these impulses, the escapement, has a large effect on their accuracy. The quest for higher accuracy in mechanical clocks and watches has mostly been a search for better escapements, which disturb the oscillator less.

In contrast, in higher Q oscillators such as quartz crystals, the higher Q makes the oscillator insensitive to disturbance from the electronic oscillator circuit that provides the impulses to keep it vibrating. These oscillators are more influenced by environmental factors such as changes in temperature. In the most accurate oscillators of all, the vibrating atoms in atomic clocks, the Q is actually too high to be measured, and the accuracy of these clocks is limited by the resolution of the measuring equipment, such as the lifetime of the atoms in the apparatus. Current research to develop higher accuracy atomic clocks focuses on making the atoms "hold still" for longer periods, using lasers to cool them, so their vibration rate can be measured more accurately.

Type of clock Oscillator
(frequency)
Controller Counter chain Indicator Peak accuracy
(Typical accuracy)
Water clock none water flow through an orifice gear train analog dial or bell 15 min / day
1 hour / day
Verge & foliot clock foliot
0.25-1 Hz
verge escapement gear train analog dial or bell 15 min / day
1 hour / day
Mechanical watch balance wheel
2-5 Hz
lever escapement gear train analog dial 10 sec / day
1 sec / day
Pendulum clock pendulum
0.5-2 Hz
deadbeat escapement gear train analog dial 4 sec / year
10 sec / month
Torsion pendulum clock torsion pendulum
0.05-0.125 Hz
escapement gear train analog dial
4 min / month
Marine chronometer balance wheel
2-5 Hz
detent escapement gear train analog dial 0.1 sec / day
0.3 sec / day
Electromagnetic pendulum clock Invar pendulum
0.5-1 Hz
Electric switch & solenoid circuit gear train analog dial 1 sec / year
-
Synchronous electric clock AC power line
50 or 60 Hz
synchronous motor gear train analog dial sync'd to AC power
Tuning fork watch tuning fork
360 Hz
oscillator circuit gear train analog dial
2 sec / day
Quartz watch or clock quartz crystal
32,768 Hz
oscillator circuit digital counter digital LCD or dial 3 sec / yr
15 sec / month
Digital clock quartz crystal or AC oscillator circuit digital counter digital display -
Computer real time clock quartz crystal
32,768 Hz
oscillator circuit software counters computer display screen sync'd to UTC
Precision quartz chronometer quartz crystal
5 MHz
oven controlled
crystal oscillator (OXCO)
digital counter digital display 1 sec / 2000 yrs[7]
1 sec / 20 yrs
Rubidium atomic clock Rubidium atoms
6.835 GHz
microwave cavity oscillator
and phase-locked loop
digital counter digital display 1 sec / 2,000,000 yrs
1 sec / 20,000 yrs
Cesium atomic clock Cesium atoms
9.192 GHz
microwave cavity oscillator
and phase-locked loop
digital counter digital display - primary standard 1 sec / 2*109 yrs
1 sec / 2,000,000 yrs

# For Mechanical watch

## Terminology

Mechanical watches are a mature technology with a long history, and a number of specialized terms are used to describe them:

• Adjusted - high quality mechanical watches are made more accurate by a process of adjusting the balance wheel and balance spring to eliminate errors due to temperature changes, and the effects of gravity on the balance wheel when the watch is in different positions. The usual adjustments are: heat, cold, isochronism, dial up, pendant up, pendant right, pendant left, pendant down.
• Arbor - the axle or shaft of a watch's gear wheel.
• Automatic or self-winding watch – a watch in which the mainspring is automatically wound using the natural motions of the wearer’s wrist, to make manual winding unnecessary.
• Baguette - a watch in which the length of the case is at least three times its width; a long, narrow, diamond shaped watch.
• Banking or knocking - an abnormal running condition in which the balance wheel rotates too far in each direction, causing the impulse pin to strike the back of the pallet fork. This is usually caused by too much drive force from the mainspring, and makes the watch gain time.
• Barrel - a cylindrical box in a watch movement in which the mainspring is coiled, with gear teeth around the circumference to drive the wheel train.
• Breguet key - a winding key with an attached ratchet allowing winding in only one direction.
• Breguet spring or overcoil spring - a type of balance spring in which the end is bent up over the plane of the spiral, to increase accuracy.
• BPH - beats per hour.
• Bumper - a watch with an early type of self-winding mechanism in which a pivoted weight bumps back and forth between spring stops.
• Calendar watch – a watch that displays the date, and often the day of the week.
• Chronograph – a watch with additional stopwatch functions. Buttons on the case start and stop the second hand and reset it to zero, and usually several subdials on the face display the elapsed time in larger units.
• Chronometer – a watch that has met the high standards of accuracy of the Controle Officiel Suisse des Chronometeres (COSC) of Switzerland.
• Click - the pawl which stops the mainspring from turning backward and unwinding. It makes the 'clicking' sound when the watch is wound.
• Complication – additional functions on a watch besides the basic display of time
• Crown - knob on the outside of the case used to wind the watch, and usually to set the time.
• Damaskeening - a decorative pattern of wavy parallel lines often used on the plates of watch movements. An American term, in Europe it was called Fausse Cotes or Geneva stripes.
• Ebauche (ay-boesh) - an unfinished watch movement, lacking the balance, balance cock, mainspring, and with the plates unpolished. This is the form in which watch movements are sold by movement manufacturers. Watch manufacturers buy them, finish them, and put their own name on them.
• Equation of time - a dial which displays the difference between the time kept by clocks and the time as indicated by the position of the sun, which varied during the year. This rare complication originated when watches had to be set by the passage of the sun overhead.
• Escape wheel -
• Flyback - a type of chronograph, in which pushing the stopwatch button successively causes the seconds hand to start, stop, and then return to zero. Also used more generally for a hand on the face that doesn't rotate continuously, but traverses a scale and then jumps back to the beginning of the scale.
• Fusee - a conical pulley with a chain wound around it, used in the earliest pocketwatches to equalize the force of the mainspring.
• Going barrel - the type of mainspring barrel used in modern watches, with a ring of teeth around it to drive the gear train.
• Going train - the part of the gear train that transmits power from the mainspring to the balance wheel
• Grande sonnerie (grand strike) - a repeater watch that chimes the hours and quarter hours at the press of a button.
• Hacking or hack set - a feature that stops the second hand while the watch is being set, enabling the watch to be synchronized to the precise second. Mostly seen in military watches.
• Hairspring - the balance spring of a watch.
• Hunter case - a pocketwatch case with a hinged metal lid to protect the face that must be opened to see the time. The term originated with pocketwatches made to be carried on horseback by hunters.
• Incabloc - trade name for a patented Swiss shockproof mounting system for balance wheel pivots.
• Isochronism - means that a watch runs at the same rate regardless of the drive force; that is regardless of whether the mainspring is fully wound up or almost run down. The term is also used for the adjustments to the balance spring to achieve isochronism.
• Jewels - bearings made from synthetic rubies or sapphires for the pivots in a watch, to reduce friction.
• Jump hour watch - a mechanical watch which indicates the time with digits displayed in windows, instead of rotating hands.
• Key set - an older pocketwatch in which the time had to be set with a key.
• Key wind - an older pocketwatch in which the watch was wound with a key.
• Keyless work - the mechanism used to set the time in a modern watch, so called because it doesn't use a key as in older watches.
• Lever - 'T' shaped lever in the lever escapement. It has jewelled pallets on the arms that engage the escape wheel, and a fork on the end which gives impulses to the impulse pin on the balance wheel.
• Lever escapement - the type of escapement used in modern watches. It has a 'T' shaped lever which is pushed by the escape wheel, which in turn gives pushes to the balance wheel to keep it oscillating.
• Ligne - an old French measure used to express the size of watch movements. 2.256 millimeters.
• Lugs - projections on a wristwatch case used to attach the strap.
• Minute repeater - a watch that chimes the time audibly to the minute at the press of a button. This rare complication was originally used by blind people.
• Moon phase dial - a complication that displays the phase of the moon on a dial with a painted moon face on a rotating disk.
• Movement - the mechanism inside the watch case that keeps time and moves the hands.
• Pallets -
• Pair case - a pocketwatch that has two cases, an outer decorative one and an inner plain one to protect the movement. Needed because the outer case had to be opened frequently to wind the watch.
• Perpetual calendar - a calendar mechanism which automatically adjusts for the different length of the months and for leap years.
• Power reserve indicator or wind indicator - a dial that shows how much power is left in the watch's mainspring, usually graduated in hours the watch has left to run.
• Rattrapante - a feature on chronographs to measure split or lap times. The watch has two second hands which start the timing interval moving together. A second push of the timing button stops the lap hand, so the lap time can be read, while the other second hand continues. Another push of the button causes the lap hand to catch up to the second hand again.[8]
• Regulator - lever in the watch movement on the balance spring which is used to adjust the watch's rate.
• Remontoire - in some antique watches, a small secondary spring which is wound up repeatedly by the mainspring, and in turn runs the movement. Its purpose is to even out the force of the mainspring.
• Repeater - a watch that chimes the hours audibly at the press of a button. This rare complication was used before electric lighting to check the time in the dark, and by the blind.
• Shockproof - watch company terminology for any of several systems for mounting the balance wheel pivots with springy mountings that absorb shock, to prevent the pivots from breaking if the watch is dropped.
• Skeleton watch - a watch with the plates and bridges of the movement decoratively carved and cut away to allow the works to be seen. The face and/or the back is transparent to allow this decoration to be seen.
• Stackfreed - a cam device used occasionally in the earliest watches to equalize the force of the mainspring.
• Stopwork - devices used on the mainspring barrel of early watches to stop the spring from being wound all the way up, to prevent the mainspring from being broken by careless winding.
• Tank watch - a watch with
• Tonneau watch - a watch shaped like a barrel, rectangular with convex sides.
• Tourbillon - an expensive elaborate complication that was originally designed to make the watch more accurate. The effect of gravity on the balance wheel makes watches run at slightly different rates when in different positions. In a tourbillon, the balance wheel and escapement are mounted in a cage that rotates slowly to eliminate the errors due to gravity. Usually the tourbillon is exposed on the watch's face to show it off.
• Train - the gear train of a watch.
• Transition watch - an early wristwatch converted from a pocketwatch. When wristwatches became popular in the early 1900s, the only movements that were available were pocketwatch movements. They are larger than later wristwatches and the crown is at the 12 o'clock position as in pocketwatches, not at the normal 3 o'clock position.
• Trench watch - An early style of wristwatch worn by soldiers during World War 1. They typically had wire lugs that the strap was threaded through, and often had a metal shrapnel guard or a leather pocket on the strap to protect the face.

# For Regulator clock

A regulator clock or just regulator was a precision pendulum clock that was used to set other clocks.

From their invention in 1656 until the 1930s, pendulum clocks were the world's most accurate timekeepers. The term 'regulator' originated in the 18th century, when a need arose for clocks more accurate than ordinary domestic pendulum clocks for scientific research, astronomy, surveying, and navigation. British clockmaker George Graham made the first regulators To achieve accuracy, these clocks are always weight driven, have temperature compensated pendulums, and omit unnecessary complications such as striking mechanisms, calendar works, and moon dials.

By the 19th century, several different categories of regulator clocks were made. The most accurate clocks were called astronomical regulators, and were used in astronomical and naval observatories, and as primary standards for the first national time distribution services. Then manufacturers produced high grade wall and floor clocks to serve as precision timekeepers for industry. These were installed in workplaces, post offices, railroad stations, and jewelry stores to schedule work and 'regulate' other clocks. Toward the end of the century, the word 'regulator' became used as a promotional term, and was applied to ordinary clocks that were not exceptionally accurate, such as vienna regulators and schoolhouse regulators.

## Characteristics of regulators

These are the features that distinguish precision pendulum clocks:

• Weight drive: The timekeeping rate of all clock mechanisms varies with changes in the drive force applied to it, a problem called lack of isochronism. The drive force provided by a mainspring decreases during the clock's running period as the spring unwinds, while the force provided by a weight suspended from a pulley by a cord is constant. So all regulators used weights for power.
• Temperature compensated pendulum: The largest source of error in early pendulum clocks was expansion and contraction of the pendulum rod with temperature changes. As the temperature rises, the pendulum rod gets longer and the period of oscillation gets slower, causing the clock to lose time. All regulators had pendulums that compensated for temperature changes so the rate of the clock was unaffected. The most common type was the mercury pendulum. See below for explanation of temperature compensation.
• Precision escapement: The escapement is a major source of error in a pendulum clock, because of its disturbing influence on the pendulum. Most regulators used the deadbeat escapement, introduced by George Graham in his regulators around 1715. In the 1800s a few used the Dennison gravity or pinwheel escapements. Astronomical regulators sometimes used special escapements such as the Riefler escapement. Often the escapement pallets were made of jewels, to reduce friction. By the turn of the century electromechanical escapements began to be used. These used a switch contact on the pendulum to turn on an solenoid or electromagnet to impulse the pendulum, and
• Simplified wheel train: In order to reduce friction and backlash, which resulted in varying force applied to the escapement, the wheel trains of regulators was made as simple as possible. Unnecessary features such as striking, calender dials, and moon phase dials were omitted. For additional simplification, the traditional clock face with central coaxial hour and minute hand was dispensed with, to eliminate the extra gears (motion work) that ran it. The hour and minute hands were run directly off separate wheels of the train, whose axles were brought out through the face. So the hour and minute hand were located in separate subdials on the clock face, while the large second hand was located in the center with graduations around the rim. The hour hand often rotated once in 24 hours. The hands were thin and light, and often counterbalanced so they didn't exert varying torques on the train at different angles. The faces were devoid of decoration, with fine black engraved graduations on a white background.
• High tooth count: The finer the teeth of the gears used in the wheel train, the more even was the force transmitted to the escapement. In ordinary clocks, the pinions, or small gears, usually had 6 teeth. Regulators used pinions of 8, 10, or even 12 teeth. The large gear wheels had proportionately larger numbers of teeth also, to keep the gear ratios correct.
• Jewelled bearings and pallets: To reduce friction, the pallets of the escapement and sometimes the bearings of the wheel train were jewelled.

## Temperature compensated pendulums

The largest source of error in early pendulum clocks, particularly in the unheated buildings of the time, was expansion and contraction of the pendulum rod with temperature changes. A temperature increase of 60° F causes a clock with a steel pendulum rod to expand ___% and lose ____ seconds per day. Early regulators often had wooden pendulums, which expand less and only lose ____ seconds.

The first pendulum compensated for temperature changes was the mercury pendulum, invented by George Graham in 1721. In this, the bob is replaced by a container of the liquid metal mercury. As the temperature increases, the pendulum rod gets longer, lowering the pendulum's center of gravity, but the mercury expands and its surface rises in the container, raising the center of gravity. By using the correct amount of mercury, these changes cancel out, leaving the pendulum's center of gravity, and its period, unchanged with temperature. Mercury pendulums were the most widely used compensated pendulums in regulators. Their only disadvantage was that the mercury was slow to come to the new temperature after a temperature change, so the compensation lagged behind a little. This was often dealt with by using several slender jars of mercury.

Another type of temperature compensated pendulum used in regulators was the gridiron pendulum, invented by John Harrison in 1726. In this device, the pendulum rod was made of several parallel bars of two different metals, usually zinc and steel. The zinc has a larger thermal expansion than steel, so the zinc rods expand more when warmed. The rods are connected together at top and bottom in such a way that the zinc rods shorten the pendulum when they expand. By using the correct lengths, the shortening effect of the zinc rods exactly compensates for the lengthening of the steel rods, leaving the pendulum's length unchanged with temperature. Gridirons had the disadvantage that during expansion or contraction the rods had to slide through holes in their supports, and this microscopic sliding action occurred in a series of 'jumps', causing the rate of the clock to jump discontinuously. So gridirons were used in early regulators but fell out of use in regulators in the 19th century. However, they became popular in house clocks. In fact they became so closely associated with precision that many 'regulator' house clocks had 'gridiron' style pendulums that had no actual temperature compensation ability, but were just for show.

By the turn of the century, Invar pendulum rods began to be used in some high precision astronomical regulators. Invented in 1896 Charles Édouard Guillaume, this nickel steel alloy had a very low thermal expansion of ____ and this small thermal expansion could be compensated by a few inches of aluminum under the pendulum. Later fused quartz pendulum rods were used, which had even lower expansion.

# For Clockmaker

The first clocks were large turret clocks in cathedrals and town squares. These unique mechanisms were often designed by educated philosophers, who hired blacksmiths to do the actual metalwork. In the 1400s clocks were gradually made small enough to to be used in private houses, and domestic clocks and chamber clocks appeared, but these were

## References

1. ^ "Resonance Width". Glossary. Time and Frequency Division, US National Institute of Standards and Technology. 2009. Retrieved 2009-02-21.
2. ^ a b Jespersen, James (1999). From Sundials to Atomic Clocks: Understanding Time and Frequency. New York: Courier Dover. pp. 41–50. ISBN 0486409139. Unknown parameter |coauthors= ignored (|author= suggested) (help) p.39
3. ^ Matthys, Robert J. (2004). Accurate Pendulum Clocks. UK: Oxford Univ. Press. pp. 27–36. ISBN 0198529716.
4. ^ "Quality Factor, Q". Glossary. Time and Frequency Division, US National Institute of Standards and Technology. 2009. Retrieved 2009-02-21.
5. ^ Matthys, 2004, p.32, fig. 7.2 and text
6. ^ Macey, Samuel L. (1994). Encyclopedia of Time. New York: Garland Publishing. pp. p.265. ISBN 0815306156.
7. ^ Macey, Samuel L. (1994). Encyclopedia of Time. New York: Garland Publishing. pp. p.265. ISBN 0815306156.
8. ^ Rochkind, Mark. "Flyback vs. Rattrapante".

# For Balkan dance

Balkan dance refers to the folk dance of the Balkan countries: Albania, Bosnia, Bulgaria, Croatia, Greece, Kosovo, Macedonia, Montenegro, Romania, Serbia, Slovenia, and Turkey. These are sometimes considered as a single category within folk dance because they share distinctive regional characteristics, and because, due to the unique degree of ethnic mixing in the Balkan region, dances don't break down along national but along ethnic lines, with small ethnic enclaves in different countries in the region developing local variations of the same dance. The common characteristics of Balkan dance include: the dominance of line dance forms, with lines or circles of dancers holding hands without partners; complicated rhythms with distinctive asymmetric meters composed of combinations of different length beats; complicated footwork, and similar handholds, footwork, and styles.

A major source of interest in Balkan dancing outside the Balkans is the international folk dance movement, within which Balkan dance forms a popular specialty ever since the "kolo mania" of the 1940s and 50s. Hundreds of amateur folk dance groups worldwide learn Balkan dances for recreation or performance.

## Music: asymmetric meters

Although Balkan dance music includes pieces with standard 'Western' time signatures of 2/4, 3/4, and 4/4, it also includes meters with 5, 7, 9, 11, 13, and 15 beats per measure. These are called asymmetric meters. They are often described as composed of combinations of two different length units or "beats", which are themselves composed of different numbers of the underlying metric beats. For example, the Macedonian dance Lesnoto is done to a seven beat measure (7/8), with emphasis on the first, fourth and sixth beat. These can be grouped as one "slow" unit of 3 of the underlying metric beats and two "quick" units of 2 beats: (BEAT, beat, beat), (BEAT, beat), (BEAT, beat), often written as slow-quick-quick or 3-2-2. It is important to understand that Balkan musicians do not describe their music's rhythms in these terms, this is a simplification used by western musicians and does not capture the full complexities of the subtlely-changing Balkan rhythms.

Each Balkan dance family uses a distinctive combination of these basic units, such as Paidushko (5 beats: 2-3), Eleno Mome (7 beats: 2-2-1-2), Rachenitsa (7 beats: 2-2-3), Daichovo (9 beats: 2-2-2-3), Kopanitsa (11 beats: 2-2-3-2-2), and Bučimis (15 beats: 2-2-2-2-3-2-2).

## Formations

Many dances are done in a line, with all dancers facing perpendicular to the line, and holding onto the hands, shoulders, or belt of the neighboring dancers. Originally many dances were gender specific; exclusively women's or men's dances. In the ones that were not, men and women danced in separate lines, or in a gender-segregated line with women at the front and men at the back, sometimes However today the same dances are often done in mixed lines. Long lines are curved in an arc, with dancers facing in. In most dances the line moves to the dancer's right, but some move to the left, or in and out. The dancer on the front end of the line in the direction of motion is the "leader", with responsibility for leading the line, and calling any changes in step. Many dances have "called" variations, in which the leader periodically calls out the name of a variation and the line changes its step to that variation. In others, the leader, or individual dancers, may improvise variations or embellishments. In others, the leader is a "solo" performer, executing showy acrobatic moves while the rest of the line performs the basic step. Dancers joining the dance always join at the end of line, never the front leader position. Another common formation for dances is circles, large or small, with dancers facing in, in which case there is no leader. Other formations are short straight lines, two lines facing each other, or solo dancing without contact.

## Handholds

These are the most common handholds used in Balkan line dances. The names given are merely descriptive, not necessarily translations of names used in the native languages, but have some currency among international folk dancers.

• "V": The hands are held down relaxed at the side of the body, holding the hand of the neighboring dancer on each side. The right hand is palm up, the left hand palm down.
• "W": The arms are held up with elbows bent in a "W" shape, hands at shoulder height, holding the hand of the neighboring dancers, right hand palm up, left hand palm down.
• "Teacup": The left hand is placed on the stomach or holds the belt buckle, and the right hand is looped loosely through the next dancer's left arm.
• Front basket: The hands are held down as in the "V", but hands are joined with the two dancers on the far side of the neighboring dancers, in front of the neighboring dancers, so alternate dancers in the line are linked.
• Back basket: Like the front basket, except the hands are joined behind the backs of the neighboring dancers.
• Belt: Each dancer wears a belt or sash, and holds the belt of the two neighboring dancers, in front over the stomach. This links the line of dancers together securely, and so it is found in fast moving acrobatic dances.
• Shoulder: The arms are held out horizontally to the sides, with the hands on the shoulders (deltoid muscle) of the neighboring dancers.
• "Pinkie": Similar to the "W" hold, except that the hands are made fists and the extended, curved, little fingers are linked, right hand up, left hand down
• "Halay": Seen in Turkish dances, the dancer stands straight upright, as close to the next dancer as possible, with arms straight down and rigid at his sides, holding the hand of the neighboring dancers.

Some dances incorporate changes in arm position, or swinging or pumping motions of the arms.

# For Screw

## Analysis of square thread screws 2

Square threads have lower friction and higher efficiency than the other types of threads used in screws: Acme, trapezoidal and V-threads. This is because the outward angle of the bearing surface in the other types increases the normal force on the surface, and therefore the friction. Therefore square threads are used for screws that carry power, such as lead screws and screw jacks. This important class of screws can be analyzed as a simple inclined plane. The slope of the thread bearing surface is simply equal to the distance ratio ${\displaystyle l/(2\pi r)\,}$, so the pitch angle of the thread is given by

${\displaystyle \tan \theta ={\frac {l}{2\pi r}}\,}$

The "angle of repose" φ, the angle that the resultant Fr = FN + Fμ makes with the surface normal, is

${\displaystyle \tan \phi =\mu \,}$

where μ is the static coefficient of friction between the screw threads.

The body carrying the moving screw threads, when considered as a free body, has three forces acting on it:

• The rotational force on the edge of the shaft Fin, which acts horizontally (tangentially)
• The axial load force on the shaft Fout, which acts downwards, parallel to the screw's axis
• The force of the stationary screw threads on the moving threads. This can be resolved into two components:
• The normal force Fn of the stationary threads on the moving threads. This is directed perpendicular (normal) to the thread surface.
• The frictional force Ff of the moving threads on the object, which acts parallel to the thread surface, and is always in a direction opposite to the motion of the object. It is equal to the normal force multiplied by the coefficient of friction μ between the two surfaces.

Using Newton's second law of motion the load will be stationary or in steady motion if the sum of the forces on it is zero. Since the direction of the frictional force is opposite for the case of forward and reverse motion, these two cases must be considered separately:

• Forward motion: The screw thread is moving in the direction of the applied (rotational) force, so the frictional force is directed opposite to it, opposing the applied force.
${\displaystyle \sum F_{x}=-F_{n}\sin \theta -F_{f}\cos \theta +F_{in}=0\,}$
${\displaystyle \sum F_{y}=F_{n}\cos \theta -F_{f}\sin \theta -F_{out}=0\,}$
${\displaystyle F_{n}\sin \theta +\mu F_{n}\cos \theta =F_{in}\,}$
${\displaystyle F_{n}\cos \theta -\mu F_{n}\sin \theta =F_{out}\,}$
${\displaystyle \mathrm {MA} ={\frac {F_{out}}{F_{in}}}={\frac {\cos \theta -\mu \sin \theta }{\sin \theta +\mu \cos \theta }}={\frac {1-\mu \tan \theta }{\tan \theta +\mu }}={\frac {1-\tan \phi \tan \theta }{\tan \theta +\tan \phi }}\,}$
Using a trigonometric identity
${\displaystyle \mathrm {MA} ={\frac {1}{\tan(\theta +\phi )}}\,}$
${\displaystyle F_{in}=F_{out}\tan(\theta +\phi )\,}$
This gives the amount of force required for "impending motion" of the screw forward, in the direction of applied rotational force. If the input force is greater than this, the screw will rotate forward. There are 2 cases:
1. ${\displaystyle \theta +\phi <90^{\circ }}$: The mechanical advantage is positive. The screw will rotate forward.
2. ${\displaystyle \theta +\phi \geq 90^{\circ }}$: The mechanical advantage is zero or negative, so the screw is "locked" to forward motion and can't be rotated forward. This only occurs with very large pitch screws, and "backwards" screws like the push drill.
• Reverse motion (overhauling): The screw thread is rotating backwards, against the applied rotational force, so the frictional force is directed opposite to it, in the same direction as the applied force.
${\displaystyle \sum F_{x}=-F_{n}\sin \theta +F_{f}\cos \theta +F_{in}=0\,}$
${\displaystyle \sum F_{y}=F_{n}\cos \theta +F_{f}\sin \theta -F_{out}=0\,}$
${\displaystyle F_{n}\sin \theta -\mu F_{n}\cos \theta =F_{in}\,}$
${\displaystyle F_{n}\cos \theta +\mu F_{n}\sin \theta =F_{out}\,}$
${\displaystyle \mathrm {MA} ={\frac {F_{out}}{F_{in}}}={\frac {\cos \theta +\mu \sin \theta }{\sin \theta -\mu \cos \theta }}={\frac {1+\mu \tan \theta }{\tan \theta -\mu }}={\frac {1+\tan \phi \tan \theta }{\tan \theta -\tan \phi }}\,}$
Using the same trigonometric identity as above
${\displaystyle \mathrm {MA} ={\frac {1}{\tan(\theta -\phi )}}\,}$
${\displaystyle F_{in}=F_{out}\tan(\theta -\phi )\,}$
This gives the amount of load force required for "impending motion" of the screw backward. If the load force is greater than this, the screw will rotate backwards, overhauling. There are 3 cases:
1. ${\displaystyle \theta <\phi \,}$: The mechanical advantage is negative, so the screw is "locked" and will not turn backward with any amount of load force on the shaft, even with some negative (backward) rotational torque on it. This is the case with most ordinary screws.
2. ${\displaystyle \theta =\phi \,}$: The 'angle of repose'. The mechanical advantage is infinite. The screw is "locked" to backward motion, but the slightest negative torque on it will cause it to rotate backwards.
3. ${\displaystyle \theta >\phi \,}$: The mechanical advantage is positive. The screw will rotate backwards and overhaul

It can be seen from the above that a screw will be self-locking if and only if the arctangent of the coefficient of friction φ is greater than the helix angle θ.

# For Glow discharge

A glow discharge typically occurs in a partially-evacuated glass tube with two metal electrodes, containing a gas at a pressure of 0.1 to 10 torr about 1/10,000 to 1/100 amospheric pressure. The tube doesn't

# For Negative feedback

A block diagram of a negative feedback loop.[1] The box P represents the process to be controlled. Its output y is continuously compared to a "reference signal" r representing the desired output. The difference between the two r - y, called the "error signal", e, is used by a controller (C) to alter the process, moving the output level y closer to r.[1]

Negative feedback occurs when the result of a process influences the operation of the process itself in such a way as to reduce changes. Negative feedback tends to make a system self-regulating or self-correcting; if the state of the system is moved away from the equilibrium state due to external disturbances, over time it will return to the equilibrium state.

To have negative feedback a process must have a feedback loop, in which information from the output of a process is fed back as an input signal to control the process; in engineering this is called a closed-loop system.[2] In a system controlled by a negative feedback loop, the level of some output of a process is continuously compared to a (possibly variable) reference value which represents the desired output.[2] The difference, called the error signal, is used to control the process, altering the output in a direction to reduce the error, with the result that the output becomes closer to the desired value.

An example of a negative feedback loop in biology is the self-regulating role of hunger.[3][4] As time passes since our last meal, we get hungry. The hunger acts as an "error signal" stimulus, causing us to respond by eating. As we eat, we become less hungry, and eventually stop eating. So the response to hunger acts in a "negative" direction, to reduce the hunger. The purpose of this feedback loop is to provide a steady flow of nutrients into our bodies.

In control systems theory a feedback loop has negative feedback if the feedback signal is subtracted from the reference signal to get the error signal,[1][5] as above. The other kind of feedback is positive feedback, in which the feedback signal is added to the reference signal. Instead of tending to correct the error, and cause the output to converge on the reference value, positive feedback acts to increase error, moving the output away from the reference value. Positive feedback can cause the output of a process to be unstable; to fluctuate or oscillate, or increase without bound.

Negative feedback is widely used in mechanical and electronic engineering, and in industrial plant control, but it also occurs naturally within living organisms, and can be seen in many other fields from chemistry and economics to social behaviour and the climate. Ktesibios, an ancient Greek engineer, built one of the first known negative feedback mechanisms, a flow controller in a water clock, in the 3rd century BCE .[6] The first industrial negative feedback control system was the flyball governor for steam engines invented in 1767 by James Watt.[6] The mathematical condition for feedback stability, the Routh-Hurwitz stability criterion, was discovered independently by Edward John Routh in 1876 and Adolf Hurwitz in 1895.[6] The mathematics of negative feedback was further developed by Harold S. Black at Bell Telephone Laboratories in 1933[6][7][8] as the basis for electronic systems. General negative feedback systems are studied in control systems engineering.

## References

1. ^ a b c Lobontiu, Nicolae (2010). System Dynamics for Engineering Students: Concepts and Applications. Academic Press. pp. 11–4. ISBN 0123859174, Check |isbn= value: invalid character (help).
2. ^ a b Owen-Jackson, Gwyneth (2001). Developing Subject Knowledge in Design and Technology: Systems and Contro. Trentham Books. pp. 6–7. ISBN 1858562430. Unknown parameter |coauthors= ignored (|author= suggested) (help)
3. ^ Sundar, Nathan (2009). AP Biology Study Guide. FastPencil Inc. p. 14. ISBN 1607468867. Question 40
4. ^ Pastorino, Ellen E. (2011). What is Psychology? Essentials, 2nd Ed. Cengage Learning. p. 290. ISBN 1111834156. Unknown parameter |coauthors= ignored (|author= suggested) (help)
5. ^ Bolton, W. (1991). Industrial Control And Instrumentation. Universities Press. ISBN 8173713642.
6. ^ a b c d Gopal, M. (2002). Control Systems: Principles and Design, 2nd Ed. Tata McGraw-Hill Education. p. 14. ISBN 0070482896.
7. ^ Black, H.S. (January 1934). "Stabilized Feedback Amplifiers" (PDF). Bell System Tech. J. American Telephone & Telegraph. 13 (1): 1–18. Retrieved January 2, 2013.
8. ^ Bennett, Stuart (1993). A History of Control Engineering: 1930-1955. IET. p. 70. ISBN 0863412998.

## Handholds

These are the most common handholds used in Balkan line dances. The names given are merely descriptive, not necessarily translations of names used in the native languages, but have some currency among international folk dancers.

• "V": The hands are held down relaxed at the side of the body, holding the hand of the neighboring dancer on each side. The right hand is palm up, the left hand palm down.
• "W": The arms are held up with elbows bent in a "W" shape, hands at shoulder height, holding the hand of the neighboring dancers, right hand palm up, left hand palm down.
• "Teacup": The left hand is placed on the stomach or holds the belt buckle, and the right hand is looped loosely through the next dancer's left arm.
• Front basket: The hands are held down as in the "V", but hands are joined with the two dancers on the far side of the neighboring dancers, in front of the neighboring dancers, so alternate dancers in the line are linked.
• Back basket: Like the front basket, except the hands are joined behind the backs of the neighboring dancers.
• Belt: Each dancer wears a belt or sash, and holds the belt of the two neighboring dancers, in front over the stomach. This links the line of dancers together securely, and so it is found in fast moving acrobatic dances.
• Shoulder: The arms are held out horizontally to the sides, with the hands on the shoulders (deltoid muscle) of the neighboring dancers.
• "Pinkie": Similar to the "W" hold, except that the hands are made fists and the extended, curved, little fingers are linked, right hand up, left hand down
• "Halay": Seen in Turkish dances, the dancer stands straight upright, as close to the next dancer as possible, with arms straight down and rigid at his sides, holding the hand of the neighboring dancers.

Some dances incorporate changes in arm position, or swinging or pumping motions of the arms.

# For Screw

## Analysis of square thread screws 2

Square threads have lower friction and higher efficiency than the other types of threads used in screws: Acme, trapezoidal and V-threads. This is because the outward angle of the bearing surface in the other types increases the normal force on the surface, and therefore the friction. Therefore square threads are used for screws that carry power, such as lead screws and screw jacks. This important class of screws can be analyzed as a simple inclined plane. The slope of the thread bearing surface is simply equal to the distance ratio

# For Limiting

In control system engineering and electronics limiting, also called clipping, saturation or saturation nonlinearity is a characteristic of a process or device in which the output amplitude is prevented from exceeding predetermined limiting values. In engineering, saturation is considered a property of the transfer function (input-output function) of a device. As the input of the device is increased, the output increases up to a maximum value, but remains at that value with further increases of the input. Similarly, as the input is decreased the output decreases to a minimum value but remains there for further decreasing input. Saturation is a very common response of many types of electronic, mechanical, and pneumatic equipment to excessively large amplitude driving or control signals, a result of the fact that the output of any mechanism has limits.

Saturation is a nonlinear function and therefore can cause distortion and harmonic generation in linear systems. For example, excessive levels of gain (volume) in an audio system can cause the sound to become distorted when the amplifying devices (vacuum tubes or transistors) saturate. The characteristic distorted sound of types of rock music is caused by the guitar amplifiers saturating when the volume is turned up.

In electronic circuits and mechanical linkages, saturation is the most common type of nonlinearity.

Saturation can refer to "hard limiting" (clipping), in which a signal between the limits is passed through normally but parts of the signal outside the limits is "sheared off" when threshold. It can also refer to "soft limiting", a type of variable-gain audio level compression, in which the gain of an amplifier is changed very quickly to prevent the signal from going over a certain amplitude.

• Hard limiting ("clipping") is a limiting action in which there is
• (a) over the permitted dynamic range, negligible variation in the expected characteristic of the output signal, and
• (b) a steady-state signal, at the maximum permitted level, for the duration of each period when the output would otherwise be required to exceed the permitted dynamic range in order to correspond to the transfer function of the device.
• Soft limiting is limiting in which the transfer function of a device is a function of its instantaneous or integrated output level. The output waveform is therefore distorted, but not clipped.

## Definition

The transfer function of a hard "clipping" type saturation nonlinearity is

${\displaystyle y(x)={\begin{cases}L_{\text{max}},&x\geq L_{\text{max}}\\x,&L_{\text{max}}>x>L_{\text{min}}\\L_{\text{min}},&x\leq L_{\text{min}}\end{cases}}}$

Often the saturation is symmetrical about the zero point of the signal

${\displaystyle y(x)={\begin{cases}L,&x\geq L\\x,&L>x>-L\\-L,&x\leq -L\end{cases}}}$

{{FS1037C MS188}}

# For Wheel and axle

## History

The wheel is widely mentioned as one of the most important inventions in history,[Bulliet, 3] but since it was invented in prehistoric times, many points about its history are in dispute. Perhaps the earliest functional application of the wheel was the potter's wheel, a horizontal rotating platform for making clay pots. The first hand-turned potter's wheels, called tournettes, appeared in the Middle East toward the end of the Neolithic period, around 4500 BC. [Higgins, 10]

The most famous and significant application of the wheel was in the invention of the wheeled vehicle. Wheels were applied to carts in the late Neolithic period and they have been ubiquitous in transportation ever since. Before the wheel, loads were transported by draft animals dragging various forms of sleds and the travois, a load-carrying platform supported between two poles joined at the end in the shape of a "V"; the point of the "V" dragged along the ground as it was towed. The application of wheels to carts eliminated the friction of the cart dragging along the ground, resulting in a great reduction in required motive power and increase in load-carrying ability. There are two theories of how wheeled vehicles were invented:

The older theory, promoted by Stuart Piggott was that two-wheeled vehicles similar to the chariot evolved by the application of wheels to the travois. [Bulliet, 93]

A newer theory proposed in 1983 by Mary Aiken Littauer is that the first wheeled vehicles were four-wheeled carts, which developed from load-carrying platforms which rolled along the ground on wooden rollers. [NYT]

References: