Pendulum clock Isochronism The tautochrone problem Escapements Pendulum and pendula Commentary

Christiaan Huygens horology

Pendulum clock

• For centuries, clocks were regulated
• by verge escapements
• with a balance wheel or foliot,
• a horizontal bar with adjustable weights.
• A vertical rod with two pallets
• engage the teeth of a crown wheel
• to swing the wheel or foliot
• first in one direction from a pallet
• hitting a tooth at the top of the crown,
• then in the other from the second pallet
• hitting a tooth at the bottom of the crown.
• Galileo had investigated
• using a pendulum as a regulator.
• Around 1637, late in life,
• he invented an escapement.
• Since he was blind, he described it
• to his son, Vincenzo.
• Vincenzo began to build
• a clock of this design,
• but the clock was never completed.
• So Christiaan Huygens was the first
• to build a pendulum clock.
• He used the verge escapment
• and took a lot of effort with the math.
• He found that the ideal path of the swing
• isn’t a circular arc, but a cycloid,
• and he gave a formula for calculating
• the period for a pendulum of a given length.
• After the pendulum, Huygens invented the balance spring,
• a pendulum for a pocket watch.
• He didn’t know that Robert Hooke
• had already invented it fifteen years before.

Isochronism

• Galileo Galilei, in 1581,
• was the first to discover
• that each swing of a pendulum
• took about the same amount of time
• whether swinging widely or narrowly.
• In his church in Pisa
• he counted the beats of his heart
• as a chandelier swung overhead.
• Each swing took the same number of beats
• when calmly swinging a few degrees
• or when pushed by a gust from an open door.

The tautochrone problem

• The path of a pendulum
• is not exactly isochronous;
• that is, wider swings
• are slightly faster.
• However, Huygens showed
• that a cycloid path is isochronous,
• which is interesting because
• Galileo studied the cycloid,
• although he failed
• to determine its area.
• Huygens also showed
• how to correct the path of a pendulum,
• suspending the pendulum from a string
• that is constrained by cycloidal curbs.
• Too bad this design
• did not result in a more accurate clock.
• The improvement in timing
• for getting rid of the circular error
• was offset by the energy
• it took to bend the string,
• at least for small swings,
• where the difference
• between circle and cycloid
• is very small.

Escapements

• Various variations of the verge escapement
• were used in pocket watches and clocks,
• including turret clocks across Europe, since the fourteenth century.
• The verge escapements continued to be used
• after the pendulum replaced the foliot or balance wheel.
• A verge escapement allows a clock driven by a spring
• to slow down as the spring unwinds. It also causes recoil,
• driving the crown wheel backward a little during each tick and tock.
• Furthermore, when regulated with a pendulum instead of foliot,
• it swings the pendulum as much as eighty to a hundred degrees.
• Robert Hooke invented the anchor escapement around 1657,
• reducing the swing of a pendulum to as little as three degrees,
• thereby reducing error due to the tautochrone problem,
• but this escapement still produces recoil.
• In 1675, Richard Towneley invented the deadbeat escapement,
• which is an anchor escapement designed to eliminate recoil
• by adding locking faces to the impulse faces at the ends of the anchor.
• The pin wheel escapement is a robust version of the deadbeat escapement
• used for turret clocks.
• The gravity escapement, developed over a hundred years
• from around 1750 by many including Bloxam and Lord Grimthorpe,
• was used in turret clocks because its rate is unaffected
• by variations in the forces on the gear train.
• John Harrison invented the grasshopper escapement in 1722.
• This escapement requires no lubrication and has two pivoting levers
• that alternately arrested the escape wheel.
• Subsequently, Harrison invented the gridiron pendulum
• and competed for the Longitude prize with his “sea watches.”
• Many escapements were designed for pocket watches.
• Thomas Tompion invented the cylinder escapement in 1695,
• Thomas Mudge invented the lever escapement in 1750,
• and Thomas Earnshaw perfected the detent escapement around 1800.
• Robert Hooke invented the duplex escapement around 1700,
• which provides separate sets of locking and impulse teeth
• and provides an impulse to the balance wheel only during its counterclockwise turn.
• Improvements in escapements included decreasing the degrees of swing,
• and detaching the movement of the pendulum or spring wheel from the gear train,
• isolating the escapement from variations in drive force.
• eliminating recoil or backlash, and reducing friction.
• In general, we want to reduce wear and improve isochronism.
• For pocket watches we also want a self-starting escapement.
• Many more escapements have been invented, including several
• for decorative and wooden clocks. For people today,
• more accustomed to clocks with quartz movements,
• it’s important to note that escapements
• allow the gear train of a clock to escape
• only in rhythm to the swing of a pendulum or balance wheel.

Pendulum and pendula

• Swingers were married people who took other partners,
• and swing dancing was like square dancing only not for squares.
• We were in the Cold War. The Vietnam war had not begun.
• The nation swings to the right, then it swings to the left.
• We repeat mistakes that we have forgotten from our brief history.
• We restage the great works of the Victorian Age.
• Retro is in fashion; rhymed verse has come back as rap lyrics.
• I thought that Darwin had settled the matter of natural selection.
• I recognize that some people have a different opinion,
• but opinions cannot change reality, nor the lessons of the past.
• I still believe people have a responsibility
• to create their own culture, not to get the money to buy it.
• It seems to me that I’ve become an old fart,
• but I’m betting that being an old fart is coming back.