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.
The area under a cycloid is exactly three times the area of
the circle that is used to generate it. Galileo compared these
areas by tracing the curves on sheet metal, cutting them out, and
weighing them, but his result was about 3.1, so he mistakenly
concluded that the ratio was irrational.
Christiaan Huygens’s father, Constantijn Huygens, was
a friend of Marin Mersenne, Descartes, and Galileo. So it is
interesting to inquire how many of his interests Christiaan picked
up from them. Descartes invented analytic geometry; Christiaan
taught analytic geometry to Leibniz. Mersenne was interested in
music theory and so was Christiaan, who rediscovered 31 equal
temperament. Mersenne and Galileo were interested in vibrating
strings and in the cycloid, and so was Christiaan. Galileo was
interested in the pendulum and using it to regulate a clock and so
was Christiaan. Galileo improved the telescope and so did
Christiaan. Galileo was the first to observe the rings of Saturn
and Christiaan was the first to identify them as rings.
Furthermore, as a student, Christiaan corresponded with Fermat,
who with Pascal invented probability theory; well, Christiaan
wrote the first book on probability theory. But Christiaan Huygens
was also important in the development of the internal combustion
engine; Denis Papin was his assistant at one time. Papin
contributed to early steam engines.
The area under a cycloid is exactly three times the area of the circle that is used to generate it. Galileo compared these areas by tracing the curves on sheet metal, cutting them out, and weighing them, but his result was about 3.1, so he mistakenly concluded that the ratio was irrational.
Christiaan Huygens’s father, Constantijn Huygens, was a friend of Marin Mersenne, Descartes, and Galileo. So it is interesting to inquire how many of his interests Christiaan picked up from them. Descartes invented analytic geometry; Christiaan taught analytic geometry to Leibniz. Mersenne was interested in music theory and so was Christiaan, who rediscovered 31 equal temperament. Mersenne and Galileo were interested in vibrating strings and in the cycloid, and so was Christiaan. Galileo was interested in the pendulum and using it to regulate a clock and so was Christiaan. Galileo improved the telescope and so did Christiaan. Galileo was the first to observe the rings of Saturn and Christiaan was the first to identify them as rings. Furthermore, as a student, Christiaan corresponded with Fermat, who with Pascal invented probability theory; well, Christiaan wrote the first book on probability theory. But Christiaan Huygens was also important in the development of the internal combustion engine; Denis Papin was his assistant at one time. Papin contributed to early steam engines.
See also in The book of science:
Readings on wikipedia: