Double Pendulum

Resonance Clocks

John Kirk

1
 Topics
• Introduction
• Resonance
• Early Makers
• Janvier’s Clocks
• Breguet’s Clocks
• Modern Clocks
• “Reproductions”

2
 Topics
• Introduction
• Resonance
• Early Makers
• Janvier’s Clocks
• Breguet’s Clocks
• Modern Clocks
• “Reproductions”

3
 Introduction
• While there are three and four pendulum
clocks, most multi-pendulum clocks have two
pendulums
– Clocks with more than two pendulums will be the
subject of another presentation
• Resonance clocks have two or more
pendulums locked to each other in rate, which
aids rate stability and can compensate for
disturbances

4
 Topics
• Introduction
• Resonance
• Early Makers
• Janvier’s Clocks
• Breguet’s Clocks
• Modern Clocks
• “Reproductions”

5
 Resonance (1 of 4)
• Two mechanical oscillators, such as balance
wheels or pendulums, can influence each to
become resonant
• For this to happen,
– The oscillation of one must be detected
mechanically by the other, such as two pendulums
on a common slightly soft mounting
– The two oscillators must have close to the same
period of oscillation
6
 Resonance (2 of 4)
• When two pendulums influence each other of
almost the same frequency, the two will trade
energy until they swing in anti-phase
• This occurs because swinging in anti-phase
has the lowest system energy level
– All resonant systems “relax” total system energy
to the lowest level
– This lowest level also requires the least energy to
keep both oscillators in the system oscillating
7
 Resonance (3 of 4)
• The “Thursday Mystery” is well-known among
repairers of tall-case clocks
– The owner complains that his clock always stops
on Thursdays, but isn’t run down
– If he watched it happen, he will say that the drive
weight started swinging on its rope or chain, and
swung more and more wildly while the pendulum
swung in smaller and smaller arcs until it stopped
What happened, and why?
8
 Resonance (4 of 4)
• At the time the trouble began, the length of the
weight rope or chain was about the same as the
pendulum rod, and the two had nearly the same
period
• The pendulum, swinging back and forth rocked the
case from side to side
– It was on a “soft” floor, such as thick carpet, or was
otherwise free to move from side to side
• Energy from the swinging pendulum was transferred
to the swinging weight at the expense of its
amplitude until the pendulum could no longer unlock
the escapement

9
 Topics
• Introduction
• Resonance
• Early Makers
• Janvier’s Clocks
• Breguet’s Clocks
• Modern Clocks
• “Reproductions”

10
 Early Makers
• Daniel Quare (1648 – 1724)
– His Dictionary of National Biography entry states that
“There is … at the Royal Hospital, Greenwich, a very
curious clock by Quare with a double pendulum.”
• This is indeed a double pendulum clock, with two separate
movements. However, the movements run at mean solar and
sidereal rates, which are different enough in period (~.3%) that
they wouldn’t lock up given reasonably stiff suspension supports

• William Scafe (1687 - ca. 1764)

11
Scafe (1 of 3)
• This ~ 11 ft tall clock
(~1740/1750) has an
unusual dial and
movement
– The lower half of the dial is
marked 1-11 for hours,
with the 12 in its usual
place at the top
– The hour hand moves at
“normal” speed from 1 -11,
the bottom half of the dial
– Between 11 and 1 it moves
across the top half of the
dial

12
Scafe (2 of 3)
• The hour and minute
hands cannot be
adjusted; one must stop
the clock then restart it
at the correct time
• There is a sliding
rise/fall regulation cage
for two pendulums on
one escapement with a
double crutchpiece
13
Scafe (3 of 3)
• It appears that the two
pendulums are not
mounted at the same
height
– This shouldn’t affect
resonance operation
• Precisely how the
escapement works isn’t
clear…

14
 Topics
• Introduction
• Resonance
• Early Makers
• Janvier’s Clocks
• Breguet’s Clocks
• Modern Clocks
• “Reproductions”

15
 Janvier (1 of 5)
• This is probably Janvier’s first double
pendulum clock, sold in 1804
• It has only one movement, but two
escapements, each with one pallet
attached to one pendulum
• The two escape wheels are on the same
arbor, so the two pendulums must be in
perfect synchronism for the clock to run
• In starting the clock, if neither pallet is in
contact with its escape wheel, the
movement would run freely at high
speed, likely to disaster
16
 Janvier (2 of 5)
• This gorgeous double pendulum clock
by Janvier has two complete
movements, both indicating civil time
• The pendulums run in anti-phase
resonance
• The circular disk in the middle is the
driving weight, suspended by cords
around each movement’s barrel
• The compensators are just above the
pendulum bobs 17
Janvier (3 of 5)
• The dials are not
identical

18
Janvier (4 of 5)
• Note the numbering on
the two seconds dials;
the hand on the right
movement turns
counterclockwise, as
does that in the dial
above it
• The right-hand
movement is likely a
mirror image of the left,
but without the hour
wheel
19
Janvier (5 of 5)
• This fascinating mantel clock has
an unusual escapement
• The impulses are applied to the
free ends of the pendulums below
the bobs

20
 Topics
• Introduction
• Resonance
• Early Makers
• Janvier’s Clocks
• Breguet’s Clocks
• Modern Clocks
• “Reproductions”

21
Breguet No. 3177 (1 of 2)
• This double pendulum clock was sold to
Louis XVIII of France in 1821, and is
currently in Musée des arts et métiers in
Paris
• The movements and pendulums are
mounted on a massive backboard, with
the common driving weight down in front
• The front of the case lifts off, and is likely
both heavy and awkward
– Fortunately, there are two holes in the front
glass, one for each movement, for the
winding key
22
Breguet No. 3177 (2 of 2)
• The movements are identical,
with Graham deadbeat
escapements at the top
• Presumably, there are
conventional crutches to the
two gridiron pendulums, but I
couldn’t see them when I
visited the Musée des arts et
métiers to look at this clock
• Note the lovely French silver
dials
23
Breguet No. 3671 (1 of 6)
• This marvelous clock by The Master
was sold in 1825, after Breguet’s
death to King George IV and
remains in the Royal Collection
• Like the second Janvier, there are
two movements driving the
seconds hands in opposite
directions, clockwise on the left
• Note the triple-stacked gridirons
• This clock was fabricated for
Breguet by Bourdier
24
Breguet No. 3671 (2 of 6)
• The two movements are
dissimilar, though both show civil
time
• The left dial has the hour display
in the window, with minutes and
seconds on separate dials
• The right movement has a
conventional time display, plus a
minute hand for apparent solar
time and the date on the
equation-of-time cam arbor
25
Breguet No. 3671 (3 of 6)
• In this view, the massive backplate
and pendulums support plate and
tongue are clearly visible
• The movements have pinwheel
escapements , with pallets attached
to the lower suspension spring
clamps
• The rectangular structure with
plinth below the backplate is the
stack for a charcoal furnace in the
bottom of the case to warm it in
very cold weather 26
Breguet No. 3671 (4 of 6)
• Another view of the dials
• The Equation of Time
mechanism is mounted on
the back of the right dial
– Note that the right dial has
a variety of pivot tips and
holes in it
– There are no jeweled arbors
in this clock
• The right dial second hand
runs counterclockwise
27
Breguet No. 3671 (5 of 6)
• This is the back of the
right movement dial
• Note the Equation of
Time cam and pivoted
follower, with the other
end near the wheel on
the lower end of the V-
block

28
Breguet No. 3671 (6 of 6)
• This is the underside of the
V-block, with the sensing
finger for the apparent solar
time minute hand position
• Each hour the outstretched
finger is set by brushing the
upper end of the cam lever,
and the balanced racks set
the apparent time minute
hand
29
 Topics
• Introduction
• Resonance
• Early Makers
• Janvier’s Clocks
• Breguet’s Clocks
• Modern Clocks
• “Reproductions”

30
 Gagneux-Haldimann
• Stephan Gagneux, a retired Swiss
physicist, became interested in
resonance
– He designed and built test rigs to
determine and optimize the
conditions for achieving it in clocks
– A joint effort of Stephan Gagneux
and Beat Haldimann led to this clock
shown at BaselWorld 2000

31
Gagneux (1 of 2)
• This spare clock has two civil
movements
• The two pendulums swing fore and aft,
in resonance, in a partially evacuated
glass case
– It makes the clock look as if it’s walking
towards you
• The suspension design assures that the
pendulums affect each other equally
– In the Gagneux-Haldimann clock, the
front pendulum is less rigidly attached
and thus more strongly affected by the
resonance than the rear pendulum
32
Gagneux (2 of 2)
• The movements
impulse the pendulums
by strong magnets
• A series of levers in ball
races convert the
pallets’ side-to-side
rocking to the magnets’
fore-and-aft rocking
• Damned clever

33
Haldimann
• Beat Haldimann made this
clock for and it is displayed in
the Musée international
d'horlogerie, La Chaux-de-
Fonds, Switzerland
• It shows local time at
Greenwich on a 24-hour dial
(UTC) and local time at La
Chaux-de-Fonds, Switzerland
on a 12-hour dial

34
Frisch & Shauerte (1 of 3)
• Made by Florian Frisch and
Claude Schauerte, students
at the Swiss Watchmakers
School (Bienne)
• Two pendulums swinging
fore and aft, with one
movement
– They claimed that a single
movement with two
pendulums in resonance is
unique, apparently unaware
of Janvier’s work (slide 16)

35
Frisch & Shauerte (2 of 3)
• The carbon fiber covered
backboard was made by a
snowboard manufacturer
– It carries a marble block with a
brass plate to which the
pendulum mounting and
movement are attached
• The pendulum rods are carbon
fiber
– They acknowledge that carbon
fiber is unproven compared to
Invar, but “wanted to build a
unique 21st century clock”
• Wires for the two weights
come off the top (left) and
bottom (right) of a single 36
barrel
Frisch & Shauerte (3 of 3)
• The drawing shows the
escapement from the back looking
forward
• The deadbeat escapement anchor
rocks a horizontal crutch AB that
impulses the pendulums LM
through the balls JK
• AB is in two hinged sections,
aligned by the spring E, also
rocked by the anchor, so that the
pendulums can be driven
independently
• Screws FG adjust the degree of
linkage between the pendulums 37
 Topics
• Introduction
• Resonance
• Early Makers
• Janvier’s Clocks
• Breguet’s Clocks
• Modern Clocks
• “Reproductions”

38
 Blake (1 of 2)
• This copy of Breguet 3671 was made by
Maurice Blake, an Irish engineer and
amateur horologist, in the 1980s
• He apparently made a series (at least five!)
of these, running for one, three, or twelve
months
• Pendulums are steel/zinc compensated, 20
lbs. each, both driven by a common 11 lb.
weight (for which duration not stated)
• In his first clock the mounting was so rigid
that he had to slit the support a bit with a
saw to achieve resonance, and later
discovered that Breguet had also done this
39
Blake (2 of 2)
• Pinwheel escapements, usually
• Dials show the usual hours,
minutes, seconds, though
some have “lunar, solar, and
equation of time trains”
• Data from a report of AHS Irish
Section 12/2/1986 meeting in
Antiquarian Horology, March
1987, pp. 488-489

40
 Noakes (1 of 6)
• Made by Deryck Noakes and his father
DBA Buchanan of Chelmsford
– They moved from South Africa to England in
1999, but have since moved on to Australia
• This clock is described by its owner as
“an hommage to Breguet”
– The dials, movements’ backplate, and
driving weight certainly follow Breguet’s
3671
– The wall-hanging case seems closer to
Janvier’s floor-standing double-movement
clock

41
Noakes (2 of 6)
• The two dials resemble
Breguet’s No. 3671, but
are swapped left for
right
• The left clock display
and movement, except
the escapement, are
like Breguet’s

42
Noakes (3 of 6)
• On the right movement, the
top and middle dials display
sidereal time, though the
hours window runs only
from I to XII
– Sidereal time is always
reckoned on a 24h scale in
Arabic numerals; it has no
“am” or “pm”
• The seconds hand displays
civil, not sidereal, seconds
– Sidereal time gains 3m 56s per
day, or a second about every
6m on mean solar time

43
Noakes (4 of 6)
• The drawing shows that
Noakes generally
followed Breguet’s
design for the Equation
of Time / apparent
solar time mechanism
– See slide 28

44
Noakes (5 of 6)
• This is a drawing of the
escapement
– There are both pin and
toothed escape wheels, with
a remontoire spring in
between
– This is a gravity escapement,
A is the gravity arm, which
drops and rolls on the arm G
attached to the pendulum
for each impulse
– Each pendulum rides on a
knife edge
45
Noakes (6 of 6)
• The escape arbors are each
suspended by anti-friction
wheels
• This clock is spectacular, but has
challenges
– Dirt can get under the knife edges
easily
– Dirt can settle on the anti-friction
wheels
– There are an awful lot of delicate
parts to become disarranged
• Unlike the Noakes’ customer,
Breguet believed in elegance and
simplicity
46
David Walter (1 of 11)
• This gorgeous clock is David’s Dual
Pendulum Resonance Clock No. 1
• The case is a scaled-up version of
Breguet 3671 (see slide 24)
• Unlike Breguet’s clocks, which had
no jeweled arbors, all arbors are
jeweled, including the barrels
– Both movements together contain 71
jewels, including four on the escape
pallets

47
David Walter (2 of 11)
• The dials are also scaled-up
from Breguet’s, and
– Breguet’s mean and apparent
solar display moved from the
right to the left side, with the
seconds hand turning clockwise
– A sidereal time and spherical
lunar phase display on the right,
with both the escape wheel and
the sidereal seconds hand
turning clockwise

48
 David Walter (3 of 11)
DWC No. 1 Breguet No. 3671

49
David Walter (4 of 11)
• The LH dial shows mean solar time
(blued hands) with apparent solar
minutes (golden hand)
• The aperture just below the dial
shows (simple) calendar date, on
the equation-of-time cam arbor

50
David Walter (5 of 11)
• The RH dial shows sidereal time
and the Moon phase
• This display required a sidereal
conversion gear train and a lunar
display train for 29.61… sidereal
days rather than 29.53… mean
solar days in a synodic month

51
David Walter (6 of 11)
• The solar escapement is
on the left and the
sidereal on the right
• Both escape wheels
turn clockwise
– Breguet’s, Janvier’s, and
the Noakes’ RH escape
pinwheels turned
backwards
– David found that pallets
on the RH pinwheel
needed to be shaped
differently from those on
the LH pinwheel
52
David Walter (7 of 11)
• This is the sidereal
movement escape
wheel on a pipe
– It turns at solar rate of
one turn per minute
• The sidereal conversion
train is below it, driving
the seconds arbor
through the pipe at
sidereal rate

53
 David Walter (8 of 11)

• Sidereal side escape wheel with pipe, pallets, sidereal

conversion train, and coaxial sidereal seconds arbor
54
David Walter (9 of 11)
• This movie
shows the
escapements in
action
• They are
fascinating to
watch

55
David Walter (10 of 11)
• This is DPC No. 0P, the
prototype
• It is mechanically identical to
DPC No. 1, which was actually
finished first
• The case was inspired by
Breguet’s 3177 (see slide 22)
• It has a conventional door
rather than a lift-off front on a
massive fixed backboard
56
David Walter (11 of 11)
• I claim that this is the
best-dressed living room
wall in Santa Barbara
• The clock on the left is
David’s Vienna Transition
No. 1, which he made for
me in the late 1990s
• For scale, the top of my
head is at the level of the
center of VT1’s dial
57
58
David Walter (Providing Scale)

59