The
following project is the hard work of Ron Lebar. We are
continuing to update it as and when Ron is able to let
us have a report of his progress.
If you need any further information about the clock
please contact Ron by email at
info@alphaentek.com
or True Point at our contact email address.
I am building a prototype mechanical clock, with advanced specification. The
instrument will include a calendar display using a
rotating brass disc which is already made. This will
utilise Trochoidal wave reducers instead of gears and
will keep track of the Gregorian calendar until the year
2399 (if it survives that long).
Appearance: The design is
for a single main dial clock, with centre seconds hand.
The brass chapter ring is 250 mm outside diameter, 154
mm inside diameter. Numerals are Mayan, pierced through
the dial and optionally backlit.
Three
hands are counter-balanced within the mechanism for less
frontal clutter. The seconds and minute hands are
aluminium to minimise rotating mass.
The
glazed case will be approximately six foot high without
its adjustable feet, twenty inches wide and one foot
deep. Most of the mechanism will be visible through the
dial aperture or the sides. Rear panel is meranti,
frame is oak.
Glass
shelves allow the clock to double as a display case. It
will be dust tight, the door locked, the dial glass
screwed shut.
Power
sources: The free pendulum
power will be provided by a small battery, maintained by
a mains trickle charger. This should last for at least a
year without the mains connected. The pendulum will send
a timing pulse to the clock once a second. Mains will
also provide optional dial and case illumination.
The
clock itself is essentially a slave mechanism, entirely
mechanical apart from the electro-mechanical
escapements. Movement driving power will be two springs,
wound by a temperature sensor mounted behind the rear
panel.
Temperature
Sensor: The sensor
consists of thirty (30) vertical one metre long acetal
rods, each six millimetres in diameter. These are capped
at each end by substantial aluminium sections. The lower
one is attached to the rear panel. The upper is
connected to a one hundred to one lever system.
Acetal
has a coefficient on linear expansion (C.L.E.) of one
hundred and thirty (130) parts per million (PPM) per
degree Centigrade. Meranti wood has an approximate C.L.E.
of three point one (3.1) PPM.
The
differential movement of the sensor is thus over 125
microns for a one degree centigrade change in
temperature. Magnified by the levers this becomes twelve
point five millimetres. Six such changes, up or down
will rotate the spring arbour double acting ratchets one
full turn.
Running
train ratios are chosen so ten (10) turns of the spring
will provide power to the minutes hand for four hundred
days.
If main
springs are fully wound the sensor levers will be
disconnected and diverted to wind the chiming mechanism,
a lower level of priority.
It may
be decided to add barometric pressure and humidity
sensors to provide additional power. Particularly for
the seconds hand train.
Design:
The design is intended to be accurate, reliable and self
powering. With that in mind, minimising friction has
been a priority.
The main
usage of power in mechanical clocks, is the constant
acceleration and stopping of the entire main gear train.
Equivalent to taking a car journey by alternately
stamping on the throttle and the brake. What would the
MPG be and how long would the car last?
It says
a lot for the quality of construction of clocks that
they can last centuries despite this non-stop 'stop-go'
cycle. This cycle is the main cause of the loud tick of
a pendulum clock.
Atmos
and anniversary clocks solve the problem by using a
torsional pendulum. This swings much slower, for a given
size. So the escapement operates less frequently, less
power, less noise.
The idea
was to isolate the running train from this perpetual
stop-start cycle and have it running steadily. This
should then require less power. To do this an approach
was taken that is similar to switching regulation, also
efficient (explanation available if required).
The
design has two running trains, one for the seconds hand
and one for the minutes This division enables the clock
to be set without winding the seconds hand round
thousands of times. There are no slipping clutches,
drive is solid and direct. Similar to a radio controlled
clock in this respect.
The
seconds train runs sixty times faster than the minutes,
power is proportional to that speed. The same approach
is however applied to both trains.
The
escapement underwent some mental evolution, originally a
pin-wheel design was chosen. Thinking about it revealed
a problem, The pins being parallel to the axis require
robust support. Hence high rotating mass, concentrated
at the fast moving circumference.
Finally
a star wheel was chosen, with least mass at the
periphery. Made from thin, fully hardened spring steel.
This will be driven a spring, wound by the running train
seconds shaft (rear shaft).
The
escape wheel in turn will be coupled to the seconds hand
shaft (front shaft) by another spring. The elasticity of
each spring will be set, in conjunction with the driven
mass, to give a 'time constant' of one second.
With
this arrangement the front and rear shafts will be
turning at a constant rate of one revolution per minute.
In between the light star wheel will rotate gently in
one second steps. It should be interesting to watch.
The
minute hand will be driven in a similar way, so will
move from one minute to the next over a period of one
second.
Gear
train: The 'gears' will be
Trochoidal drives, with all wheels rotating in the same
direction.. A drawing of how they work will be included
soon. It must be mentioned that these are untried. Tools
to make them do not yet exist and must be made.
This is
to eliminate the rubbing friction of counter rotating
gear teeth. Replaced by simple rolling resistance, a
couple of orders of magnitude less. A greater ratio in
a single step should be possible.
Free
Pendulum: A one-point-two
metre Invar rod with a four inch bronze bob near the
bottom. Conventional thermal compensation, a wheel that
does not need re-inventing.
 
Pivots:
A twelve mm horizontal pivot rod, forty mm long, lies
front to back at the top. In two bronze blocks, with
twelve point one mm holes. A central seven mm vertical
drilling allows the six mm pendulum rod through, with
clearance.
Near the
top of the pendulum rod is a two mm left to right cross
drilling. Through this is pressed a two mm silver steel
rod, which sits in a groove in the top of the pivot rod.
This supports the pendulum rod, allowing it to find its
own front to back angle.
This is
to prevent differential stress on the two jewelled
pivots. In each end of the pivot rod are stepped
vertical drillings. The upper larger part holds a cup
sapphire with its cup down, held against the step by a
pre-loaded spring.

 
In the
bottom of the bronze blocks are matching drillings,
these take upward facing diamond cones, to mate with the
cup sapphires. These are adjusted by a screw, to just
lift the pivot rod out of contact with the bronze
support blocks.
The
whole arrangement is designed to only allow 50 microns
of movement in any direction to protect the pivot jewels
if the clock receives a shock. Also to ensure even weigh
distribution between the jewels if the clock is not
level.
Pendulum
Sensor: Just below the bob
is the sensor, this will detect the centre point and
amplitude of the swing. Two horizontal steel rods, one
each side. Partly within a pair of coils wired in a
Wheatstone bridge arrangement.
The rods
vary the inductance of the coils differentially, at the
pendulum's rest point both coils are the same. They are
energised by a push-pull ten Kilocycles per second
(10Kc/s) signal, giving a one millisecond resolution.
As the
pendulum moves away from centre the bridge is
unbalanced, giving an output. The phase of that output
indicates which way the pendulum has moved, the
amplitude indicates how far it has swung.
Circuitry processes this signal and decides if the
motor needs energising and which way. As the pendulum
reaches its exact centre of swing the motor is given a
pulse, in the correct direction, if the swing is not
sufficient.
The
duration of this short pulse will be tailored to
gradually restore the swing to optimum. If the circuit
detects the pendulum has stopped a series of stronger
pulses will be applied to restart the clock. An alarm
will indicate a time error.
As the
pendulum reaches its centre, regardless of any signal to
the motor, a pulse will be sent to the seconds
escapement. Also to the minutes escapement at the
sixtieth second.
At the
hours and quarters this pulse will also be sent to the
chiming mechanism, which will decide what to do in
response. At midnight it will be sent to the calendar
train, which will also decide what to do.
Seconds,
minutes, hours and date signals will also be available
as an external output for any other slave clocks.
Motor:
About half way up the pendulum rod are two horizontal
rod magnets, left and right with like poles together.
These are partly engaged within coils, similar to the
sensor.
These
coils are wired in series anti-phase. A pulse in either
direction will attract one magnet and repel the other,
providing motive force to the pendulum.
To take account of the leap century at 2400 it would
require another reducer which is probably overkill. The
chapter ring, already made in rough form, and uses Mayan
numerals which are a few centuries older than Roman
numerals, but look intuitive and modern. It will be based on a one second, just less than one metre, free pendulum.
This requires bearings designed to minimise friction, as
does the rest of the clock. The running train will be
powered entirely by small atmospheric changes.
The pendulum will weigh around 4 Kilogrammes. My thought
is to support it on two conical diamonds sitting in
sapphire cups. The movement will be minimal; the swing
at the bottom end will be 15 mm on average.
The bearing structure will be supported against
over-travel in all directions and spring loaded to
absorb any applied shock.
My initial thought was a 6mm diameter silver steel cross
shaft, with the cups set in each end, facing down. These
ends will rotate in steel (or brass) blocks reamed to
6.1mm, giving a 50 micron radial clearance.
The diamond styli will sit in the lower part of these
blocks, facing up, with their tips contacting the
sapphire cups. They will be adjusted in height until the
shaft is centered in the gap; this is checked by
electrical contact being broken.
Axial clearance will be set to 50 microns, so if the clock gets a jolt, the pendulum assembly can only move
50 microns in any direction. As downward thrust can fracture the jewels, the diamonds will be held up by springs, preloaded to just take the assembly's weight at rest, (an idea inspired by a 'shockproof' watch balance).
Excessive movement of the lower end will be restricted by strong support rings around the shaft, 'just' clear of the bob above and below. Swing will be 15mm total on average, so not a lot of clearance is needed.
Trochoidal wave reducers are a form of what is usually
called a cycloidal reducer. A hollow ring has a
cycloidal wave pattern cut on its inner surface with a
set number of lobes, for example 60. Within it sits
another ring, slightly smaller, with an inverted
cycloidal pattern cut in its outer circumference. This
pattern has one less lobe (59).
This
ring has a central ball race, on an eccentric shaft. The
inner ring is constrained to allow movement but not
rotation. As the inner shaft rotates, the inner ring
rolls around the outer.
When it has completed one rotation, having one less
lobe, it will have rotated the outer ring by one lobe
out of sixty, in the same direction as the input shaft.
Friction is very low, compared to gears, only rolling
contact, no sliding. So it is easier to design a clock
to use minimal drive power. The down side is no tools
are available to cut the rather tricky lobes, so these
tools have to be made. Also they can only reduce speed, as with
a worm drive another technique is needed to step up
speed.
I enclose a photo of the rough cut
chapter and date rings.

This shows the Mayan numerals. I probably
won't use them for the dates; they get trickier to read
at a glance above 19. The Maya used base five and base
twenty for smaller numbers, and base 18 for larger
numbers so that it would tie in with their calendar.
The following photo is of
the temperature sensor that powers the movement. It is
in an unfinished state, the rods will have guides to
keep them parallel.

The meranti back panel is
now French polished, using an old technique of mine.
Meranti looks good enough, once polished, to use for the
entire frame, apart from oak corner pillars. It is a
very stable wood, paler than mahogany, with a coarser
and more open grain. It will not be stained, we like the
lighter colour.
My polishing technique does not use grain filler, so the
subtle natural figuring is quite distinct, unlike some
highly polished mahogany clocks I have seen. In the old
days wood was almost ubiquitous. Builders often
concentrated on displaying their superb craftsmanship
and hard work in polishing. Rather than highlighting the
natural beauty of wood, it is a matter of individual
taste.
Next step is to mount the sensor and pendulum. The lyre
for the 'chimes' will be on the lower back, visible
behind the pendulum. Originally a choice between struck
rods, solid hung bars, tubular bells and plucked reeds.
A 'final' decision is to use plucked strings, a form of
harp, based on a prototype instrument of mine from 2001.
The plinth, containing the control system, will double
as sound board and resonant chamber.
Date: 26/05/2014
I have some photos of the
pendulum assembly, during machining. Not a complete
set, the jewels are slowing me down, due to the
precision required.
Shortly I hope to send microscope photos of that part of
the work. The first job for completion is to get the
whole assembly swinging, so it can be timed.
I have a suspicion that the seconds shaft may need ring
jewels and the star wheel pallets may also need to be
jewelled. I will start with steel and see how friction
and wear pan out.
Date: 29/05/2014
When the pendulum is
finally sitting on the jewels it will be started. So its
timing can be set and monitored while the rest of the
clock is built. Most mechanical parts will be polished,
including structural rods etc.
The date ring has been redesigned. It will be co-axial
with the chapter ring and use a window, to show only the
current day number and month. Date numbers will be
Mayan, we will just have to get used to them, they are
easier than Roman.
Date: 04/06/2014
The pendulum is now
hanging and swings. The sensor and motor are not yet
made. The coil winder has to be fired up and bobbins
turned etc.
  

Date: 08/06/2014
The pendulum is finally swinging on
its jewels but without a source of power. First time it
touched the spindle it started swinging, about an inch.
After an hour it was still at about the same amplitude,
but next morning it had stopped.
One of the diamonds was then adjusted, until electrical
contact was broken and corrected the spindle azimuth. It
then swung for four hours before declining to one third.
But still moving slightly several hours later.
This equates to a
'Q' factor of about 45,000 which is not bad in air.
The sapphires and diamonds do the job well. Probably
better than knife edges on agate, the usual standard.
The best 'Q' documented was 110,000 in a vacuum tank, in
1921. We are unlikely to match the Q of a quartz
crystal, a vacuum tank is not pretty.
Date: 13/06/2014
A substantial design
change has been made after testing the pendulum. It
works fine and has a high 'Q' as already established,
but there is a chance that the position sensor, plus the
motor may compromise the thermal compensation and
increase air drag. Also that the motor may have a slight
effect on the pendulum's natural accuracy.
So a new pendulum bob is being made, combining the
position sensor, swing sensor and motor. The pendulum
will now be driven and sensed at the exact 'centre of
oscillation' (CoO) . This is the one point where drive
pulse energy will not affect or reflect from the pivot
point.
Later, if you wish, I will add drawings and text on the
design, including the new motor design and a means of
accurately finding the 'CoO' for this design.
The likely effect of these changes will probably be very
small (apart from slowing completion). But if I am to
achieve the goal of beating a quartz clock everything
must be taken into account.
Date 15/06/2014
Making the new pendulum bob
will not be a waste. It is more or less a copy of the
first one, so that the first is still available if the
modifications fail to work well.
If the second bob is a success the first will probably
receive the same modifications. There will then be two
if it is decided to change to a dual pendulum. The case
layout has room for this.
If this is done it will not be a hit and miss
arrangement like the marvellous Shortt clocks or David
Walters' beautiful creation (D)W5.
I like simple elegance in design, both electronic and
mechanical. Both pendulums would be adjusted to exactly
the same period and encouraged to synchronise.
The anti-phase swing should lessen the effect of any
outside influence, including minor earth tremors.
Incidentally the low friction pivots have given us a
surprise. I noticed that the
un-powered pendulum never quite stops. Even if not
touched for many hours.
Date 23/06/2014
The first pendulum uses the
cup jewels you supplied, cups down. Supported on conical
diamonds, point upwards, these in turn are supported on
pre-loaded springs.
For the slave pendulum I wondered if steel points, about
the same tip radius, would be sufficient instead of the
diamonds. Probably more robust, so less protection
needed. Not to save money.
The slave pendulum may be used to trip the seconds
escapement pallets instead of the original idea of
electro-magnets.
It could be used to directly kick round the seconds
shaft as in (D)W5. This would save a lot of
construction, but then that part of the clock would not
be atmospheric.
I think the time has come to stop making changes and
stay close to my original design. The second pendulum
was always an option, but only to raise the 'Q' of the
first.
 
The
pendulum thermal compensation is based on the Riefler
astronomical clock, pushing the bob from the bottom.
The bob thus acts as part of the compensation, which
creates a potential theoretical delay problem. The bob
will heat and cool slower than the invar rod.
In case it does matter the second pendulum will have a
more theoretically correct form. Supporting the bob from
its centre of mass, slightly more complex.
We can then compare the two when the clock is running.
Date: 26/06/2014
I have decided to drop
the Riefler style compensation in favour of a more
compact design. Based on Mr. Riefler's ideas but
hopefully an improvement.
I had toyed with the idea of putting the primary
pendulum in a partly evacuated plate glass enclosure
within the clock case.
At one time I considered having a glass back and
evacuating the entire clock case. But that caused
problems sealing the mechanical drive shaft for the
weather sensors.
However when researching the ideas, a problem reared its
ugly head. It turns out that silicon rubber, used to
seal fish tanks, is gas permeable!
So if that road is to be tried another transparent glass
sealer must be found, still looking.
Regarding V bearings, is a slight pre-load advisable? To
ensure the horizontal shaft stays in the V centre or
will that increase friction?
I had considered the escape wheel not having a shaft at
all. Just located between the seconds pinion and hand
shaft kept in place by its very soft input and output
springs.
Date: 21/07/2014
Enclosed are some photos,
the faceplate, with rear brass action plate fitted. The
centre boss carries the front V jewel, the rear jewel
will be on the rear plate. The four support rods will
carry various action parts, the chapter ring and the
wooden escutcheon etc.
There is also an annotated photo of pendulum three's bob
etc. This weighs just over 250 grammes, with its Invar
rod and compensator.
The bob is supported at its geometric centre by the
silica tube, which has a coefficient of expansion of 3.3
parts per million per degree Centigrade. The geometric
centre is close to the centre of oscillation due to the
stepped drilling, which makes the top half heavier. So
the bob should cause very little thermal rate shift.
Thermal compensation is at the pivot, my method. I also
include a photo of the 14 Kilogramme counter mass for
the third pendulum. This is used because, as mentioned
in the text already sent, pendulum three has no vertical
movement correction. Although it is intended to correct
one and two vertically.
The counter mass is 300 mm square by 19.5 mm thick. It
consists of three six mm steel plates and a one point
five mm brass plate, for cosmetic purposes and a bit
more mass.
Two of the plates will be behind the back and two in
front. To minimise stress on the wood. The two parts
will be bolted together through the back with spacers to
give clearance.
With oversize holes, lined with felt, so that the mass
does not touch the back, inside or out. Felt washers
will act as dust seals both sides, as well as preventing
contact.
The weight of the counter mass will be supported by
springs on the inside and outside. The idea is the any
earth tremors are isolated from the pendulums, all of
which are referenced to this mass. Such tremors can be
caused by passing heavy vehicles, as well as more
distant seismic activity.
As an extra photos of the three pivot assemblies are
included, for reference. If the third pendulum is a
success I will probably need another couple of S8
jewels, to raise its Q.
Incidentally I include a microscope photo of the diamond
tip obtained for pendulum two. This shows that the tip
radius is not as well formed as the first two (already
pictured). I will probably need to find a source of
better, more expensive, diamond styli.
Date:
21/07/2014
Enclosed are some photos,
the faceplate, with rear brass action plate fitted. The
centre boss carries the front V jewel, the rear jewel
will be on the rear plate. The four support rods will
carry various action parts, the chapter ring and the
wooden escutcheon etc.
.jpg)
There is also an annotated photo of pendulum three's bob
etc. This weighs just over 250 grammes, with its Invar
rod and compensator.
The bob is supported at its geometric centre by the
silica tube, which has a coefficient of expansion of 3.3
parts per million per degree Centigrade. The geometric
centre is close to the centre of oscillation due to the
stepped drilling, which makes the top half heavier. So
the bob should cause very little thermal rate shift.
Thermal compensation is at the pivot, my method. I also
include a photo of the 14 Kilogramme counter mass for
the third pendulum. This is used because, as mentioned
in the text already sent, pendulum three has no vertical
movement correction. Although it is intended to correct
one and two vertically.
The counter mass is 300 mm square by 19.5 mm thick. It
consists of three six mm steel plates and a one point
five mm brass plate, for cosmetic purposes and a bit
more mass.
Two
of the plates will be behind the back and two in front.
To minimise stress on the wood. The two parts will be
bolted together through the back with spacers to give
clearance.
With oversize holes, lined with felt, so that the mass
does not touch the back, inside or out. Felt washers
will act as dust seals both sides, as well as preventing
contact.
The weight of the counter mass will be supported by
springs on the inside and outside. The idea is the any
earth tremors are isolated from the pendulums, all of
which are referenced to this mass. Such tremors can be
caused by passing heavy vehicles, as well as more
distant seismic activity.
As an extra photos of the three pivot assemblies are
included, for reference. If the third pendulum is a
success I will probably need another couple of S8
jewels, to raise its Q.
Incidentally I include a microscope photo of the diamond
tip obtained for pendulum two. This shows that the tip
radius is not as well formed as the first two (already
pictured). I will probably need to find a source of
better,
more
expensive, diamond styli.
Date: 23/07/2014
The first two styli have a
good profile and do the job, even though they were not
sold for the purpose, but as security engraving styli.
Are your pivots able to support a one Kilogramme
pendulum, between two of them, supporting the S8 jewels?
I do not see the need for several Kilogrammes for a free
pendulum. Just more stress on the pivots. Air resistance
is accounted for, plus varying barometric pressure and
humidity.
I was studying Mr. Fedchenko's write-up on his pendulum
and clock. Very interesting, some of his ideas are
similar to mine, but he made it all work well.
I will not be controlling air pressure, just allowing
for it. That is why I like the ancient Mayan
civilisation. They did not try to change things, just
take them into account.

Date: 27/07/14
I have just ordered a bunch
of fused quartz rods 8mm and 6mm from Ohio in the U.S.A.
together with some fused quartz tubing to make the bob
holders.
Shipment is over three times the material cost. This
will be the most expensive clock components to date.
Later if it works, I will try to import the material in
bulk, by some other method.
I have decided the glass case plates will be bolted in,
with visible brass bolts like the face plate in. No
conventional glazing.
Date: 05/08/14
The one part of the clock not intended to be powered by the weather now will be. I am investigating the best type of photo-voltaic panel.
To charge the battery for the pendulums' drive, chapter ring back-light and case illumination. So no dependence on mains power.
I now have the fused quartz rods and tubes from Ohio, import duty was levied on them. Even more expensive than the wood for the case.
The coefficient of expansion of synthetic fused quartz glass is so small that compensation can probably be done electrically.
Using the same method as for barometric and humidity compensation. This may mean that the average peak to peak swing is greater than the
original specification of fifteen millimetres.
This is part of my original idea of taking an age old problem and making use of it.
Date: 09/08/14
The fused quartz rods are to
replace the Invar rods for the two main pendulums. The
fused quartz tubes will replace the silica tubes to
support the bobs internally at the centre of
oscillation.
The expansion of the rod and tube exactly cancel.
Ensuring that the bob remains at the same position on
the rod regardless of temperature.
The bob's expansion will
cancel, due to support at the centre of oscillation.
This should eliminate the need for any mechanical
temperature compensation on both main pendulums.
The tiny expansion of fused quartz, 5.5 parts in ten
million per degree Centigrade, can be dealt with
electrically. Together with the other relevant
variables, humidity and barometric pressure.
So weather parameters will not only power the clock.
They will be measured and allowed for in the pendulums'
drive.
A detailed explanation, with or without a schematic
diagram.
Almost all studies of pendulums that I have seen use
arithmetic and/or vector analysis. These methods are
non-intuitive and do not really show what goes on.
Dividing a pendulum's motion into horizontal, vertical
and rotary components shows everything needed for a true
analysis.
That is my opinion and is what has been tried in the
drawings sent. Admittedly not including the rotary
component, which cancels with two anti-phase pendulums.
By the way, the aspects of weather not made use of
include wind and rain. I'm working on it.
Pendulum
Control System.
Sensor and
motor. Design information.
Two versions of the sensor have been designed,
inductive and capacitive. The inductive version is
described here. Only an inductive version of the motor
has been designed. A capacitive version is considered
impractical.
Inductive
Sensor
Horizontal steel rods are mounted on the left and right
sides of the pendulum bob Adjusted to the height of the
Centre of Oscillation, these two rods form both the
pendulum motor armatures and the sensor actuators. Their
outer ends are each encircled by two stationary
co-axial coils.
The inner left and right pair of coils form the position
sensor, the other pair are the motor stator. The sensor
coils are wired in series, energised by a 'push-pull'
signal, at a frequency of ten thousand cycles per second
(10Kc/s).
When the pendulum is vertical, at rest, the two coils
are of equal impedance (balanced), so no signal is
present at their junction (sensor output).
If the pendulum is displaced from rest, the coils are
unbalanced. One coil's rod enters it further, raising
its inductance and impedance. The other coil's rod is
partially withdrawn, lowering its inductance and
impedance.
A 10Kc/s difference signal is produced at the sensor
output. Its phase depends on which way the pendulum has
moved. Movement to the left is arranged to give a signal
in phase with the master oscillator. To the righ gives
an out of phase signal. This difference is decoded as
direction information ('DVI').
A one bit digital memory (flip/flop) holds 'DVI' for use
by the motor. The signal is also rectified, giving a DC
Voltage. The peak level of this Voltage indicates the
peak swing (VS). This value is stored in a peak hold
circuit for use by the motor comparator.
As the pendulum swings back the swing signal decreases.
As it reaches zero the appropriate motor coil,
(determined by 'DVI') receives a Voltage pulse. The peak
hold circuit is discharged, ready to measure the next
swing
The amplitude and duration of the motor pulse are
determined by comparing VS with a corrected preset value
(VC). This value is adjusted by the environmental
sensors to maintain the correct swing rate.
Using full wave decoding, the theoretical resolution of
the swing centre detection is fifty microseconds. One
part in twenty thousand of the 15mm peak to peak swing,
for the one second pendulums.
This is .75 of a micron, in practice, due to circuit
noise, processing delays etc. this high resolution is
unlikely to be achieved.
Rate
correction:
What is normally called 'circular error' (CE) is a
reduction of a pendulum's swing rate with increased
amplitude.
As with the Pythagorean comma in music, it is not truly
an error, but a factor, to be allowed for or used.
The idea of using 'CE' was one of the first to be
considered when the clock was planned.
The value 'VC' is initially adjusted to give a peak to
peak swing, measured horizontally at the centre of
oscillation, of 15 millimetres. This arbitrary value was
chosen to give a small 'circular error', it may need to
be changed.
Air temperature, pressure and humidity are measured by
sensors. The values obtained, suitably scaled, are added
to 'VC'. The purpose is to adjust swing amplitude to
correct the rate.
A rise in temperature will extend the quartz rod, 5.5
parts in ten million per degree centigrade, slowing the
pendulum by the square root of that change. The
temperature signal is inverted and summed with 'VC',
reducing its value.
The swing amplitude is reduced, speeding up the
pendulum. The two changes cancel.
Likewise a fall in temperature will tend to speed up the
pendulum. In this case a change in the temperature
signal will increase 'VC'. The swing amplitude is
increased, slowing the pendulum. Again the changes
cancel.
The same method is used to correct for rate changes
caused by barometric pressure and humidity. The idea is
to eliminate the need for mechanical compensation.
'Time' will tell if it works satisfactorily.
The critical parameters are the relative linearity’s of
quartz's temperature coefficient, the various correcting
signals and 'CE'. These can only be truly determined by
careful measurement once the system is operational.
Potential errors with pendulum rate compensation
systems.
The coefficient of thermal expansion of pendulum (CTE)
rod materials is only approximately linear, over a
limited range of temperatures.
The non-linearity may be different, over different
ranges for various materials. Thus compensation may not
be truly accurate when using, for example, bi-metallic
compensation.
Fortunately commonly used materials have 'fairly' linear
'CTE' around comfortable room temperature. This includes
fused quartz glass.
So thermal compensation, using two materials with
different 'CTE', works 'fairly' well. It is not 'exact'
compensation, over the full range of temperatures a
clock may encounter.
Other factors, not amenable to compensation, affect a
pendulum's rate. Such as variations in pivot friction
due to age, wear etc. In the case of spring suspension
the spring material will suffer gradual fatigue.
The best thermal compensation methods achieve accuracies
sufficient that the uncontrollable errors are the major
component. The Shorrt clock from 1921, when carefully
set up, is accurate within 220 microseconds per day,
80.03 milliseconds per year.
That is one second in over twelve years, assuming error
is cumulative, which is almost certainly not the case.
So all is not lost, greater accuracy than this is hardly
ever needed.
Electrical compensation using Circular Error (CE) is a
different case. The relationship between 'CE' and swing
amplitude is not linear.
Like many nonlinear factors, it can be assumed
approximately linear over a small range. As any curve
can be approximated by a number of straight lines.
The trick in obtaining sufficiently accurate thermal
compensation here is to apply a compensating
non-linearity to the correcting signal.
The aim at the outset was to produce a clock with a
non-cumulative error of no greater than one millisecond
per week. One second in over nineteen years, better than
any production quartz clock.
Quartz oscillators are, when carefully adjusted, very
accurate at one temperature. The characteristics of a
quartz crystal change, like any material, with
temperature.
This thermal change, at room temperature, is much less
in quartz than most metals, even INVAR. This is why a
quartz clock can be more accurate than a more expensive
mechanical clock.
A problem is that the common, lower frequency crystals
used have a quadratic temperature coefficient of
frequency. They are calibrated at their best
temperature, usually around 25 to 28 degrees Centigrade.
Any change from this temperature, in either direction,
causes a drop in frequency, following a square law.
For high accuracy, quartz oscillators are frequently
placed in thermostatically controlled ovens, to
eliminate temperature effects. Time standard clocks made
after 1929 used this principle.
The best accuracy was around one part in ten million,
just over 3 seconds a year. Regardless of room
temperature. Not nearly as good as the Shorrt clock,
which it never-the-less superseded. Newer is better?
Good makes of quartz watches use a similar principle,
the metal case back conducts the wearer's stable body
temperature to the crystal. This of course only works
while the watch is worn.
Most current radio clocks use a crystal controlled
mechanism which is periodically corrected (reset) by
radio signals from a national time standard. The
accuracy between these resets depends on the quality of
the clock.
National time standards are synchronised by atomic
clocks. These expensive and power hungry devices have
accuracy beyond the capabilities of any mechanical
system (at present).
Date:
14/09/2014
I
enclose photos of pendulum number three, the half
second, second order device. This has a simpler leaf
spring for shock protection. This is easier, due to it
being one quarter of the mass and with a thinner rod.
Apart from that it now uses a similar pivot block to the
two one second pendulums. Its rod is three millimetre
INVAR, effective length is 248.5 millimetres. The bob is
supported, at its centre of oscillation, by a quartz
tube, adjusted for rate by a brass nut.
It pivots on two of your S8 sapphires, supported by the
two tungsten carbide pivots you made for me. The brass
part above the pivot is the temperature compensation.
It is looking good, the 'Q' can only be determined when
the full assembly is together, in the case.
The counter-mass is too heavy to set up until the case
is fully built. The glazed case will now be mostly
meranti framing, as well as the back. The four full
height pillars will be sapele, better for turning and of
a matching colour.
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Date: 19/09/2014
I have
been researching the characteristics of a number of
precision clocks. In particular the investigation of
Shorrt # 42, probably the most accurate pendulum clock.
It achieves a relative accuracy of 200 microseconds a
day, but as with all precision pendulum clocks is at the
mercy of gravity.
This is far from the constant it was once thought to be,
the earth is in a constant state of flux. Tiny changes
in gravity limit the ultimate accuracy of a pendulum.
These changes cycle, but the effects do not always
cancel out over time. I am going to experiment, when
'time' permits, with compensating for these changes
electrically.
It may not prove practical, but nothing ventured,
nothing gained.
Date: 11/10/2014
A conclusion has been
reached regarding pendulum three's bell crank. The idea
of using ball bearings as pivots will probably be less
efficient.
We will go back to jewels at these points, but reduce
the pivots from four to two. One for the crank centre
and one for the coupling. The assembly is thus free to
move fore and aft. So it becomes self levelling.
The spring plate for the pendulum coupling is now made.
I will send a schematic drawing and photos soon. Also
the arithmetic for the pendulum and crank ratios etc.
Also another two S8 cup
jewels. This will mean the complete pendulum assembly
will have sixteen jewels. Including the two tungsten
carbide pivots you made for me.
That is four for each pendulum, two cups and two styli.
Plus the same for the crank.
Date: 31/10/2014
You will see that the half
second pendulum pivot has lost its angle bracket.
This was a decision to balance the assembly, using a
lightweight 'cage' construction, rather than the
original idea of a solid metal crank at the back.
This crank sits on the mounting plate (the last picture
sent). It translates the minute vertical movements
caused by pendulums one and two into a small swing at
its base. It has a linear magnification of 8.75.
This should synchronise pendulum three (half second) to
the other two and vice versa. The idea is to isolate the
entire system from outside world mechanical influences.
In like vein we will probably dispense with the angle
brackets for pendulums one and two. This should look
neater and again improve balance.
Date: 4/11/2014
Pendulum three, the second
harmonic pendulum (P3), is now swinging on its bell
crank. It appears to have a reasonable 'Q' factor, but
probably nowhere near as good as pendulum one.
This is to be expected, it is intended to couple with
the other two, to their mutual advantage. On its own it
is comparatively lightly mounted, on the sheet metal
bell crank.
It will be interesting to see what happens when all
three swing together. I enclose a picture of P3
swinging, with the plate in a vice on our saw.
Date: 5/11/2014
As promised a few photos,
showing the mounting plate in various stages of dis-assembly.
Plus some showing it with the bell crank and short
pendulum mounted.
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1: Brass spring plate. This shows that the milled slots
isolate the central rectangle. This area, which holds
the pendulum mounting plate, is only connected by the
series of L shaped strips.
These act as springs, allowing some movement in any
direction. |
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2: Steel plate with bearings. The milled cups are part
of four thrust bearings. Five balls in each stabilise
the brass central rectangle, allowing movement in only
one plane. |
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3: Pendulum mounting assembly: This is screwed to the
brass plate's central area, so can also move in one
plane. The two main pendulum pivots are mounted on this
plate, as is the bell crank transfer bearing. |
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4: Front thrust bearing: An annular groove, milled in
the mounting plate contains twelve steel balls. In
conjunction with an outer race, they prevent the plate
assembly tilting forward under the pendulums' weight. |
 |
5: Thrust bearing with adjustable outer race and lock
nut. |
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6: With friction sleeve fitted. This, with a flat spring
(not shown), damps fore and aft movement of the bell
crank assembly. |

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7: Two views of the
front bearing.
The top view also
shows the gap between plates, caused by the rear
bearings. |
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8: Assembly with styli. This
shows the assembly set up on our saw. The brass pillars
carry the two diamond styli, clearly visible. The left
pillar is mounted on the steel plate, part of the 14
Kg., spring supported, counter mass.
This
provides a stable reference for the entire system. The
right pillar is on the pendulum mounting plate. Via its
diamond it transfers the reaction thrust of the two main
pendulums, to the bell crank and vice versa.
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9: Assembly with bell crank
and pendulum three, which is swinging. Its 'Q' factor is
fairly good. It should be a lot better when it can
interact with the other pendulums.
The knurled brass nut, to the right of pendulum three's
pivot, adjusts the force on the transfer pivot.
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10: Method of operation. assume only pendulum one is
swinging. Its reaction is transferred, via its pivot, to
the mounting plate. Taking just the horizontal motion,
the plate will move, very slightly, left and right.
This will absorb energy from the pendulum, lowering its
'Q'. Now assume that pendulum two is also swinging, in
exact anti-phase to one. Its reaction will tend to shift
the mounting plate in the opposite direction.
The two reactions cancel, the plate does not move, no
energy is lost. Each pendulum will see the mounting
plate as having a high mass, the ideal condition for
maximum 'Q'.
Two similar pendulums will naturally tend to settle into
this stable anti-phase condition. Nature prefers
stability. In addition, the effects of external
horizontal movements tend to cancel.
However the vertical motion has not yet been taken into
account. Assume the two pendulums have a peak to peak
swing, measured on the horizontal axis, of 15
millimetres.
From the table of pendulum movements, the vertical
movement is about 30 microns upwards, for each half
swing. This movement is thus twice per full swing, the
second harmonic.
As mentioned previously, this vertical movement is in
phase, so the loss from each pendulum adds rather than
cancels. Thirty microns is small but is still part of
the equation.
In addition, it means that the pendulums are influenced
by vertical earth movements. From passing heavy vehicles
or distant seismic activity etc. They measurably affect
precision clocks.
The horizontal movement, of a pendulum one quarter the
length, is at the same frequency as this vertical
movement. This suggests a way of providing some
correction, although the waveforms are not the same.
The bell crank has two downward facing cup sapphires.
These are supported on the two upward facing diamond
styli. vertical movement of the mounting plate is
transferred, via the right hand stylus, to the crank.
This causes a greater horizontal movement at the bottom
of the crank. The half second pendulum's pivot is
mounted here, so is affected by this movement.
Thus the horizontal swing of the half second pendulum is
coupled to the vertical movement of the two one second
main pendulums.
This should provide the same advantages, in terms of
vertical movements, as the horizontal coupling of two
pendulums. Will this, in practice, cancel the effect of
earth tremors? 'Time' will tell.
Trying something unusual is not a waste of time, even if
not successful. Failing to try, dismissing as not worth
the effort, is the true waste of time.
All this tinkering has cost more in time and money than
the original project. If a job is worth doing it should
be done as well as it can be.
Date: 9/11/2014
Soon we are going to replace
our old, defunct, table router. Then the meranti
framework can be rebated to allow assembly and glazing.
We are toying with the idea of making the four full
height pillars from polished aluminium rather than
hardwood. This will mean the whole thing is very
different in appearance from other tall clocks.
We do not want it to look like a 'retro' copy. Turning
the 'twiddley bits' on the pillar ends is more difficult
with metal, another challenge.
One shame, we have poor FM reception. With metal, the
pillars will be the correct length, five feet, to make a
multi-element half wave FM aerial. But they will be
vertical. FM polarisation is horizontal!
We are also looking forward to mounting the pendulums in
the case. Then the 'gear' trains need to be built.
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