Continue Sun / Moon rise/set module, complete Great Anomaly & Projection
variable differentials -
I have taken a more detailed look in this segment at what normally would be
a small component comprising a dozen or so wheels. However, these
differentials, first employed by Antide Janvier in the late 16th century are
rarely found in any clock other than the few examples he created as well as
the great clock in Strasburg, France by Jean-Baptiste Schwilgué in 1842.
They employ a beautifully stunning and at the same time mentally perplexing
way of depicting astronomical data. Be sure to view the videos at the end of
the page, if nothing else they are entertaining as well as challenging to
anyone interested in how these components work.
This drawing is the
proposed design for one of the slant wheel variable differential frames, the
Great Anomaly. The large sickle is a counterweight. Notice how this conforms
to the same design for the Tellurion assembly in keeping with a consistent
design. Buchanan writes:
Here is the process of fitting an angled cock. First we have a
blank cock and the wheel that needs a upper bearing. Next I mark the taper
pin holes and the screw hole on our skeletonised frame scribe marks
the red is the final area covered by the foot of the cock.
Next the holes are drilled for the steady pins and the
fastening screw. Next part of the frame is cut
away so excess material from the already fitted slant
cock can be removed.
Next he marks out on the slant wheel cock from the
frame. Next the scribe marks outlining the foot of the cock on the
slant wheel frame
The cock is glued into place.Then the screw and taper pin holes are drilled
through the cock using the main plate as a guide.
A taper broach is used to create the taper pin holes. The plate is now
tapped for the cock screw.
Fitting the taper pins and then the cock is removed from the main plate.
Next is chamfering the pin holes and then cuttiong the pins and screw to
length using the square cutter.
The cock is now mounted. Next is the setting up of the main frame on the jig
borer with the jewel hole exactly center to the machine spindal. The
magnification equipment is a must for this job.
The cock is mounted on the plate and the bearing hole is center drilled.
Next the pilot hole is drilled.
He now drills the bearing hole to fit the jewel. Next the jewel is just
starting to enter the hole it is now correct for a press fit.
Excess material is machined away to make way fir clearance of the slant
wheel center post. Next the center post is fitted.
The variable differential slant wheel is now in place. This operation took
about four hours.
The gear train is now basically complete. Now Buchanan begins the decorative
Now the wheels begin to be spoked
The sickle shaped counterweight is now fabricated.
Left is the beginnings of the Projection variable differential, right the
The Great Anomaly variable differential wheel works complete. The assembly
is now ready for the drive wheels and transfer fork.
The two variable differentials are now complete. Great Anomaly left and
A front and rear view of the Projection variable differential.
The two differentials in profile. Next the transfer forks and their jeweled
cranks are fabricated.
These four photos show the completed differentials with their transfer forks
and associated cranks are now installed within a demonstration Plexiglas
The beautiful creation is held aloft by the creator's hand, this photo also
gives the viewer a good perspective of the the size of these differentials.
The differential assembly is positioned into place where it will eventually
reside on the upper right quadrant of the machine.
The pair of variable differentials is shown here and at
this point are disconnected from each other. The one on the left is spun
rapidly while the one on the right is stationary. Watch the crank pin which
is located on the perimeter of the large spinning slanted wheel. The pin
appears to slowly move from about 35 degrees left of vertical to 35 degrees
to the right. This is the same part as the small cylindrical object at 12
o'clock on the stationary slant wheel on the right differential.
This crank slides within a transfer fork encompassing
the crank’s travel from end to end. The fork is not shown in this video but
is seen in later videos. This fork is connected to the differential output
wheel and that sliding along the fork causes the output wheel to have a
varied speed according to where along the fork the crank is. It is analogous
to a variable transmission not unlike a fusee which varies the torque of the
chain, however if the cone where a spiral toothed surface turning at a
constant rate and a wheel of given diameter were then meshing along that
cone track, it would turn faster at the base of the cone and slower at the
tip. There are further complications introduced in one of the differentials
(the Projection) from additional wheels within the differential adding
variability to that differential’s output.
This type of differential was first applied by Antide
Janvier in the 1780’s to clockwork, and may have been invented by him also,
to illustrate uneven movements of celestial bodies due to a number of
factors including eccentric orbits, gravitational effects from other bodies
like the sun, and in the case of the moon also the gravitational effect from
These two differentials account for the two greatest
orbital anomalies associated with the moon's orbit. There is another five
other anomalies that together accounts for the complex orbital pattern of
the moon, but all of those other five are a fraction of the anomalies
accounted for by the first two. We have chosen to address the two largest
anomalies known as the Great Anomaly, which has to do with the moon's
elliptical orbit around the Earth and the Projection which accounts for two
factors; Earth's elliptical orbit around the Sun as well as the tilt of the
Earth in relation to the ecliptic. For those who are versed in celestial
mechanics the Projection is composed of the same two functions that are used
in calculating the equation of time and that mathematical function is
represented by a kidney-shaped cam to produce the output computing the
difference between Sun time and clock time.
The next video shows a front elevation of the differential pair.
The differential pair is now connected together as they will be practice and
the transfer forks are attached. Rotation is supplied from the left. The
output of the left differential is then fed into the first fork which then
rotates the second differential to the right so that the output present at
the second fork is a combination of both differentials resulting in a
complex rate of rotation. The two differential sets will always be moving in
relation to each other, never in lock step.
The first video shows the right three-quarter elevation of the differential
set. The pair is now connected together as they will be practice and the
transfer forks are attached. While they are connected to a common input,
each differential will never rotate in lock step to each other. Power is
supplied from the left and the right differential is driven from the output
of the left.
Next is the left three-quarter elevation of the
differential set. This video may be a bit confusing. In order to allow a
better view from this angle the power is being fed from the “wrong” end. In
other words the fork all the way to the right is being powered. There is no
mechanical reason why the input of an individual differential could not be
fed in reverse; but of course one would not get the same results!
In the first video we fast forward the differentials and
then briefly stop at various points. The Projection assembly is in the
foreground. Look carefully at the crank pin which begins near the center of
its travel within the fork and then progressively moves to the left and then
towards the right. But this is not a simple smooth back and forth; the crank
pin follows an uneven back and forth. Exactly as would be produced by the
kidney cam describing the same movements for the equation of time. This
device simply does it with more style.
The second video demonstrates the sliding action of the
drive pin from the slant wheel along the output fork. Notice the jeweled
roller moving along the fork track. The effect is subtle but the output of
the arbor attached to the fork changes speed as the roller moves along the
fork because the roller is changing its distance from the center of the
output arbor axis. The closer to the center the faster the output , the
further away the slower. The roller moves because the wheel is slanted
relative to the output arbor. If the wheel were to be parallel, the roller
would remain stationary within the fork and the output would not have a