Continue Sun / Moon rise/set module, complete Great Anomaly & Projection variable differentials - February 2017

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 cutting 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 flourish.

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 Great Anomaly. 

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 Projection, right.

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 frame.

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 the Earth.

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 variable speed.