Sidereal, equation drives, kidney cam, equation of time system complete  - November 2014                     

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Here Buchanan has finished up the arbors to the sidereal and equation worm drives. Next the complex curvilinear frames for the demonstration drive is further refined


Next some further refinements to the complex dual potence that supports the sidereal and equation worm drives. Next the two worm drive wheels are positioned.

Here is a close up of the dual potence. Look at how they appear to be almost organic in shape or as if they may have been originally a straight profile and Buchanan simply twisted them into these shapes with a pair of pliers. Of course this shape is the result of a complex set of machining steps. Also look at the main wheel. Here we have both a conventional and contrate wheel formed from one piece of metal as well as the ornamented wheel collets.

These photos show the equation differential drive with the outboard wheel at its minimum and maximum positions corresponding to the kidney cam follower. Photos taken in July 2010. So this assembly has been waiting for over four years to be completed with the addition of the kidney cam this month.


Shown here are the equation cam follower arm and jeweled roller positioned in their extreme lower and upper positions, white arrows. Notice how this changes the position of the differential gearing controlling the equation hand, yellow arrows. The outboard wheel depicted by the yellow arrows will significantly rise and dip twice throughout the year, see clip below.

The video demonstrates the swing of the differential wheel set as controlled by the equation kidney cam. The diagram illustrates the mathematical representation of the equation of time. It is the graphical combination of the Earth's elliptical orbit combined with the earth's 23.50 degree tilt to the ecliptic. The shape of the cam represents this combined set of sinusoidal waves as represented by the black line.

This is the disc from which the equation kidney cam has yet to be cut. Next the wheel to which the setting dial is attached is spoked with the piercing saw and then the dial and mockup bezel is tested for fit. Notice the kidney follower arm has been substituted for a temporary one that is designed to ride on the surface of the disc as shown here in the third photo rather than to ride on the rim as will be the case when completed. This will be used in the making of the kidney cam. The thick dial hand is temporary.

Now begins the fabrication of the kidney cam that will control the equation of time dial hand. First accurate division marks are made on the main dial with zero at the twelve o’clock position and a set of marks on either side in one minute increments from one to sixteen. This will allow Buchanan to make direct readings of the differential between the mean time, which is denoted by the black hand, and the equation hand denoted by the gold hand. In this way the difference between mean and solar time can be measured throughout the year. The mean solar hand is always kept at the zero point with the gold hand measuring the difference between it and the solar time. Next a scribe mark is made outlining the modified follower wheel which corresponds to each mark in the second photo of the difference between the mean and solar time. There are 73 markings, each mark represents a five day interval. From this reading of the dial to the cam the initial cam outline is drawn from the line touching the interior apex of each scribed circle.  


The first iteration of the kidney cam is seen mounted to its annual drive wheel which is also fitted with a calendar setting dial. The next photo shows how the error measurements are recorded on the cam. Each dot represents one minute of deviation with a line equaling one-half minute. These are simply the time quantities and have nothing to do visually with the outline of the cam. The actual cam deviations are much smaller than the areas shown by the dots, only a millimeter or so for the error.


These two photos show the second and the last, sixteenth, iteration of the error logs used in the shaping of the kidney cam. The first column is the month, next the date divided into five day increments. These are the 73 individual stations or measurement points taken around the perimeter of the cam. The third column is the difference in minutes that should exist between the solar time as dictated by the kidney cam for that day and the minute hand for regular clock time (mean solar time). This difference being the equation of time. The next column is the actual reading off the cam; the last column is the difference between the correct number of minutes and those read off the cam, the error. For each set of log readings the cam is rotated through the 73 stations and a new set of readings are taken. Then further refinements are made to the cam perimeter and the next sets of 73 readings are taken and so on through sixteen iterations. Obviously this is a labor intensive process. It is the same process Buchanan used to create the missing kidney cam for the Pouvillon astronomical clock restoration project two years ago.

The difference in the errors from the first iteration and the sixteenth are on an order of 1.5 magnitudes. For example March 5th has an original error of 4.2 minutes and finishes at 0.1 minute or six seconds. On March 5th the difference between mean solar time and the actual position of the sun when it is at its zenith, directly overhead, noon for the sun’s position is 13.5 minutes. In other words when the sun is directly overhead the clock will read 12:13:30. At this time of the year the sun is slow compared to standard clock time. One must keep in mind that this cam is rather small at just under 3” or 7cm at its widest point. The smaller the cam, all other factors being equal, the harder it is to achieve accuracy.

 Here are the examples of the cam being marked and then shaped by hand filing.

Next Buchanan asked about the spokes to be created for the cam. I suggested undulating spokes reminiscent of how the rays of the sun are sometime portrayed. What could be more appropriate than the ‘sun time’ cam having sun rays for spokes? The tightest wave was chosen.

The kidney with the chosen spoke design is put back into place to check for aesthetics. Next the fancy spoke work is cut out on the jeweler's saw.

The cam spoke are now cut. Notice even the small spaces between the rim and the sun rays on the top of the cam in the background are cut out and that each ray is tapered from the hub to the cam rim.


The completed cam is shown attached to the helical drive and setting dial. Once again we have another beautiful part to add to the clock."


The equation cam is now installed into the movement. This will later be, as will the rest of the machine's parts, further refined and polished. The winding square shown in the second photo allows the operator to demonstrate the equation of time function. (see video clip below).


The sidereal dial support structure is now being fitted to the drive hub. The six screws that secure this part have been shortened and given an oval head rather than the standard cheese head profile used elsewhere. In cases where there are a large number of screws close together, sometime the taller profile of the cheese head screws are unattractive. Another example where this change was made were in the strike hammer cam carousels.


The dial support ring is mounted into the movement. Note the drive wheel behind the ring which is driven by the worm gear. This ring will reside just inside the main time dial and will rotate counterclockwise twice yearly. The reason this is twice yearly rather than once is because it is a twelve hour dial. The total difference between sidereal and 'clock time' in a year is one complete day or 24 hour cycle. A discussion about this design was illustrated last September.

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We now turn to a few components that were not included when the strike train was completed back in July of this year.

These photos show portions of a control lever that will connect the strike selection dial to the strike train. Note the detailing of the curvilinear parts and the decorative collars that are on each end of the lever rod in the first two photos. The next photo shows the upper end of the lever installed. The fourth and fifth photos show selector cam and lever locking work.

The completed lever is shown here with arrows indicating the upper and lower ends. The middle arrow shows where the lever actually contacts the strike trip lever with in the strike train. The long brass lever that projects diagonally to the upper right quadrant is the repeat on demand lever. This photo gives the viewer a good impression of the complexity involved with combining a conventional quarter striking clock with petite and grande sonnerie striking and a repeat on demand function.

This set of photos show the fabrication of the selector switch and dial for the strike train. It will allow the operator to select between silent, petite sonnerie and grande sonnerie striking. A separate lever performs the quarter repeat on demand for each.

Next the artwork for the dial is prepared and a plastic blank is cut reflecting the slight curvature that the final, enamel dial will will have. It will have the same diameter as the equation of time setting dial which is mirrored on the opposite side of the clock in an effort to retain overall symmetry. The third photo shows the equation dial as an example, not the actual strike selection dial.

Here we have the dial work attached over the completed repeat selection parts. Note the lower dial has stenciled in hand the selection options, later to be refined into a font replicated in the rest of the dial work.

This final photo shows an overview of the movement with nearly all of the dial work attached. The sidereal dial is seen within the main time dial to the left. Below that dial is the equation setting dial and mirrored to the right is the strike selector dial. The dial in the left-center of the movement will be a world time dial showing a half dozen major cities. The hands will later be refined. The mirror to this dial on the center right position will be a thermometer. These four dials are currently mockups and are yet to be sent to China for reproduction in enamel. One other dial that is missing is the planisphere which will be located between the second and third main barrel winding squares.

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