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