Begin Orrery, preconstruction planning
The orrery is the last mechanical module in this project. Due to its
complexity the month of June was taken for planning and preliminary fitting
of the design into the machine. First a bit of history and background.
The design for the
orrery is based on Philipp Mathaus Hahn’s Weltmaschine, world machine,
built in 1780 when he was in Gotha, Germany. His orrery is the component on
the right in the photo above. To the far left is a tellurian. A celestial
sphere is in the center. The dial located below the celestial sphere has
clockwork for current time on the small dial at the six o’clock position.
The dial at the twelve o’clock position is a calendar indicator with days,
weeks and months. The perimeter dial indicates twenty four hours and to this
dial hand is also attached a small hand-crank. The four smaller dials that
run in sequence across the center is a digital counter with the dials
indicating zero through nine. The left dial pair runs clockwise and the
right pair runs counterclockwise. These presumably delineate the number of
days with each dial multiplied by ten; when the crank is turned one
revolution representing one day, the first counter moves to one. So to move
the fourth dial by one full revolution the hand crank must make 10,000 turns
or that same number as represented in days. The orbital period of Saturn
takes about twenty nine years or 10,585 days, so the span of the counter is
entirely appropriate. In reality one would not be able to easily do this.
The entire mechanism is driven by an eight-day clockwork wound from the
front dial. The machine measures 39”w x 27.5”h x 16.25”d.
This photo shows the
orrery mechanism by itself. Considering that the depth of the world machine
enclosure is 16.25” one could reasonably subtract two inches for the
enclosure lip to arrive at the diameter of the orrery at 14.25”. We only
have about 13” or about 90% of the space. An even greater constraint is in
the height. In Hahn’s design there is no obstruction to the vertical
dimension. But this is not the case here, where Saturn must sweep just below
and between the two remontoire fly frames as will be demonstrated a few
illustrations below. Do not be fooled by the apparent open look of the gear works. Both
Jupiter and Saturn have eccentric orbits so that space is needed for those
times where both planets orbits come closest to each other. When that occurs
there will be very little room across the entire mechanism.
This is one
of the more complex orrerys made as a single unified device.
This is Hahn’s original
parchment drawing for his orrery design.
This schematic is the
wheel / tooth count of Hahn’s orrery as illustrated the drawing folio set included
in the two volume German-language publication Astronomische Uhren und Welt-Modelle
der Preistermechanniker in 18. Jahrhundert, by Ludwig Oechslin. This
proved to be invaluable in the creation of the orrery providing a large
reduction in design time and was besides being a beautiful design, a major
reason for our choosing this. The tellurian was based on an example in this
book that was also by Hahn. The orrery has the planets out to Saturn. In
addition Jupiter has four and Saturn five orbiting moons as were known in
These are for Jupiter (Io, Europa, Callisto
and Ganymede) and Saturn (Tethys, Dione, Rhea, Titan and Iapetus).
The elliptical orbits of Mercury,
Mars, Jupiter and Saturn are represented. The orbits of Earth and Venus are
fairly circular in comparison. There are 105 wheels in the mechanism.
These five sheets represent the gear ratios and and mathematical equations
for them. The German verbiage in the right column describes the components
that those gear sets drive. These
are also from the German-language
publication Astronomische Uhren und Welt-Modelle der Preistermechanniker
in 18. Jahrhundert, by Ludwig Oechslin.
This screen grab is
from a video Buchanan made of a plastic wiper-a sweep gauge, outlined in yellow, which
sweeps around the axis of where the orrery will be mounted and is made to
the exact outline of the maximum space that can be occupied by that wiper to
check for any conflicts within that swept space. The notched area indicated
by the upper arrow is where that wiper must pass below the inner portion of
the remontoire fly fan cages; one which is seen in the background just above
the arrow and is our upper vertical dimensional constraint; the lower is the
upper main frame pillar of the center celestial train, lower arrow. The
outermost component of the orrery is Saturn and this must fit below that
notch to be able to fully utilize the horizontal space which is critical as
the area is already so constrained as to require many of the components to
be on the scale of a pocket watch and are at the size limit of the tooling
I have spent a few days now working on the planning for the orrery.
First I took Saturn and worked out the sizes of the gears that projected out
the furthest. Then I worked back to Saturn’s centre pivot. I also calculated
how tall it would have to be using safe minimum wheel thicknesses and plate
thickness. I drew this on a piece of paper and fitted it in to a drawing of
our available space. Then I worked out the same for Jupiter. This was
much simpler as there is no tilt in Jupiter. Both planets have a chapter
ring as well and Saturn also has a personal ring as well. This shows that I
can reasonable fit the orrery in on diameter.
Then I started on the overall height and here the problems start to appear.
In the photo you can see, down the centre, just below the date in red, a
column of numbers in pencil. Each of these lines represents a layer of
gears. A total of 37 layers! At three points (red ringed)I need to fit a set
of two bearings between a two wheels, this adds an extra 3.5mm each.
The total distance in height that I have, from below
the sun, to, the bottom of Saturn’s arm, is 80 mm, less 3 X 3,5 m is 70mm.
If you divide70mm by 37 layers, I have 1.9 mm to fit in a gear and some
clearance. But I also have to fit in the enamel chapter ring and some extra
clearance between the planet arms. This will leave me about 1mm per layer of
gears. This is rather too tight for comfort on a mobile mechanism like this.
I am looking for more space but there is not much place
You will see that I have given myself 18,2mm (3/4 inch) to fit in 12 layers
and a cock and 2 frames in the main centre (yellow) gearbox. That is as
thick as 2 pocket watch movements!
So things are really tight.
Here is some more information. I would like to call it progress but I don’t
know if I can.
If I assume a wheel thickness of 0.6 mm 24 /1000 inch
and a similar space between wheels, as a minimum; I took a look at an
English fusee pocket watch and measured the thickness of a few wheels. See
This is what we are talking about.
I took the drawing and enlarged it to the size that
matches our diameter. Photo 0008,
this shows clearly there are height problems. I also worked out the height
of the inner gearbox with o.6 mm wheels and it is around 20 mm. This shows
that Hahn’s drawing is, as far as I can see, a correctly scaled drawing.
Now I took the drawing and cut away any area where I
thought I could save height. I was drastic in this respect. The result
is photo 0010,
A lot of height gone but when we overlay the sweep gauge you can see that
there are still problems. Ref photos 0011 and 0012,
fourth and fifth
photos, these are;
1. We will have to use some ball races to minimise wear problems and reduce
friction, more so, as we have reduced the height of a lot of critical
bearings. I don’t think I have left enough space for this in Saturn.
2. The bottom of Saturn collides with the big dial.
3. The level of Saturn and her moons are below the level of the other
Possible moves in the right direction are:
1.Reduce the height of the bezel of the main dial.
2. Accept that we don’t have all the planets at the same level. I can
see if I can rework the gearing on Saturn to step down after the dial. (this
won help much because Jupiter is too close to Saturn)
works for me.
3. Make more space under the fly fans so that we can
lift Saturn some more. (This will spoil the look of the fly fans lower frame
but I could get another 5/8 inch. Photo 014,
yellow arrow, sixth photo, I
would need to remove the inner pillar or, both the inner and outer pillars,
they are not strictly necessary.)
4. We could delete the eccentric orbit of Saturn. But
this would not save much more than the height of a set of wheels as this is
all we could lift the Saturn arm before it touches the Jupiter arm. Have
you noticed that Saturn, Jupiter. and Mars all have eccentric orbits?
Yes and I like
Note the size of the planets. We could possibly make them a little larger
but this could make things look crowded. The moons will have to be 2mm
in diameter max.
I am now going to look at the absolute minimum height I can make the Saturn
assembly and see if I can fit it in at all.
These wheels are indicative of the scale we are working with, some may be
even a bit smaller. The next photo is that of the center section with the
concentric tubes holding the inner planets telescoped out. Normally they
would all be tucked together. Buchanan will stabilize this nest using a rod
through the center for the sun and the outer tube with a ball bearing. The
tubes will also alternate metals of brass and steel for the same reasons
wheels and pinions are made of brass and steel (this photo is just a mockup
and is using only brass at the moment).
The first illustration is the initial drawing Buchanan has made of the
orrery. The second photo shows how small this really is going to be.
I have been working on Saturn today. In the end I made an Excel spread
sheet for Saturn’s wheels with the numbers of teeth and the cutter
sizes to give me all the gear size options. I also doubled the tooth
count. Then I set some diameter constraint’s to be highlighted.
In the photos the pink bars are each one cutter or
tooth size. The first column is the number of teeth. The red blocks are
possible gear sizes that can be stretched or shrunk enough to work.
Each tooth number is the total number of teeth in one set of two gears. This
is because they have to all fit on the same arbour set. It is easy to
work out long hand but EXCEL is just quick and tidy and makes all the
options obvious. I an now drawing them onto a loose sheet of paper to see if
I can fit them all into the space we have left or if I need to drop
down a tooth size for all the wheels.
Unfortunately I have a fixed selection of cutters. They are closely spaced
in 0.05 module steps but they are still finite steps and in reality I only
have 0.2, 0.25, 0.3, and 0.35 that I want to use. This gives us a 0.2
teeth on some wheels that are almost half the size of 0.35 teeth on other
wheels. It is visually interesting but mechanically challenging. We have a
theoretical centre distance variation of 29.5mm to 34.3 mm that have still
to be stretched or shrunk to fit onto the 31.24 average spacing.
Here one can see the integration of the schematic from the German
reference book, pasted sections at the bottom, into Buchanan’s construction
drawing; that drawing is three times actual size of the orrery.
show Saturn, the second the space occupied by the rotation of Saturn’s tilt.
The main Saturn and Jupiter arm details I hope to
finish tomorrow, I cannot Buchananise too much of this thing, as space is at
a premium, as well as, the nature of the gearing, but I will do what I
can. It will still look very different.
Buchananise or Buchananization refers to his way of manipulating gear ratios
and sizes to make a mechanism look more complex and to fill space. That
method is evident throughout the project.
This photo shows the entire hand-drafted drawing on the drawing board
and gives an idea of the scale of the drawing compared to the proposed final
product at 1:3.
The total number of parts for this assembly is estimated at a bit under
900 making this nearly twice as complex as the calendar, tellurian or
sun/moon rise-set complications.
The entire tellurian is now designed and fitted
into the area outlined by the red perimeter; similar to that outlined at the
beginning of this month's segment using the wiper gauge. A small compromise
is made by lowering the Saturn set a bit below the plane of the rest of the
planets to fit just below the notch representing the remontoire fly fan
cages. Notice the double planet depictions for Mercury, Mars and Jupiter,
representing their eccentric orbits. Saturn also will have this, but has not
been drawn doubly for clarity, see prior photo for this. In this
illustration it becomes clear that there is little room between the three
main rotating components - the inner planets, Jupiter and Saturn. The red
lines show the path of the
drive to Saturn's outermost moon, Iapetas.
As we know the space is very tight for the complexity
and number of components that are needed. Buchanan will tackle this by
building the device from the outside, inward. In other words the Saturn's gear
box which is under the outermost planet represented will be first to be
constructed. In this way we know exactly how much room is left for the other
components. This eliminates the risk that we run out of room after most of
the other components are already made.
This illustration shows the intricacy of the layered wheel works and the
numerous ball bearing pivot points. The area shown is the gear box for the
inner planet section. Friction is the great enemy of complex systems as
represented in an orrery. The use of modern materials and the bearings will
make this component far more reliable than could have been achieved in
The first three photos
show a scale drawing of the orrery within the context of where it will
reside within the rest of the machine. The second photo is interesting in
showing how Saturn will slightly cantilever past the vertical plane of the
adjacent dial work. The third photo shows how the orrery will neatly tuck
between the diagonal pendulum cross braces. The diminutive scale of the
orrery components are in stark contrast to the robust pendulums and
remontoire fly cages. The fourth photo shows the orrery against the
tellurian. Again there is a large difference between the scale of the orrery
and the tellurian. The tellurian contained about 400 parts; the orrery will
have twice that many.
This photo shows the wood mock up of the orrery dial support bracket.
Buchanan shows four visual areas that we want to keep from being covered
since they provide a strong visual movement. The two outer, larger circles
represent the front escapement antifriction wheel set. The smaller, inner
circles represent the celestial train's Robin remontoire chain pulleys. The bracket design
will be made to compliment these features.
Buchanan now begins the design of the orrery central
support and dial support arms and brackets. The main support is shown in the
first illustration. The initial hand drawn free-form design for the dial support
bracket is begun. The next two illustrations show the formulation of the
curvilinear ivy design that has been used throughout the project. The first
try was too short the second was correct. The fourth illustration shows the
correct support bracket beneath the dial support arm and adjacent to the
main support piece.
The first illustration shows trials of the center
support cross members of the dial support from above. The next illustration
shows the final design for the center cross and dial support arm from above.
The center dial support is shown with the actual orrery
dial. Next the support bracket drawing is seen next to the original wooden mockup
bracket created back in July of 2006. This is one of the last mockup pieces
to be replaced with a metal fabricated part.