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Orrery, begin preconstruction planning and design  - June 2018

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 Matthäus 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 orreries 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 Hahn’s day. 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 Buchanan has.


Buchanan writes: 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 to go.  

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.




Buchanan writes: 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 photo 0007, first photo. This is what we are talking about.

I took the drawing and enlarged it to the size that matches our diameter. Photo 0008, second photo, 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, third photo. 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 planets.

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) This 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 it.

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. 


Buchanan writes: 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. 


These illustrations show Saturn, the second the space occupied by the rotation of Saturn’s tilt.

Buchanan writes: 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. The term 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 Hahn's day.  



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.

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