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The complete Orrery. (6/9/18)
What follows is a chronicle I made during the design and construction of the Orrery. It’s fairly long, but would be pretty helpful to anyone else who might like to make one.
A couple of months ago I bought a box of large brass gears on eBay. The box I received contains around 60 gears of various sizes. The picture below is just a portion of what I now have. The gears in the picture are all of the 32 DP variety.
Looking around for a new project I thought it would be fun to build an Orrery solar system model. An Orrery is a mechanical model of the solar system. Using gears it will rotate the planets through there orbits at the relative rates seen in astronomical observation. The image below is a picture of a typical Orrey.
My plan is to use my box of gears to build the device. I will be building a Coppernican Orrey. This contains the six planets Mercury, Venus, Earth, Mars, Jupiter and Saturn. Uranus and Neptune as well as Pluto are left out. The Model will also include the Sun at the center and Earths moon. I am hoping to be able to use various combinations of the gears I have in order to get the orbital times correct.
So far I’ve looked at some of the things others have done in making Orreries, but my plan is to come up with my own design. I’ve done some research and have checked and verified some pertinent facts about the solar system.
I will use this chart not only to calculate the ratios of gears I will need to get the orbital times correct for each planet, but also the relative sizes and distances from the sun. There are two rotation ratios on my table. The first column is relative to Mercury the fastest moving planet. The second column is relative to the Earth. So when Mercury goes the sun once, one Mercurial year, the Earth will only move around the sun about a quarter of the way.
This week I’ve been working on the base design and figuring out what ratios of gears to use. The figure below is the basic concept.
There will be a series of brass tubes slid inside one another that can rotate independently around a central axis. There will be one tube for each planet. Two tubes for Earth more on that later. A solid rod will support the Sun. In this diagram I’ve simplified things to just Venus and Mercury but the rest of the planets will be similar. Mercury will be driven directly by turning Gear B. This will most likely be a worm gear driven by a motor, but I haven’t decided on a drive mechanism yet. By driving Mercury directly I eliminate the need to come up with gear combinations for this planet. When Gear B is turned it rotates Gear A which rotates the shaft attached to Mercury making it orbit the Sun. Gear B is mounted on the same shaft as Gear C so it will turn at the same rate. Gear C drives Gear D which is attached to the shaft for Venus. By choosing gears A, B, C, D at the correct ratios the relative rotation rates between the planets can be adjusted to the proper speeds. For Venus and Mercury the overall ratio in rotation is 2.55. That is for every one orbit of Venus, Mercury will orbit 2.55 times.
The pictures above are the brass tubes that will be used for each planet. There sizes are 1/8, 5/32, 3/16, 7/32, 1/4, 9/32 and 5/16 inches.
Not only can outer planets be driven by the inner Mercury tube, but as we go out the planets can be driven by the tube for any planet closer to the Sun than it is. So Saturn can have Gear A for it driven by any of the other planets shafts. This is handy because as we move outward more and more gear combinations will become available. This is important because I have a limited number of gears and I don’t want to make/buy more if I can help it.
With that in mind the table above was calculated showing the rotations of all the planets relative to one another. For example the first column, labelled “Mercury” are the rotations of the planets relative to Mercury. Each other column is similar.
So now to figure gear ratios for each of the planets. The first thing I did was count the number of teeth on each gear I have. This took a while. I have large sets of 15 tooth per inch (TPI) gears and 10TPI. The table below is the gears as I counted for each one (twice).
In order for the system to work properly the total number of teeth in Gears A plus B must be equal to the total number in Gears C plus D. This will ensure the planet tube will remain parallel to the outer shaft in the figure above. For each planet I can use either 10TPI or 15TPI gears for the four gears, but I cannot mix 10TPI with 15TPI or my teeth won’t mesh and my shafts will not remain parallel.
So I came up with an Excel spread sheet that will help me with these calculations. I use the “solver” function in Excel and enter gears A and B and Excel calculates gears C and D based on the required ratio and keeping the number of teeth in A+B equal to that in C+D. Even with Excel this is a tedious process. If I were a better programmer I could probably make a spread sheet to do the whole thing automatically, but alas I’m stuck doing things more slowly. The table below are the gear combinations I’ve come up with so far.
So I’ve got a bunch done, but many more to go. When this list is complete I will hopefully have enough gears to meet the requirements. If not I’ll have to make or find them somewhere else.
Well I have finally completed all the calculations for the gears I have in my collection. The two sets of gears I have are actually 48 DP (Diametral Pitch) for what I was calling the 15TPI and 32 DP for what I called the 10TPI. I know this now because the gears I am using are still made, even though they look old, by Boston Gear and use the same part numbers. So instead of counting all the gear teeth on each gear I could of just looked them up here.
Oh well live and learn, in this case I’m learning a lot about gears. Below is the list of all possible combinations of gears that I have that will work for each planet that I generating using Excel.
I then went through and selected a few promising combinations, one of which is below.
Each one selected uses just the gears I have enough for when I combine them. I also tried to keep the error level to less than 1%. In most cases I was able to have 0-0.5%. Good news is I won’t have to fabricate any gears. In case you cannot see it above, I’ve pretty much settled on the combination of gears below.
This portion of the project took quite a while. Things will get more interesting now even though the pace will be slow. I need to complete the design for the overall gear box and then start construction. All of the gears have different bore sizes so I’ll be making a lot of bushings in some cases and boring them out further in others.
When I went to collect the gears together for all of the planets as shown above I ran into a problem. The 60 tooth 32DP gears used as gear C for earth was not the proper size for making the four gears A, B, C, and D line up when Orrery was assembled. The rest of the gears I was going to use were all manufactured by Boston Gear. The 60 tooth was an odd gear I had found in the box of gears in my collection. The distance between centers when gears C and D were meshed together was about 1/64th of an inch shorter than the distance between centers for gears A and B. I went back into my list of gear combinations and came up with a new set of gears.
So this is my final set of gears. I’ve managed to keep all of the orbits within 1% of the actual values. This is when all gears are considered, remembering that some planets are running off of other planets with their own gears and errors.
Above are the gear sets for Venus.
Above are the gear sets for Earth
Above are the gear sets for Mars.
Above are the gear sets for Jupiter.
Above are the gear sets for Saturn.
Above are the gear sets for the Moon.
Just a note on how the moon is made to go around the Earth. The large gear above gets mounted onto a tube that is fixed and does not rotate. This tube is the one just outside the rotating shaft/tube for Earth. The stationary tube that is outside rotating tube for planet Earth is the same radius as the hub for large fixed gear (192 teeth 3 inch radius). A shaft with a small gear (16 teeth) is mounted vertically through the Earth so that the teeth will mesh with the large gear. This small gear will be rotated by the movement of the Earth around the Sun. If a moon is attached to an “L” shaped bracket attached to this gear it will rotate around the Earth 192/16=12 times for every time the Earth goes around the Sun. This is pretty close to the approximately 13 times the Moon actually orbits the Earth in a year.
This idea I found on Instructables.com here. MatthewS3 was making an Orrery from plywood gears and used this technique for the orbit of the moon.
The next step is to make some detailed measurements of each gear set and draft together a more detailed design for the Orrery than the one in my head. Once that is completed the hole in each gear will need to be adjusted the the diameter of the tube or shaft it will be mounted too. In some cases I will be making bushings, in others the holes will need to be made larger.
So I’ve been working on even more calculations and design. It seems like I’ll never get down into the work shop, but with all of the pieces that need to come together the design part was particularly important for this project.
Above are the measurements for all of the gears that I will be using. The gear diameters and radius are the most important information here and are highlighted in yellow. This information was used to design a layout for all of the gears. This allowed me to see how many individual sections/levels I would require for the complete gear train. The rod/tube diameters are the second most important information. These are the hole diameters that each gear will require in their hubs in order to mount to the tubes and rods required. The tubes are highlighted in green with the rods left white in the same column. The tubes will nest inside one another in one central shaft area. The rods will be placed parallel to the main shaft and will hold the gears A and C for each planet in the diagram above. Each planet will have it’s own outside rod.
I used the gear diameters in the table combined with the final gear combinations above (also in my post of 3/11/18) to design a 3D model of the gear train. I used Sketchup for the design. This took a while because I had to learn to use it first. I had drafting in high school, but we used drafting tables, triangles and pencils. At first I was going to us Sketchup as a 2D electronic drafting table. After working with it, however, it seemed that with the way it was designed it was easier to do the 3D model. I’m no expert yet, but I was able to get a pretty good 3D layout developed after working with Sketchup for a few hours. Below are some captured images of the 3D gear layout.
Angled view of all of the gears. A couple are hidden under other gears.
Another angled view where the gear designations are a bit more evident.
In this side view all of the gears can be seen. It looks like I will be using five levels. The first level will house all of the gears A, B, C and D for Venus and A and B for Jupiter. The second layer will hold gears A, B, C and D for earth and gears A and B for Mars. The top plate for this level will have the stationary tube attached to it that will support the 192 tooth gear used to rotate the Moon around the earth as described earlier. The Third layer will contain only gears C and D for Mars. The fourth, gears C and D for Jupiter. and The fifth level the A, B, C and D gears for Saturn. The sixth plate is the top plate holding the main shaft and the rods for Saturn in place. At least that’s the plan for now. As there are always problems in a first prototype like this I expect some tweaks along the way.
My next step will be boring out gears where the hub holes are too small, making sleeves for the holes that are too large, and adding set screws where needed. Some gears have no hubs so they will be fabricated from scratch.
Over the past week I spent a lot of time working on the gear hub hole sizes. Each gear needed a specific hole size to fit a specific shaft. Almost all of them needed set screws added to the hubs. I took a lot of pictures and had to adjust about 22 gears to the right size.
This gear had a hub that was too small so a new hub was created and the smaller one was removed. In this picture a brass rod is being bored to the same size hole currently in the gear.
After boring the brass was machined flat and then cut to length on the lathe.
The new hub is seen here sitting on top of the gear it will be added too.
Before attaching to the gear the hub was drilled and tapped so it would accept 6-40 set screws when done. I am making two set screws per hub. This will help keep the gear from shifting sideways when the set screw is tightened.
The the surface of the gear was lightly sanded. Flux was coated onto the mating surfaces of the hub and gear. The hub was centered onto the gear and held temporarily in place using a 1/4 inch screw with washers and a bolt. Finally the gear/hub combination was heated with the torch and solder was applied.
The gear with the new hub attached. The old hub remains in place at this point.
The gear was chucked up in the lathe and the old hub was machined off of the surface. The hole was then bored out to the proper diameter on the lathe.
The completed gear before boring the hole to the proper size.
After boring the “new” gear was temporarily attached to the shaft with the set screws in place in order to check the fit.
For this gear the hole was too large so a brass sleeve was turned on the lathe. First the outside dimension was turned to the correct diameter.
Then the center of the sleeve was bored to the proper size.
Then the sleeve was fit into the existing gear hole. Finally the hub would be drilled and tapped in order to accept set screws.
All an all I had to make adjustments to 22 gears. Four for each of the planets; Venus, Earth, Mars, Jupiter and Saturn, and then two for the Earth/Moon combination as described above.
Completed gears for Venus.
Completed gears for Earth.
Completed gears for Mars.
Completed gears for Jupiter.
Completed gears for Saturn.
Completed gears for the Moon.
After I had the hubs completed I had enough information to continue on with the design in more detail using SketchUp.
This is the 3D model with all of the gears adjusted to the correct thickness with hubs attached. The various shaft sizes are correct also.
This is a 2D version of the same design. Next I’ll need to start cutting each shaft to the correct length and from the correct tube or bar stock.
I was able to start working on the Orrery mechanism this week. The first step was to cut each of the brass tubes to the correct length based on the design above.
This picture shows all the tubes inserted into the respective gears and then slid into one another.
This close up shows how the tubes are nested inside one another.
Brass plates that were 6 x 12 inches originally were cut to the correct dimensions. The bottom two plates were cut to 6 x 7.5 inches. The top four are 6 x 5.875. Thicknesses varied from 0.0625″ to 0.03125″.
After cutting to size the corners of each plate were drilled 1/4 inch from each edge to create mounting holes. Here the smaller plates have been screwed together through the holes. This is for drilling the main gear shaft. By drilling all the plates at once it can be assured that the holes will line up from one layer to the next.
The gears were placed on top of the plates in order to determine exactly where to drill each side gear shaft.
Here the plates were set over the first layer gear to check fit. The height of the support rods for this layer could also be verified/adjusted. I wound up adjusting the support rod length of this layer to 1.75 inches. These are 1/4 inch brass rods cut to length and then threaded on each end to accept 6-32 screws.
Here the two plates are screwed together.
Another view. This layer contains the tubes for Mercury and Venus. The side shaft for the Venus drive gears C and D are visible in the front right. The long shaft rising up the the rear right is the drive shaft for Jupiter. This runs off of the Venus shaft, so gears A and B for Jupiter are also found in this first layer.
In this view the gears for Earth and Mars have been set in place in preparation for drilling the plate that are part of the first layer. The next plate will also require drilling for all these tubes and rods.
Today I made quite a bit of progress with the remaining gear levels.
First I had to drill holes for the gears on the next level that contains all the gears for Earth as well as gears A and B for Mars. This is a picture of the gears in the bottom level with the top plate removed.
After drilling the gear holes the next plate was set in place to make sure everything lines up. Of course it did.. Thanks Sketchup.
Next I made the support posts for the Earth/Mars level top plate.
This level is now complete. Gears C and D for Mars could also be attached.
A side view better showing the internal gears.
The Top plate for the Mars level was completed and gears C and D for Jupiter could be attached.
The base plate for the next level is set in place for measuring the post height for this plate.
The Saturn Gears are seen here temporarily set in place.
This is where I am as of today. The top plate has been set in place. I still need to make the support posts for this level and drill the holes for the Saturn A and C gears. The Shaft for these gears also needs to be made. When that is done the drive mechanism for the Orrery will be complete. Then I’ll move on to cleaning things up and making a base. The planets will need to be made as well as the rods that support them.
During the week I finished attaching the top plate to the Orrery. Here are some pictures of the unit at that point.
This weekend I worked on cleaning up the mechanism and adding spacers and washers to the shafts that needed them. I also adjusted the lengths of the tubes that weren’t quite the correct length. I then spent some time motorizing the unit.
I went through my box of old motors (yes I have a box of old motors) and found this 120VAC clock motor. I like the idea of using a clock motor as they are fairly quiet and turns at a very low speed with a lot of strength. They are also designed to be run continuously if I were to want to just leave the Orrery running.
This is the location where I decided to add the motor. In this location I can add a shaft to the motor with a gear and drive Mercury directly by impinging my drive gear onto Venus gear A.
A 1/4 inch hole was drilled into the top and bottom plate so the shaft would be supported by the plates.
A 1/4 inch shaft was cut that could be slid through the holes and hold the gear in place. The gear also has a 1/4 inch hole.
A hole was bored down the center of the shaft and set screws were also added. Set screws were also added to the hub of the drive gear.
The motor and shaft in there final location. All that is left is to drill some holes for the mounting screws. These will go through the holes seen on the mounting brackets that are part of the motor.
Before I put everything back together I started on the wood base. I needed the bottom brass plate to get the correct hole locations so I thought I would do that while the Orrery was disassembled.
A close up of the wood base temporarily attached. You can also see one of the screws holding the motor in place by the mounting bracket.