- About the Solar System
- Orrery Design Concept
- Counting Gears and Teeth
- Gear Selection
- Orrery Gear Ratio Calculator
- How to make a Gear
- Making a More Difficult Gear
- Gear Calculator for Rotary Table
- Gear Making Vide0
Initial Thoughts 4/1/21
It’s been a couple of years since I created the Orrery Solar System Model found on this Technology Imagined website. I found it to be a lot of fun to make and have been thinking about building another one for some time. This time around I wanted to make something a bit smaller. I’m thinking of something that would fit on a desktop or shelf. The new Orrery will be made using more available gears scavenged from old broken wind up clocks.
But first a review of some solar system facts that will be relevant as I move forward with the construction of the new Orrery.
The table 1 above shows the planet diameters and orbital lengths (radii) for each of the planets out to Saturn in kilometers. Two things are evident. First, the Sun is incredibly huge. It is about 100 times larger than the earth. So if I were going to make planets all the correct size relative to the Sun, I would either need to make the Sun very large in order to see each planet as more than a dot, or make the planets very small and have a reasonably sized Sun say one inch (2.54cm) in diameter. At one inch diameter the Earth would need to be about 0.009 inches (0.23mm) in diameter. Very Tiny.
Second, the solar system is very spread out. Which brings us to the next problem. The orbital radii are absolutely huge compared to the size of the planets or even the Sun. So if these radii were kept to the correct ratio with respect to the planet sizes, again the planets would have to be dots, or the Orrery would be gymnasium size. If the sun were made to be one inch in diameter (2.54cm), the radius of Saturn’s orbit would be over 1000 inches or something like 85 feet (26 meters).
Just a side note on these orbital distances. The planets do not move in circles around the Sun. They move in elliptical orbits so are traveling in more oval paths. For my Orrery I am taking the averages of the nearest distance to the Sun (perihelion) and it’s farthest (aphelion). While it would be possible to make an Orrery with elliptical planetary orbits it would be pretty difficult. Maybe someday, but not this day.
Clearly something has to give beyond changing the shape of the orbits. I want to be able to place the Solar System on my desktop. So stay tuned and we’ll travel down a path to a completed Orrery that will be as accurate as needed, but still aesthetically pleasing. I envision an Orrery where the planet sizes are of the proper ratio to one another. The orbital radii and speeds of movement will also be in proportion to one another, but not to the planet sizes. That leaves the sun diameter, which will not be in proportion to any of these. I will probably make the Sun in the 1/10th size range with respect to the scale of the plants. I want the orbit of Mercury to come pretty close to the surface of the Sun. The picture below is taken through a telescope as Mercury transit between the Earth and the Sun. You get the idea as to how small and how close Mercury is to the Sun.
Some Gears and Calculations 4/2/21
We have not talked much about the planetary movement beyond there elliptical orbits. The crux of building an Orrery is the difference in the times it takes each planet to complete one trip around the Sun. The closer the planet is to the sun the faster it moves and the less distance it has to travel. This means all the planets need to move at the proper speed with respect to the others in order to better represent reality.
This table (2) shows ratios of orbit times for each planet with respect to each other planet. For example, the first column shows how long it takes each planet to complete one orbit compared to Mercury. So obviously Mercury’s orbit will take one Mercury orbit, but Venus will not complete one orbit until Mercury has gone 2.55 times around the sun. Incredibly Mercury will complete 122 orbits in the time it takes Saturn to complete one. Each column shows this ratio compared to all the other planets. So for for Earth, when it has gone 0.24 (24%) of its way around the Sun, Mercury will have already completed a full orbit. It will take 1.88 orbits of the Earth for Mars to complete one. This is where gears and gear ratios come in. This is how we will mechanically try to replicate the relative movements for all of the planets.
The ratios in the table above are not only the ratios of the orbital periods, but also the ratios needed for gears that will produce the orbits in my Orrery.
This image (figure 2) shows the basic design concept I used for the last Orrery and will use again. The image is simplified showing only the first two planets, Mercury and Venus. Each additional planet adds an another layer that will stack on top of one another. The concept for each of the layers is the same. In this design, the shaft that turns Mercury’s orbit is powered directly so all the other planets are ultimately tied the rotation of this axle. This axle is made from a tube with a shaft going through the center that will be used to support the Sun. This “Mercury” tube/shaft/axle will have an arm attached at the top. At the end of this arm will be the sphere the represents Mercury. As the tube turns the planet Mercury will orbit the Sun. The rest of the planets will have similar tubes and arms and work in generally the same way. The difference will be that the rest of the planetary tubes will be turned by a set of four gears. I will probably be using the terms “tubes”, ‘shafts” and “axles” interchangeably. I when I use these terms I am talking about the things the gears are attached to.
So let’s take a closer look at how we will power the rotation of Venus by using the rotation of the Mercury tube. The small gear B on the Mercury tube rotates against Gear A which is larger. Gear A is mounted to a shaft that has another small gear C also attached. Gears A and C will rotate in unison. Then gear C rotates against a larger gear D. Gear D is mounted to a tube that slides over the tube that powers Mercury and is attached to the arm holding Venus. So when the Mercury shaft is rotating the Venus shaft will rotate at a slower rate based on the ratios of gears A, B, C and D. How much slower.? Well the rotation ratio of gear A to B will depend on the number of teeth each has. So if gear A has 48 teeth and gear B has 24 teeth, then the ratio of rotation will be 48/24=2 or 2:1 . Now gear A is turning gear C at the exact same rate. If gear C has say 10 teeth and gear D has 30 teeth the ratio of D:C will be 30/10=3 or 3:1. So in this example gear B will turn two times for every time Gears A and C turn once. Gear D will turn three times for every time gear C turns once. So the overall ratio will be 2×3:1 or 6:1. In this example gear B will turn six times for every time gear D turn once. This is not the ratio we need between Mercury and Venus. We need gear combinations that will result in 2.55:1 ratio not 6:1 per table 2, but you get the idea.
The rotation speed ratio equals (A-teeth/B-teeth) x (D-teeth/C-teeth)
The selection gears A, B, C, and D need to give the ratio value using this equation matching those found in the “Ratio of Planet Orbits Around the Sun” table 2 above. We will have four sets (A,B,C and D) of gears for each planet. If we are using the Mercury tube to power gear A, B, C and D for Venus we then need the ratio found in the first column labeled “Mercury” in the table corresponding to Venus. In this case 2.55 to one.
The nice thing is that each planet can be powered by any tube that is below it. So while Venus can only be powered by the Mercury tube, Earth can be powered by either Mercury or Venus. Mars by Earth, Venus or Mercury. Jupiter by Mars, Earth, Venus or Mercury. You get the idea. This opens up many ratio possibilities and that means many more possible gear combinations. This is good as we shall see it can be difficult to get all of the correct gears for all of the planets.
Some More About Gears 4/3/21
When the four gears for each planet are mounted on their tubes/axles, the shafts must be parallel in order to function. That is, when all the gears mesh properly, the axle holding gears A and C must be parallel to the tube holding gears B and D. In my first Orrery I used gears from one manufacturer, Boston Gear. If I used gears with the same diametral pitch (DP) number this parallel alignment would occur as long as the total number of teeth in gears A+B was equal to the total of C+D. The DP number is the number of teeth on an individual gear divided by the gear diameter. This number tells us about the size and spacing of the teeth on the gear. This worked great in gears from one manufacturer of quality gears like Boston Gear.
The image (figure3) above shows the collection of gears I will be working with for this Orrery. These are antique and vintage clock gears removed from old broken wind up clocks. I have a lot of these as I pick them up whenever I see them at a flea market or on eBay in larger lots. The main problem is that the DP numbers do not always match up for these gears as they have been made by different manufacturers over many decades. For example I have three different gears that all have teeth that mesh and all with 72 teeth. However, all three have different diameters. This would cause problems for getting the parallel placement of shafts for AC and BD if different ones were used in an ABCD set. This is only one example. So for this new Orrery I cannot use the A+B = C+D rule for selecting gears as I did last time. This is both a blessing and a curse. It is a curse because it limits the number of possible gear combinations I can use. It is a blessing because the gear calculations become much easier to process.
For gears of similar enough tooth size so they will mesh properly I only now can be assured of parallel shaft placement if gear A is an identical gear to D and gear B is identical to gear C. That is matching sets of identical gears. This makes gear calculations easier as the equation above simplifies to:
The rotation speed ratio now equals (A-teeth/B-teeth) x (A-teeth/B-teeth) or (A/B)(A/B) which is (A/B) Squared
This is because the number of teeth on A equals the number of teeth on D and B equals C. So how does this equation make gear calculation easier? If I take the square root of the ratios found in the “Ratio of Planet Orbits Around the Sun” table 2 above, I get the ratio required for only two gears. A/B which will be identical to D/C for each orbital/speed ratio.
So this makes things much easier to calculate. I just need to find two of the same gears for A and D with the same number of teeth, and two of the same gears for B and C with the same number of teeth. The other stipulations are that all the gears mesh properly, that is have the same number of teeth per inch, and the ratio A/B matches those found in the Square Roots in table 3 above for each planet of interest. For example, if I find two identical gears with 48 teeth for gears A and D, I will need two identical gears for B and C of the same tooth size with 30 teeth for Venus to be powered on the Mercury shaft. This gives me a ratio of 48/30=1.6, which is the ratio found in the square root table 3 above. Next will be the hunt for the gears. Stay tuned.
The Search for Gears 4/4/21
My first step was to sort each gear in my collection by the number of Teeth Per Inch (TPI) and then into identical gear types. In order to find the TPI for each gear I used a thread pitch gage found in figure 4 below.
Normally this device is used to measure the teeth per inch on a screw or bolt. If you are interested, I got this one at Little Machine Shop.com, a great place to get all kinds of metal working tools for a small shop.
You can see in figure 5 that it works pretty good for measuring the TPI for gears as well. In this example the gear has about 14 teeth per inch. Using this gage measured the TPI for each gear type in my collection.
Next I separated the gears into identical gears and then counted the teeth on each. This can be tedious. The best method I found was to photograph each gear close up and then count the teeth on the photo.
I set up this temporary photo booth (figure 6) with a piece of paper to provide a white back ground.
Then I took a closeup photo of each gear like this one. Using an editing program (MS Paint) I circled a gear roughly at the 12 o’clock position on each gear and used it at the starting point for the count. The paper in this example is labeled with a gear identifier D6. Each gear type was given a unique identifier based on the TPI and number of teeth. Don’t confuse these A,B,C and D with the gears required for the Orrery, these are just catalog numbers for my inventory. The letters group them by TPI. The numbers are arbitrary, but generally follow the pattern that lower number have more teeth than higher ones. This didn’t happen all the time as I would discover new gears that had to be added to the list later messing up my numbering system a bit.
After sorting and counting all the gears, what I came up with is (table 4) inventory of gears I have available. I have 31 types of identical gears in 4 different TPI groups. For each group I labelled the gears with an A, B, C or D and then a number. Again, these are just for cataloging the gears and to not indicate gear types found in the design concept of figure 2.
Figure 8. All the gears sorted and placed into individual bags.
Figure 9. And here they are back in the “Small Gears” storage drawer.
Selecting the Right Gears
Above in table 5 is a copy of an Excel spread sheet I used as a gear calculator. I have also added a download button below so you can use it to do calculations with any gears that you may be using. It’s not real complicated, but does require some explanation. I’ll go into some detail on how to use it for gear selection next.
Columns Labels in table 5:
- Gear – Just my catalog number for each gear in my collection.
- TPI – The number of teeth per Inch for each gear.
- Dia (in) – The diameter in inches of each gear
- V/Me- The V stands for Venus and Me for Mercury. V/Me lists the gear required for Venus to be powered off the Mercury shaft/tube using it in combination with the gear in first column .
- E/Me – E is Earth so E/Me is the gear required for Earth powered off the Mercury shaft/tube with the first gear in this row.
- E/V – This is the gear required for Earth powered off the Venus shaft/tube.
- M/E- The M stands for Mars and E for Earth. M/E lists the gear required Mars to be powered off the Earth shaft/tube.
- M/V- The M stands for Mars and V for Venus. M/V lists the gear required Mars to be powered off the Venus shaft/tube.
- M/Me- Gear for Mars powered by Mercury shaft/tube.
- J/M- Gear for Jupiter powered by Mars shaft/tube.
- S/J- Gear for Saturn powered by Jupiter shaft/tube.
If you enter all the gear tooth numbers of the gears you have to work with into the TPI column the calculator will calculate a gear tooth number required for each column for powering the planets. All you have to do then is see if you have a gear of the right size in column one. The yellow highlights in my table are gear matches or near matches that I found in my collection. These will be the gears I intend to use.
So in table 6 is the final selection of gears to be used. I have kept several options open for Mars as I have yet to decide which combination to use. I would like to use Earth to drive Mars, but I don’t have a gear combination in table 5 that will get the exact ratio. Since Jupiter and Saturn will be powered off of the Mars shaft this error will be compounded. You will notice I already have some errors entering into the Saturn and Jupiter ratios. Jupiter is giving me a 6.25:1 ratio when I would like a 6.31:1. Saturn at 2.42 versus the desired 2.48. These outer planets move very slowly so I’m not too worried about their errors. I also have not decided whether I will even include Jupiter and Saturn in my finished design. In this design I want to keep the Orrery fairly small. Adding in the orbits for Jupiter and Saturn will make this more difficult unless I make some kind of size compromise.
The other thing you will notice in tables 5 and 6 is a new 30 tooth gear inventory number C9. This is a gear not currently in my inventory. I wasn’t able to find a good combination of gears for driving Venus. I decided to make two 30 tooth gears that will mesh well with the two 48 tooth gears C4. Making these gears will be the subject of the next section.
How I Made a Gear 4/9/21
I was able to select gears A,B, C and D from my stock for all of the planets except Venus. Unable to find a set that would be in an acceptable gear ratio range to the 2.55:1 required, I decided to make gears that could be used with an existing pair. Having a bunch of 48 tooth gears you can see in table 5 that 30 tooth gears would get a ratio A:B of 1.6:1 (48/30=1.6). Doing the same for D:A I get 1.6:1 x 1.6:1 = 2.56:1 for the final ratio. This would be close enough to the target value of 2.55:1 for our Orrery.
Figure 10. Gears A and D we will be using two gears C4 from my inventory. This gear is brass and if you count the you will find 48 of them.
Figure 11. Using my thread pitch gage you can see that the gear has about 14 teeth per inch. Other gear C4 facts are:
Outside tooth tip diameter = 1.076 inches
Inside tooth bottom diameter = 0.982 inches
Outside Circumference = 3.14159×1.076 = 3.380 inches
Inside Tooth Circumference = 3.14159×0.982 = 3.085 inches
Teeth/Inch (tooth tips) = 48teeth/3.380 inch circumference = 14.201 T/in
Teeth/Inch (tooth valleys) = 48 teeth/3.085 in circumference = 15.56 T/in
Now we need to calculate the dimension of our new gears B and C. We know we need them to be 30 tooth with about 14 teeth per inch. This will allow them to mesh and have the proper ratio to gears A and D.
Figure 12 above is the scratch paper I used to help me calculate the new gear dimensions. The results of these calculations are as follows:
Specifications Gears B and C (new gears)
Teeth = 30
This means 360 degrees/30 teeth or 12 degrees between each tooth.
Need to have 15.56 T/in on the new gear inside or in the tooth valleys to mesh with the teeth per inch of the the 48 tooth gear tips of gear C4.
We need to have 30 teeth, with the outside meshing with the inside of A and D.
Circumference = 30T / 15.56 T/in = 1.928 inches
Diameter = 1.928/3.14159 (pi) = 0.6137 inches
Radius = 0.3069 inches at the inside or valleys of the teeth on the new gears.
Now we are ready to actually fabricate two new gears from the brass stock piece you can see at the bottom of figure 12. It is a six inch brass piece that is one inch wide and 0.09 inches thick. This is a standard size that can be purchased at most hardware stores. I bought mine at ACE.
So how are we going to make a gear? Part of the answer is in figures 14 and 15 above. The milling machine on the left has an X Y table mounted below a drill chuck. The X Y table allows you to center a work piece under the drill chuck and the move it an exact amount to the left or right (X direction) or back and forth (Y direction). The next piece of the puzzle is the rotary table seen on the right (figure 15). This device allows us to rotate a work piece a specific number of degrees and seconds with respect to the drill chuck.
Figure16- The hand crank on the rotary table allows the work piece under the drill chuck to be rotated an exact number of degrees and seconds. A second in angles are 1/60th of a degree. Rotating the hand crank once around on my rotary table rotates the part 4 degrees. In order to move 12 degrees for each tooth I will need to rotate this crank through 4 revolutions.
Now we are ready to start making our gear. I plan to make a You Tube video of this complete process and add it to my You Tube channel, but more details are available here.
The plan for making the gear is to cut a ring of small holes around a center. The inside edge of these holes will be the inside or bottoms of the teeth. I actually cut a second set of holes just outside but in line with the first set. This made it easier to finish the tooth shape with small files. Excess brass is then machined off using a lathe and the final fit and finish was done with small hand files.
Here the rotary table has been centered beneath the drill chuck. This was done using an edge finder and was centered both in the X and Y directions. You can see here how the brass will be held in place for drilling. The metal is too long in this picture to allow for a full rotation of the table so before starting it was trimmed a bit shorter. Underneath the brass is a scrap piece of aluminum. This is so we can drill all the way through the brass without drilling into the rotary table.
The brass has been mounted to the table in this picture and a center hole has been drilled with a #18 drill bit. This hole will serve as the center where the shaft will pass through the gear.
In this picture the X-table on the mill has been moved 0.3592 inches to the left. This is our inside gear radius plus the radius of the #61 drill bit. Now when the rotary table is turned it will make a circle around the center of the gear. the inside edge of the #61 drill bit will then be at 0.3069 inches from the center. I am using a small center drill to mark locations for holes every 12 degrees. This will result in 30 holes after one revolution. That is three turns of the crank on my rotary table as each one rotates the table 4 degrees.
The first set of 30 holes has been marked with the center drill in this picture. I used the center drill first so that the holes drilled through the plate wouldn’t walk away from there exact locations. A small drill bit like a #61 has a tendency to walk away from center when drilling. I always use a center drill when I need a precise hole location regardless of drill size.
It is hard to see here but each hole has now been drilled all the way through with the #61 drill bit.
A center drill is marking a second set of holes centered 0.04 inches out from the first set.
This image shows a closeup of the second set of holes marked and ready to be drilled. I offset them from the first ring just enough so drilling wouldn’t result in the drill bit sliding into the first set of holes.
So here the holes have been drilled and the brass piece removed from the milling machine.
The band saw was used to trim the drilled brass to a roughly round shape. The aluminum rod in this picture has one end bored and tapped to accept an 8-32 screw. This will serve as a mounting fixture for the gear.
The brass piece mounted to the aluminum rod. Ready for turning on the lathe.
The future gear all chucked up and ready for turning to the correct diameter.
The piece being turned to 0.735 inches in diameter.
In these pictures the gear has been turned to the correct diameter and removed from the lathe and mount.
A Dremel with a cut of tool is used to trim away excess brass from the teeth.
Hand files are used to remove material and achieve a close fit with the 48 tooth gear C4.
And here in these last two images are the gears completed ready for the next step in our Orrery. That would be choosing the brass tubes and rods for the shafts and then mounting the gears to them in the proper order.
I Digress- Making a 35 Tooth Gear 4/25/21
So I was looking at the gears that I had chosen and didn’t like the Mars to Venus gear combinations available. If I could get a gear set to turn Mars off of the Earth shaft it will simplify the rest of my design. When I looked at the gear combinations in table 5, I saw that I could use two 48 tooth gears in combination with two 35 tooth gears for gears A,B,C and D for turning Mars off of the Earth tube/shaft.
48teeth/35teeth = 1.37 and 1.37×1.37 = 1.88 the desired ratio for Mars to Earth.
This gear is a bit more complicated. A 30 tooth gear is pretty simple. 360 degrees divided by 30 teeth equals 12degrees/tooth. Now my rotary table moves through 4 degrees of rotation for each one complete turn of the hand wheel. 12 divided by 4 equals 3. So to drill for 30 teeth I needed to turn the hand wheel 3 rotations between each drilling. I would always land back at zero after each hole. 35 teeth is different. 360 divided by 35 equals 10.2857 degrees per tooth. This means if I get 4 degrees for each rotation of the hand wheel I will turn it 10.2857/4 or 2.5714 rotations per hole drilled. 2.5714 works out to 2 turns plus 2 degrees 17.1 seconds for each set of rotations between holes. So you wind up with these odd ball stopping points after each hole. What I decided to do is make a calculator in excel that would set up tables for me to follow while making each gear.
You can down load the excel spread sheet here:
Let me explain how this works. In the first column under “Teeth” you enter the number of teeth you want the gear to have in the highlighted box. In the D/turn (degrees per turn) box in the third column you enter the number of degrees for each rotation of the hand wheel on your rotary table. You then enter the number of teeth per inch in the “T/in” box and the diameter of the drill you will be using in the “Drill dia” box. In between these to is the amount you want to offset the X-Y table in the X direction for drilling your ring of holes.
The red box surrounds the turns, degrees and seconds required on the rotary table for each drill location. So starting at the top the first hole is drilled without any rotations. Then, in a clockwise direction, on my mill I do two full rotations plus 2 degrees 17.1seconds and drill the second hole. Then before the next adjustment I rotate the hand wheel clockwise back to Zero.
So why do I do this? First of all it is a lot easier to count turns from zero then some random location on the hand wheel dial. Second, it helps prevent errors from accumulating as I advance the gear through 360 degrees. If I mess up by a couple of seconds of arc this won’t be added to the next hole. The excel spread sheet automatically subtracts off this extra rotation from the 2 turns 2 degrees 17.1 seconds back to zero off the next turn.
You will notice that there are 5 sets of 7 turns that bring us back to the starting hole. What ever tooth number you select will start repeating a sequence at some point and you only need enough to complete your total gear tooth count.
The columns marked Check 1, Check 2, Check 3 and Check 4 are for marking each drilling. I do four sets of drillings for each tooth. A center drill marking each hole. Then a #61 drill hole. Then I offset in the X direction 40/1000ths of an inch (drill bit diameter) and do another set of center marks and drills. This means four drillings for each tooth. The way I found that works best is to drill then advance clockwise to zero, unless I am already at zero, and then check the box for that drilling. I then advance to the next hole and repeat. I continue this process until all 35 holes have been marked. Then repeat with the #61 drill bit. After that I increase the offset in the X direction another 40/10000ths and repeat the center drills and #61 through drills again.
Once all 70 holes are drilled the rest is the same as that for the 30 tooth gear described above.
In this picture you can see my 35 tooth gear prototype. I’ve started using cheaper aluminum to experiment with as I’ve been going through quite a bit of brass. That gets expensive.
Finally in table 8 is the current gear selection table with the new 48 and 35 tooth gears for driving Mars from the Earth shaft. Now I just have to make two 35 tooth gears from brass. Then I will get into selecting tubes and shafts for each gear combination. All of the gears will also need hubs attached for mounting to the shafts/tubes.
35 Tooth Gears Compete 4/27/21
It’s a couple days later and the 35 tooth gears are done as you can see above. Next up shafts and tubes and hubs. I promise.
Next hubs, tubes and shafts.