Introduction: How to Build a Precise Mechanical Planetarium

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About: My name is Guus and I'm currently a 18 year old student at the Technical University of Delft (in the Netherlands).

Hi there! My name is Guus, I'm a 17 year old student from the Netherlands and I'm in my final year of the dutch variant of High School. At the end of High School, every student has to write their own final big paper. Usually students do literary research or a small experiment. However, I felt like that would be kind of boring, so I decided to build something big and special. Obsessed with the world of time and space I decided to build a very precise mechanical planetarium.

This instructable will show you how I built my very precise mechanical planetarium. I will go over the most interesting designing steps and the building steps.

Please note that this is my very first big project in wood. I'm definitely not an expert so I've probably made a lot of silly designing and building mistakes. In the course of this project I've definitely learned a lot, but if you have any tips on how to do things better next time, please make sure to leave them in the comments!

Step 1: Goals

Before I started with the design process, I had to set myself some goals. I needed to decide what the planetarium would and would not be able to do. I had two main goals. The first one was to design and build it all by myself. I didn't want to just download some blueprints from the internet, because that would be too easy. I wanted to challenge myself and see what I was capable of doing.

The second goal was to show the difference in circulation time of the planets around the sun. I wanted to do this as precise as possible. After some research on the internet, I found the following rotation speeds for the 8 planets:

  • Mercury: 87,969 days
  • Venus: 224,701 days
  • Earth: 365,256363004 days
  • Mars: 686,971 days
  • Jupiter: 4.331,59 days
  • Saturn: 10.759,22 days
  • Uranus: 30.688,5 days
  • Neptune: 60.182 days

I was also thinking about setting every planet on the correct, relative position of one an other. However, after some test designs in Fusion 360 I noticed that this would only work for the middle 4 planets. When adding the outer 4 planets, the size of the planetarium would increase tremendously. You can see this in the pictures above. Of course I could just place the middle 4 planets closer together and still keep the planetarium small. However, placing these planets so close together would make it very difficult to give them the correct circulation speed, and this would mean that my second goal wouldn't be realized. That's why I decided to make all of the planets on the same distance of one another.

To see the 3D-design I made to create the pictures, click here: Relative distances of planets. I made this design in Fusion 360 and I added joints to every planet so they circulate the sun at the correct relative speed. Downloading the file and opening it in fusion 360 will allow to do this. If you don't have fusion 360 yet you can get a 30-day free trail here: 30-day free trail. Students can get a 3-year free trail here: 3-year student trail.

Step 2: Tools Decision

Before stating the designing process, I had to think about the tools that were available to use and the material type that I wanted to use. That is because this greatly influences the design.

There were 4 different ways of making the planetarium that were available to me and that I've considered. These were:

  • 3D-printing
  • CNC-milling
  • Laser cutting

Every one of these methods had its pros an cons.

Scroll saw

Since one of the goals was to make the planetarium as precise as possible, I knew I had to use a lot of gears . So I started off trying to make a gear with a scroll saw. Straight away I noticed that I didn't have any skills. It would take a lot of time and the result would be very bad. Using a scroll just wasn't the way to go. You can see the result of this test VS a CNC milled gear in the pictures above.

3D-printing

In my school there is one 3D-printer that is used by the science-teachers and for this project I got the permission to use it. By using a 3D-printer, I would be able to make some very small and complex parts. However, 3D-printing takes a lot of time, and afterwards I wouldn't be able to easily change parts or to make any changes to the design without having to print the parts again. I also wanted to make the planetarium fairly large to really give it the 'wow-factor'. This wouldn't be possible to do with a 3D-printer, so this option was out of order.

CNC-milling

I'm very fortunate to be the little brother of Benne who has built a CNC-router a few years ago. You can find a link to his instructable here. With his CNC-router, I would be able to mill in wood and in some metals. Because I wanted to make the planetarium affordable, I decided to use wood. The nice thing about using wood, is that I could easily adjust some parts afterwards by using a saw or just sandpaper. By CNC-milling, I would be able to get a very nice result as shown in the first picture above. However, the edges of the parts after milling would need to be sanded off, otherwise they would look like the ones in the pictures. All in all, using a CNC-router would be a good option.

Laser cutting

The great thing about using a laser cutter is that the edges of the parts don't need any sanding, and that it's usually faster than using a CNC-router. So this would be the preferred way of making all the parts. However, when starting the project, there was no laser cutter available to me. I would have had to ask a professional company to cut the parts for me and I would have had to pay them a fair amount of money. Because my first goal was to build the entire planetarium by myself, I didn't want to go for this option so I decided to use the CNC-router.

When I was around halfway through the project, my school installed a small laser cutter in the science classroom. Unfortunately, this laser could only cut trough 3mm thick pieces of plywood, and I was already using 9mm thick plates of plywood. This would mean that I would have to make three 3mm thick gears and glue them together to make one 9mm thick gear. This would take about as long as using the CNC-router. However, the CNC-router I had at my disposal wasn't perfect. It didn't have an automated emergency stop for when things would go wrong and there wasn't a connection for the vacuum cleaner. This meant that basically, I constantly had to baby-sit the machine and suck up the sawdust. The laser cutter did have automated emergency stops and it didn't produce any sawdust. This meant that I could just leave the laser running and do some homework or design new parts. This made laser cutting the ideal way of making the gears for this project and it's why you can see that halfway trough the project, the gears have changed from being CNC-milled to being laser-cut.

Step 3: Tools Used

For this project I used the following:

Tools:

  • CNC-router
  • Laser cutter (optional)
  • Drill
  • Sandpaper
  • Screwdriver
  • Paint


Programs:

  • Fusion 360
  • Gearotic motion (optional)
  • Mach 3
  • RDWorks (optional)


Supplies:

  • Birch multiplex
  • Wooden axis
  • Ball bearings
  • Bolts
  • Nuts
  • Rings
  • Small nails
  • Screws

Step 4: Design: Where to Start?

So, I had never used any designing software in my life before and now I wanted to design a complex machine. Where should I start? The first thing I needed to learn is to use the designing software. After trying some random buttons for half an hour, without any success, I decided to start watching some tutorials on YouTube. For anyone who is new with Fusion 360 I would definitely advise watching Lars Christen´s absolute beginner tutorials on YouTube. You can find them here: Tutorial 1, Tutorial 2, Tutorial 3. These are in total a one hour tutorial and if you just watch it and copy what he is doing, you will very quickly get the basic principles of 3D-designing in Fusion 360.

The next thing I decided to do was to design some different basic ways of constructing the planetarium. I did this to get more experience in using Fusion 360 and to test if some different designs that I had in mind would work, and how they would look. Afterwards, I would choose all the parts I liked from the earlier designs and put them all together in the final design.


Some designs and their thoughts

In the second picture you can see one way to support the rotating rings of the planets. The drawback of this design was that the rings would need to have sloped edges, and those are fairly difficult to make. In the third picture you can see another way to support the planets. However in this design, as the planetarium gets larger and larger, the arms to the planets will also get larger. This will cause problems, because the wood will start bending downwards, or it will start to wobble. In the fourth picture you can see one way of making the rings of the planets rotate by using the relative speeds between two planets. However, this design uses 'only' 4 gears and to make the planetarium as precise as I wanted it to be, I would have to use 6 gears. This is just a small selection of the tests I did and as you can see, all the designs have their pros and cons.

Step 5: Design: Design Decisions

Now that I had tested some of the possible ways to build the planetarium, it was time to make choices: What looks do I like the most?; What kind of drive do I want to use?; How do I want to make the planets rotate at different speeds? and many more choices and questions that I had to answer.


Looks

The two most important parts of the planetarium are the gears and the planets. For the planets I simply had two choices:

  1. Use an arm that comes from the middle of the planetarium and that supports the planet directly.
  2. Use a ring, to which the planet is connected, that can be supported and rotated in different ways.

When purely choosing by the looks, I liked the ring idea better. I felt like it would give the planetarium more of a complete feeling, and I knew from my earlier test-designs in Fusion 360 that I would be able to make this work.

Drive

When choosing the drive of this planetarium I had three options:

  1. Using a motor
  2. Using a clock/pendulum mechanism
  3. Using a hand crank

At this stage of the project I had no idea how smooth or stiff the gear to gear interaction was going to be, or if the mechanism would flatter or even get stuck sometimes. So I didn't think using a motor would be a good idea. If the mechanism would get stuck, the motor might break something or even itself.

What I liked about the idea of using a clock or a pendulum mechanism is that I could make the planets move at the speed they have in real life. However, this would mean that It would take a couple of hours to make Mercury move only one degree. This would basically mean that the planetarium would be more like a piece of art, than something cool and interesting to look at.

So the final option was to use a hand crank. This would make sure that the mechanism wouldn't break if it got stuck, because you could just stop turning the crank. It also made it possible for you to really interact with the planetarium. You could make the planets move faster or slower, go in either direction. But most of all, what is cooler than turning a crank and seeing over 70 gears spinning and interacting with one another!?

I decided to go for the hand crank for now. However, I wanted to leave the option open for if I were to change my mind another day. In order to make that possible, I decided that I wanted the driving axis of the planetarium to be very accessible so that I could change some things if I wanted to.

Different rotations

To make the planets move at different speeds I had two options:

  1. Using gears
  2. Using belts with different sized wheels

The advantage of using belts over using gears is that you only need one belt and two wheels to get the planet moving at the correct speed if you alter the wheel size, over which the belt rolls, very precisely. For example, you can't give a gear 54.6 teeth. But you can alter the circumference of a wheel very precisely if you use a lathe. Sadly a lathe wasn't available to me, and I was afraid that the belts might have slipped. That's why I chose to use gears over belts.

Step 6: Design: Inner 4 Planets - Support and Central Axis

So why divide the inner four and the outer four planets into two steps? I did this because of the difference in the way the rotating rings are driven. As can be seen in the second picture, the inner four rings are supported by arms that go to a central axis. This central axis is a collection of four hollow axes that are pushed into each other and can rotate separately from one another. The outer four rings are supported and driven differently.


Support and central axis

So each one of the rings is supported by three arms going to one of the four hollow axes; one for every inner planet. These hollow axes are, as shown in the pictures, driven by gears connected to the bottom of the axis. The section analysis tool from Fusion 360 shows this in more detail. This way when one of the gears turns, the connected hollow axis will turn and thus the corresponding planet, all at the same speed. So if I want the planets to rotate at the correct speed, I just had to make these gears rotate at the speed the planets should.

Step 7: Design: Inner 4 Planets - Gear Combinations

After having designed the way to drive the rings of the planets, I had to design the way I was going to make the gears, and thus the planets, move at the correct speed. To calculate the correct gear ratios I used the built-in calculator of gearotic motion. This gave me the following gear ratios:

Mercury: 10, 50, 50 / 59, 21, 71

Venus: 11, 92, 29 / 63, 53, 79

Earth: 11, 31, 31 / 79, 23, 85

Mars: 12, 74, 19 / 73, 73, 87

This probably just looks like a list of random numbers to you, and so it did to me to in the beginning. But let's take Mercury for example. The first gear that's used for Mercury is a gear with 10 teeth. Connected to this 10 teeth gear is a 59 teeth gear. On the same axis of this 59 teeth gear is a 50 teeth gear. Connected to the 50 teeth gear is a 21 teeth gear. And as you may be able to guess now, on the same axis of the 21 teeth gear is another 50 teeth gear that is connected to a 71 teeth gear. This 71 teeth gear is the final gear and therefore the gear that is connected to the hollow axis. So if everything went correctly, this final gear would turn at the same speed as Mercury: One rotation every 87,969 days.

To test if this gear ratio is correct, I will calculate what speed this gear ratio gives us. Firstly, note that the first gear, the 10 teeth gear, should rotate once every 25 days. This means that the second gear, the 59 teeth gear, rotates once every 147.5 days, because every tooth of the 10 teeth gear counts as 25 / 10 = 2.5 days. And because this 10 teeth gear is connected to the 59 teeth gear, the 59 teeth gear rotates once every 2.5 * 59 = 147.5 days. With this calculation, we can determine the speed at which the 71 teeth gear, and thus Mercury, rotates:

Given this gear ratio, Mercury rotates once every: 25 / 10 * 59 / 50 * 21 / 50 * 71 = 87.969 days. The perfect gear combination!

Step 8: Design: Inner 4 Planets - Gear Placement & the Sun?

Now that I knew what gear combination I was going to use, I still had the problem that there were four different sized gears that all had to rotate once every 25 days. I also wanted all of these gears to be connected to one central gear, that I could connect to the drive. To make things easy, I wanted this central gear to be rotating once every 25 days as well.

The sun

At this point in the designing process, I started wondering if the sun rotates too. After some looking around on the internet I found out that it does; once every 25.05 days. Purely by coincidence, this is almost the same speed of the central gear. By adding an additional axis connected to the central gear, going inside of the hollow axis of Mercury, I could make the sun rotate. This was not part of my initial goal, so I didn't really mind about it not rotating at a very precisely accurate speed.

Gear placement

The next step of the process was choosing where I wanted the gears to be placed. I knew I had one central gear that rotated once every 25 days, I had four gears connected to the hollow axis that rotate at different speeds and I had a ton of gears that connected the central gear to the four gears of the hollow axis to make everything turn at the correct speed. I had to make sure that all of these gears got their own place in the design without taking up too much space and without colliding with other gears. So I grabbed a piece of paper and started drawing out the positions of all the gears. After a lot of erasing and redoing, I settled with a placement that I was happy with. Now it was time to put everything together in Fusion 360 and for the first time, the planetarium was starting to really take shape.

By adding joints to every gear and motion links between the gears, I could see the planetarium work for the very first time. I added a video so you can see it moving for yourself. I'm sorry about the lag, but my computer isn't strong enough to calculate all of the gear-to-gear interactions.

Step 9: Design: Outer 4 Planets - Rings and Drive

So now that the design for the inner four planets was finished, it was time to start working on the outer four. Earlier, I spoke about the fact that the inner four and the outer four planets have a different drive. The outer four rotating rings consist of two layers. The top layer is purely for the looks, the bottom layer is a very large planetary gear, as shown in the second picture. These planetary gears are driven by a very small 8 teeth gear. This makes the planetary gear rotate a few degrees within the time that the 8 teeth gear rotates once. By using this gear interaction, the rotational speed is slowed down significantly. This is very useful, because the outer 4 planets rotate extremely slowly. The rotation speed of the outer four planets are:

  • Jupiter: 4.331,59 days
  • Saturn: 10.759,22 days
  • Uranus: 30.688,5 days
  • Neptune: 60.182 days

I gave the planetary gears a teeth count that is a multiple of 8. This way the rotation of Jupiter is slowed down 24 times, Saturn 29 times, Uranus 34 times and Neptune 39 times. As result, the speeds the 8 teeth gears need to have are the following:

  • Jupiter: 180,4829167 days
  • Saturn: 371,0075862 days
  • Uranus: 902,6029412 days
  • Neptune: 1543,128205 days

Step 10: Design: Outer 4 Planets - Gear Combination and Placement

Once again, I used the gear ratio calculator in gearotic motion. To make sure I didn't have to use super large gears to make the planets rotate slow enough, I started with a speed of one rotation every 100 days. This time gearotic motion's calculator gave me the following gear combinations:

Jupiter: 28, 71 / 92, 39

Saturn: 35, 61 / 92, 39

Uranus: 18, 47 / 92, 83

Neptune: 16, 31 / 89, 86

Once again I had to check if these gear combination were correct, so if you take Jupiter for example, that would give you a speed of one rotation every: 100 / 28 * 92 / 71 * 39 = 180.4828973 days. This is extremely close to the desired 180.4829167 days it would take for one rotation, so the gear combination definitely is correct.


Gear placement

Now that I had the gear combinations I wanted, it was once again time to start placing the gears in the correct places. And once again, I started off with a drawing on paper before making it in Fusion 360, because it's faster to make changes on paper than it is in Fusion 360. In the pictures above you can see the different layers of gears built up, and the inner and outer four planets together. Just some more finishing touches and the design should finally be done.

Step 11: Design: Additional Parts - Remaining Tasks & Supports

Now that the inner and the outer four planets all had their gears in place, there were just a few finishing touches left that I needed to do:

  • The outer 4 rotating rings needed a support
  • The four 8 teeth gears' axes from the outer planets needed an additional support at the top.
  • The inner and outer driving gears needed to be connected to one another
  • The whole mechanism needed a drive


Outer four planets support

After some looking at the design I noticed the outer four rotating rings were just floating. So I started off by making a real life sized drawing of the problem, and started designing a support on paper. I used a trident type of design so I could support all of the rings at once. By using three of these supports, I would be able to support the rings. As shown in the drawing on paper, I used a ball bearing at the bottom of the rings to make sure it didn't fall down, and a ball bearing at the side of the ring to keep it in place.

The 8 teeth axes would also need an additional support. Because otherwise the axes might start bending, which could result in the 8 teeth gear disconnecting from the planetary gear. Once again I started with a drawing on paper and put the design in Fusion 360 when I had finished the sketch.

Step 12: Design: Additional Parts - Final Gears

So only two tasks left. The first one was to connect the driving gears for the inner and outer four planets together. I had to keep in mind that the driving gear for the inner four planets rotates once every 25 days, and the driving gear for the outer four planets rotate once every 100 days. This meant that I had to add another delay. By using a 25 teeth gear that's connected to a 100 teeth gear I got the desired delay.

Now I only had one task remaining: giving the whole mechanism a drive. This was fairly easy. By adding a few gears to the driving gear of the inner four planets, I was able to give myself enough space to add the hand crank. However, the current rotating direction was horizontal, and for the hand crank I wanted it to be vertical. By adding two pin-gears I was able to fix this problem. Now I could add the hand crank.

And finally, after many hours and nights spent designing, the design was finally done! Now it was time to start building. In the final picture, you can see the finished design. You might see that the supports for the rotating rings are missing and so are the supports for the axes. Also, the connection between the central driving gear and the drive is a little bit different. This is because during the building process, I decided to change some things a little bit. However, I didn't add these changes to this design, but to some simplified designs. I did this because my computer had a lot of difficulties processing the big design. By using simplified designs, I made Fusion 360 run a lot smoother.

You can download the main design here: main design

Step 13: Building: the First Gears

Now that the design was finished, it was finally time to start building. I started off making my very first two gears to learn to work with the CNC-router and with the software. After testing these gears, I noticed that the distance between the axes of the gears had to be very precise. Too close meant that the gears would run very stiffly. Too far apart meant that there would be too much leeway. After some tweaking, I finally found the correct distance between the two. As can be seen in the video, the gears run very smoothly.

Of course in the real planetarium, I couldn't just keep drilling holes in random places till the gears ran smoothly. No, I had to find a way to make the location of the axes of the gears adjustable. I did this by making an axis holder. This holder had a slid on either side and in the middle a hole to hold a ball bearing. By using two bolts, -one in either slid- I could move the axis holder to wherever I wanted. Using this method, I would need two axis holders for every axis. This meant that I had to make way over 100 of these things.

Step 14: Building: Inner 4 Planets Mechanism

Now it was time to start building the mechanism of the inner 4 planets. I started off by making all of the gears that were needed. On average, the gears took 20 minutes for the CNC to mill, and another 10 minutes to sand. Because I had to make 31 gears to make the inner four planets move, this process took me a lot of time. I tried to do one or two gears every evening, and after around three weeks of babysitting the CNC, all of the gears were finally done.

The next step was making the wooden planks that would go between the layers of gears. Then I noticed a problem. Some of the planks were too big to be milled at once. Luckily, I found an easy solution to this problem. By dividing the plank into two parts I was able to mill them separately. Then I used a simple clamp and some bolts to lock the two parts together. And after a few days, I had finished the planks as well. Now it was time to put everything together and to test for the very first time. I added a video of the first layer of gears spinning. As you can see, it spins very smoothly, and I was really happy with the result.

The final step was to make the four hollow axes. The ideal method of making these is by using a lathe. But as I mentioned before, this wasn't available to me, so the next best option was to CNC-mill a lot of rings and glue them on top of each other. The top part of the hollow axis had to be a little bit different so I could connect the arms that go to the rings to it.

Step 15: Building: Outer 4 Planets Mechanism & Rings

So just like for the inner four planets, I started off by making all of the gears and after that, the planks. Then I assembled everything together using some spacers to keep the planks at the right distance away from each other. Thanks to the design I made in Fusion 360, this was all very straightforward. It just took a lot of time to CNC-mill everything.

Step 16: Building: Finishing Touches

At this point of the project, I only had one week left to finish it. I still had to make the rings of the planets, the planets themselves, the supports for the outer 4 planets and the drive. So with no time to waste, I started building.

The first things I made were the rings for the inner four planets, and the arms supporting them. Then I started on the rings for the outer four planets, which were really big and contained a big planetary gear. I made these rings out of four parts because otherwise it wouldn't fit in the CNC-router. When the rings were sanded, I glued all of the parts together. Whilst I was doing this, my sister was so kind to paint the planets for me, and I have to say, they are gorgeous. So a very big thank you to her for doing this.

Next up on the to-do list were the supports for the rings. I used large bolts to keep these supports in place and small nails to keep the ball bearings in place. Then I made the supports for the 8 teeth gear axis. I made a little change to the design so I could add an axis holder on the top of it. This way I could adjust the location of the 8 teeth gear to the planetary gear. After some testing, it seemed like these supports worked, so the drive was the last thing left to do. This wasn't too different from all of the other things I had made so far, so this was done within the hour. And now it was time to test.

Step 17: Building: Final Assembly!

After the first test, the mechanism got stuck. There was probably an axis holder in the wrong place, and caused for some gears to lock. So, I decided to disassemble the entire planetarium and reassemble it slowly. Every time I added a new gear, I tested if the mechanism still worked, and tweaked an axis holder where needed. This was a very tedious process and it took me a lot of time. But after a couple of hours, I could finally say that the planetarium was finished!

Step 18: Final Result

After hours upon hours of designing, drawing, CNC-milling, sanding, testing and redesigning, I could finally say that this project was finished. Over half a year earlier I had set myself two goals. The first one was to design and build this planetarium all by myself to test my abilities and see if I would be capable of doing this. And half a year later, there I was, with a fully functional mechanical planetarium built and designed all by myself. The second goal I had set myself, was to show the difference in circulation time of the planets around the sun, and to do this as precisely as possible. I had found the following rotation speeds of the eight planets:

  • Mercury: 87,969 days
  • Venus: 224,701 days
  • Earth: 365,256363004 days
  • Mars: 686,971 days
  • Jupiter: 4.331,59 days
  • Saturn: 10.759,22 days
  • Uranus: 30.688,5 days
  • Neptune: 60.182 days

With the gear combinations I used in my planetarium, I was able to give the planets the following rotation speeds:

  • Mercury: 87,969 days
  • Venus: 224,701002 days
  • Earth: 365,256362 days
  • Mars: 686,971017 days
  • Jupiter: 4.331,58954 days
  • Saturn: 10.759,2037 days
  • Uranus: 30.688,4161 days
  • Neptune: 60.182,6613 days

As you can see, all of the planets in my planetarium rotate at a speed that is nearly the exact same speed as the planets in real life. So I succeeded to give the planets a really precisely accurate rotation speed.

When looking back at this project, I am very happy with the result. I never imagined I would be able to even make the inner four planets rotate, let alone all eight. This was my first real project in wood, and it was very ambitious and complex. I had to learn how to use the designing software (Fusion 360), the CNC-operating software, the gear making program (gearotic motion) and the laser cutter software, all for the very first time. Just building a simple planetarium would have been difficult, but I had also set myself some very challenging goals. I am very proud to be able to say that I have completed both the planetarium and the goals.

If you liked this project, please make sure to vote for me in the contests!