Pocket Planetarium

Part II

December 2022

At last, the exciting conclusion to this project! It's been a long time coming. The first part can be found here - I reccommend reading it first, obviously.

But first, the preamble: it's taken me more than 6 months since my "midway point" to wrap up this project. There are a number of reasons for that, but the biggest has simply been that I had to step away from it for several months. I did this to protect my enthusiasm for this project, and hopefully, the quality of the outcome. I had become frustrated, and rather than continuing to work with the frustration, I decided to come back to the project when I was excited to work on it once again.

In hindsight, this was a great decision.

Quick Note: After doing some belated research, I've discovered that "planetarium" isn't the right term to describe this project. It could be more correctly be called an orrery (a physical model of celestial bodies) or, to be even more exact and pedantic, it is a tellurion - that is, an orrery specifically depicting the 3-body system of the Sun, the Earth, and the Moon.

Now you (and I) know!

Part 1: The Sad Prototype

Way back in July 2022, I was flying on this project. I had completed a prototype of the main gear arm for the build, and was already working on plans for the next prototype.

The main problem I was hoping to address with the new prototype (let's call it V3) was the ability to actually drive the gearchain. With V2, the little stepper motor I used wasn't really able to drive a gearchain with such a huge "gear up", which means the model didn't turn and was essential useless. The whole point is to show the rotations of the Earth and Moon.

So I devised some strategies for getting things into motion. Firstly, I tried to address friction in the system. Any amount of friction anywhere in the gearchain will increase the required motor torque (make it harder for the motor to turn). So, minimizing friction wherever possible is a pretty important consideration.

I increased each axle diameter to 4 mm, with dedicated M4 bearings for each. I had observed a sort of "locking up" of the gears in V2, and reasoned that the larger axles would be less affected by small dimensional inaccuracies in the system, thus avoiding the locking up.

I also increased the tooth size (and diameter) of my gears, and began 3D printing them. This also allowed me to customize their dimensions and characteristics in ways that were impossible with the small hobby gears I had used for V2. I reasoned that the larger gears I was printing would also help address the "locking up" issue.

Finally, I bought a proper NEMA stepper motor, which I hoped would give me enough increased torque to run the new prototype comfortably.

So, I set about the work. I spent hours in CAD, modelling all the custom components and gears I needed. I spent days and days printing everything. I got a bunch of hardware in preparation for assembling the thing. I was hoping that this prototype would put me close to finishing the project, and with some tweaking, I would be able to call it complete.

Well, it didn't turn out quite as nicely as that. V3 was, well, worse than V2. The gears were locked up and hard to turn by hand. Even my fancy new stepper motor didn't stand a chance of turning the thing. And, worst of all, I couldn't figure out why! Even if I had the gumption to continue working, I really didn't have any idea of which direction I needed to go now.

So, frustrated at the lack of payoff of so many hours of passionate work, I boxed it all up, put it on a shelf, and resolved to come back to finish it with a clear head.

Part 2: Return of the Gears

Months later, I came back to the project. Now, I had some fresh ideas, and a new desire to solve my friction problem. I was going to be careful, though, and I wanted to avoid putting too many hours of work in before verifying results. So, I first distilled the problem down to 2 gears.

The first design update was to incorporate bearings into the gears themselves, rather than the arms. This wasn't going to directly address reducing friction, but it did improve ease of assembly for the model, and helped me avoid "pinching" the gears two tightly in their supports, which definitely would be a source of friction.

The real game-winning innovation, though, was to start playing with the meshing distance between my gears.

Quick Note: Despite my degree in mechanical engineering, I'm no gear expert, so take the following statements with a *few* grains of salt.

When designing gear chains, there is an optimal distance at which one gear should mesh with another. It is at this distance that the gear teeth are designed to mesh together and transfer power from one gear to the next. Space your gears too far apart, and the teeth won't efficiently interact with each other, and may even break off.

This distance is different for each size of gear. Handily, though, it is one of the major defining characteristics of any gear: the pitch diameter. Basically, for optimal meshing, your gears should be spaced so that the pitch circles of your gears are tangent to one another. It gets more complicated than that, as you can tell from the diagram I've grabbed below, but that's the basic idea.

So how does this apply to my friction problem?

First, I had been observing that the gears I was 3D printing weren't actually perfect. No manufacturing process ever produces completely dimensionally accurate parts; mine were coming out a bit squashed at the bottom, due to a quirk of my 3D printer that would too long to explain. I could and did apply some tricks to improve the gears I was printing, but I was never going to get to the sub-millimeter accuracy I was looking for.

The trickle-down effect of this is that my gears were larger than expected at certain points -- that is, their pitch diameters could be larger than the precise values I had designed for, which could easily cause the gears to bind up.

Secondly, I realized that there was no reason to hold my design to the "optimal" gear meshing distances: by spacing my gears out a bit further, I could give my design some wiggle room for slightly mis-sized gears. Perfect! The downsides, increased backlash and increased pressure on gear teeth, didn't actually concern me. The system would only ever be driven one way, so backlash was a non-issue. I also reasoned that I wouldn't be able to put enough torque into the system to damage the gears anyway, once the friction issue had been solved.

The results were obvious: more spacing allowed the gears to spin marvelously smoothly. After some tinkering to find the ideal spacing adjustment, I set back to the task of redesigning, reprinting, and assembling a new and improved version V4.

Part 3: Final Design

First, I recreated the Earth Arm gearchain with a simple arm to support it. Unlike previous attempts, I was easily able to spin the Earth axis with finger strength at the input gear. In fact, this was so satisfying that the prototype basically became my fidget spinner for a week or two.

Next, I once again decided on a change of motors. While stepper motors are great for certain applications, this really wasn't a worthwhile use-case for one, and working with a DC motor instead would be much simpler. So, I traded in for one.

With everything running smoothly, I had at last arrived at the final engineering consideration: how to accomplish the moon's orbit.

One complicated bit with the moon is that it rotates about the same axis as the Earth's spin (at least in my heliocentric model). So, I had to design a system that would rotate around the same axis that I had just spent months getting to spin very fast, but get the new attachment to spin at a different rate. I hope that makes sense.

My idea was to branch off from the main gearchain, using the rotation of one of the intermediate gears to drive a new, parallel gearchain, culminating in a free-spinning gear on the Earth axis. Up to this point, all my gears were "free-spinning". That is, the axles were fixed in place and non-rotating, while the gears (with embedded bearings) were free to spin on those fixed axles.

The free-spinning design helped with assembly and positioning of all my components, but I would need to modify it to address this new level of complexity brought by the moon. This required the careful design of two new "custom bearing axles", with bearings embedded instead into the support arms, free-floating axles, and a combination of gears either affixed to the axle, or free to spin around it. After that, it was just a matter of printing and assembly.

Excited to see it all spinning, I whipped up a quick enclosure for the motor and switch, and a....er..... functional counterweight, artisanally crafted from a handful of screws and a plastic flowerpot.

Part 4: Putting it all Together

It's aliiiive! Finally, the functional aspects of my orrery were working! The earth arm spins, the moon gear wheels by, and the Earth axis whizzes by. It was coming together -- now, it was time to make it look good, so I set about the many small aesthetic tasks.

I replaced the counterweight with a square of iron weights that looks a bit better, at least.

I made a more permanent base and motor housing from a can I found at Daiso. I'd like to go back and paint the can with some astral scene, but that will have to wait for when I'm feeling bored and in need of a project.

For the Sun, I found a clear plastic ornament, and painted it to look vaguely sun-like. I also had the bright idea to use an electric tea light to illuminate the Sun from inside, but I accidentally got color-changing RGB tea lights. While trippy, it wasn't really the look I was going for, so I replaced the RGB LED with a fun noodle-type warm LED instead.

In order to diffuse the light, I stuffed the Sun with some packaging bubbles, and printed a small piece to mount the Sun to it's axis.

At this point, I did actually stumble upon one last engineering challenge: how to spin the Earth without it wobbling like crazy. The Earth spins very fast in my model, and the complexities of design in the axle means it isn't quite as well-supported as I would like. So, the Earth axis is a bit unstable: any imbalance would cause major, Earth-shattering wobbles. I designed a set-screw piece to fine-tune the position of the earth, and a spinning counterbalance to hang from the bottom of the axle. In conjunction with some well-placed glue, I was able to achieve fairly comfortable, non-nauseating Earth spin.

For the Earth itself, I found a printable model online, with texture for the landmasses. I painted it, going for a realistic-ish style with clouds.

For the Moon, well, I kind of phoned it in, to be honest. I made a lumpy sphere-like shape from Sculpey clay, and painted it gray. This will be the first thing to go if I ever make an improved orrery, but I was ready to call it done at this point.

And speaking of done, that's it! I'm ready to call it complete, at last. Enjoy some beauty shots -- I'm going for a beer.

I did have some trouble getting my phone camera to just expose normally. It kept trying to adjust the focus of the Sun (when it was lit from inside), resulting in the weird dark fringes you see. But, I did get a glowing review from the cat!

It feels great to put a bow on this. When I was wrapping up, I finally did a bit of benchmarking to see the kinds of orreries out there on the internet, and was blown away, particularly by this one at EngineeringCommons.org. It's absolutely mind-boggling and inspiring to see the limits that people have pursued these ideas to. For now, I'm proud of my first foray into the art of orrery.

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