Pocket Planetarium

I recently got an Arduino, and I've been thinking and looking for a good project to apply it to. I haven't done much electronics tinkering, outside of some deep dives into 3D printer maintenance, but I'm excited to tinker with the capabilities of a controller like the Arduino. I think it will be a cool bridge between writing code and building real-world projects, both of which I enjoy greatly.

The first good idea that came to mind was this: a planetarium model, with the Earth, moon, and perhaps even more astronomical bodies rotating around the central Sun. I took an immediate liking to the idea of this project, for several reasons.

First, I think the end product will be cool and non-trivial. It will be cool and uniquely mine, something I will happily play around with and proudly put on a shelf to display.

Let the analysis begin! In order to begin thinking about the motion of everything, I started sketching.

I'm going to adopt a heliocentric frame of reference for my model, where the Sun is static and everything else rotates around its axis. As astronomers have known for centuries, this results in the simplest motion of everything else.

So the obvious first move is to establish a central axis, where the Sun will rest. Now, of course I know that the Earth orbits around the Sun every 365 days or so, but I don't actually know if or how fast the Sun rotates on its orbit from this frame of reference. I kind of want to do this project with as little help from outside resources as possible, so for now, let's ignore and come back to this question later -- I'll assume the Sun is completely static in our frame of reference for simplicity.

Next up is the Earth; this rotates, or course, about the Sun. In order to accomplish this, I will design an arm, branching off from the central axis, that holds the Earth and has some rotation speed driven by a motor. Let's call this arm the Earth Arm.

At the end of the Earth Arm is (you guessed it) the Earth. This rotates on it's own axis (let's say the Earth axis). Additionally, we know that this rotation is 365 times faster than the rotation speed of the Earth Arm itself. That is, from our stationary frame of reference, the Earth will spin on its axis 365 times before it revolves completely around the Sun. (Additionally, Earth's axis is slanted, giving rise to seasons etc. But I've chosen to ignore this for now in order to simplify my initial model).

In order to accomplish this 365:1 rotational speed ratio, my mind immediately jumps to a gear chain, as the tried-and-true method for reducing and controlling rotations. More on that in a bit.

Alright, let's get out of the theoretical realm and into some design.

The first significant design hurdle is to rotate an arm about a central axis, while also spinning an Earth axis at the end of it at some different speed. This would be my initial design test.

My first design choice here was to use pulleys to transfer motion from the motor. For the final iteration I will most likely use gears, but pulleys have some distinct advantages for testing.

First, I don't have to precisely place the axes of my spinning elements, in order for gear teeth to engage; I can simply place the pulleys some distance apart, and connect them with a flexible rubber band to transfer power. But perhaps more importantly, I don't have any gears, or the immediate capability to make decent ones. Pulleys, on the other hand, are just discs with grooves around them; I can quickly and easily 3D-print serviceable pulleys at whatever diameter I want.

For the arm, I designed a simple piece, with an insert for a bearing at the end of it. This arm would mate with and be driven by a small stepper motor, which came in the Arduino kit I ordered.

The initial pulley (1) I designed to be stationary, mounted directly to the baseplate of my assembly. As the Earth Arm rotates around this pulley (1), the relative rotation of the stationary pulley (1) will drive rotation in a second pulley (2) mounted to the end of the arm. (Hopefully that sentence isn't too much of a tangle).

First off, the DC motor was entirely unable to move the arm, so I replaced with a new, NEMA 17 stepper motor that would give me more torque. The new motor can successfully drive the arm, but the motion it produces is decidedly.... jerky. You can see this in the image to the above right.

Now, there are some options to try to eliminate this jerkiness. The issue arises from the fact that steppers rotate in discrete "steps" …hence the name. Rather than rotate continuously, each current cycle drives the axle forward by some set amount (in my case, 1.8 degrees), resulting in non-continuous output rotation.

So, I could try sourcing another stepper motor, one with more steps per revolution: this would mean that each "step" of the motor is a smaller rotation, giving the appearance of smoother rotation. This is kind of analogous to increasing framerate of a video to display "smoother" motion.

However, there is another method, made possible by the motor driver I am using, that accomplishes the same thing: microstepping.

To be honest, I'm not exactly sure of the science behind how it works. But by utilizing it, you can spin the motor in half-step increments, or quarter-steps, or sixteenth-steps, effectively multiplying the discrete steps in each revolution and giving the same smooth motion!

In practice, I found that utilizing microstepping entailed decreased torque: while I could spin the arm more smoothly, I could no longer actually drive the gearchain.