I feel like that gear box is rated in RPM, however, RPH would be more appropriate.
Why do you need that much reduction?
Let’s see, the Vex motors run at up to approx. 100rpm. The sun revolves around the earth at almost exactly 1rpd. (In fact, it is so close that the error is negligible for this application.)
So, 100rpm * 60 * 24 = 144000rpd
That is way too fast for a “Solar Tracker”.
Now based on the photo, Your reduction is: 800.33/1
((84/12)^3)*(84/36))
So now your output shaft is running near 180rpd at full speed.
Using some simple control logic, you now have a very controllable solar tracking system.
May I ask what you are using to sense the position of the sun?
Nick, I told you to keep our arm gearbox a secret! 
I didn’t get the memo. I guess we better tell them the amazing feat of our arm working with the sun to destroy the competition…
The idea was to make it “follow” the sun, rather than track it and adjust accordingly. This gearbox relies on the VEX motor shown to run at 5 rotations per minute. Will it? Who knows. It was never built to fully function, just to prove the concept. However, I would love to fine tune it and make it work next September, when class resumes.
This project was for a final project for my robotics class.
-Nick
Honestly, I couldn’t say if you could get it to run reliably at 5 RPM or not.
If you are using a Vex controller, you “should” be able to. There are approximately 120 steps for forward and the same for reverse. So, that gives about .833 rmp per step. Theoretically it will work. Although, one more stage of reduction will put the motor in a much more controllable range.:rolleyes:
Put an encoder on, and it will spin 5RPM for sure.
For a solar tracker running at such a slow output speed, you could probably size the gearbox based on the load (whatever you are mounting that looks at the sun, a PV array?), not the speed. You can pulse the motor at time intervals to decrease the effective input speed (turn it on for a few seconds every 10 -15 seconds) and it will be more than adequate. 360 degrees per day is 0.07 mrad per second. The sun is 9.5 mrad in diameter, so it takes over 2 minutes to move across a focused point along the centerline. Commercial heliostat trackers send position commands every 10 seconds, and they require much higher accuracy than a CPV tracker.
Just something that made me think… Doesnt the Earth revolve around the Sun? I think that you meant to say that the “Earth rotates around its axis at a rate of almost exactly 1 rpd.” Not trying to say that you are wrong, just that your wording could throw some people off.
You are 100% correct. I was hoping that most people reading this could understand the difference and would mentally be able to negotiate the reality. (Oh man, that sounds a bit sketchy, doesn’t it?).
To be completely correct, the Earth does rotate around the Sun and it also rotates on it’s axis. Do either of these facts change the calculation of what the gearbox needs to have in the way of reduction? No.
Thanks for pointing out my error though, you are correct.
As Dennis Prager says, “I prefer clarity over agreement”.
Billbo - Don’t cave in so quickly 
The motion(s) can be described from any arbitrarily chosen reference point; so the Sun, along with the rest of the universe, does revolve around the Earth.
Also, if you want to describe the Earth-Sun situation as a two body system (and ignore all the other influences on their relative motions) you will often (but certanly not always) choose to say that the two bodies move relative to a point that is in-between their centers-of-gravity, not around the center-of-gravity of the larger mass.
So, out of the choices so far, I think the original statement involved the fewest approximations.
This opinion, when combined with $1.50, can be exchanged for a soft drink from the nearby machines. 
Blake
Blake,
So what you are telling me is that what I have always believed is actually true and can be proved mathematically. That being that the Universe, does in fact, revolve around me!
Wow, I now have a new friend. Thanks Blake!
Just to put this in perspective though: On a scale where the Sun is the size of a basketball, the center of mass of the Earth/Sun system would be approximately 3 thousandths of an inch from the center of the basketball.
~