Gearboxes are required for mechanized things in game, and they look pretty damn complicated to build especially when your only guide of building one is a weird combination like "Gearbox A250-A350 D140-200 G460-560". Fortunately Balthazarr was free to give me a tutorial at the zFree laboratory on how all this works. First thing to know is that all Gearboxes start at A1 and that position always spins at 100%. By using a variety of gears, you can manipulate the speed of the next gear as shown here:
"Same, faster, slower."
You also need to take into consideration the expenses of building the gears you use - simply put bigger gears are more costly to build. Fortunately all the math for the ratios is already done on the wiki so all you need to do is look through the range you are interested (as defined by the requirement, so A has a range of 250-350) to see which sets will be the cheapest to build. The 5/3 numbers on the side there are the number of teeth per gear to achieve that speed with five being medium and three being small.
For this range, the cheapest to build would be A333 D167 G463.
This means that we want A8 rotating at 333%, D8 rotating at 167% and G8 rotating at 463%. To get to that top line, you simply need to make a snake of gears up to the desired spot like so:
Since the gears are all the same size, D8 is spinning at 100%.
That's nowhere near strong enough, which is where using the 5/3 gear combos help to boost it up. Also, the gears can be multi-levelled so you can have a big one right above a small one or one on top of a "spacer" for example. Ultimately the final box of A333 D167 G463, which obeys the initial range of "Gearbox A250-A350 D140-200 G460-560", looks like this:
Thanks for the lesson Balthazarr! :)
Just FYI - It's worse IRL. :P