Stepper motors, plotters, millers and Arduino??? How does it work!?

So I would love to have a little help here understanding how these arduino drawing, milling, and plotting contraptions work. So I know that the stepper motor is for precision, but when you hook it up to gears and stuff, how does arduino know where the stepper motor is if its like on a track or gear? Say you have a stepper motor connected to a corkscrew gear. Some corkscrew gears may be large and others may be small. How does Arduino know where the motor is on that plane?? How do you import pictures or 3D objects to Arduino to make it draw/plot/mill?

Thanks!

Every system has to be zeroed out or set up with limit switches to zero itself out. As you said the stepper motors are precise. You give them a pulse and then move a step. That step is a small rotation that only moves a certain number of degrees. Knowing that the areduino keeps count of the number of steps taken. How that step translates into the movement of your platform depends on the kind of gearing you have attached to the motor.

Fortunatly you don't have to fully understand how it all works. There are plenty of controller boards out there that interface with the arduino to control the motors and plenty of great sketches for the arduino that are already programmed for you. You just have to run through a bunch of test prints to get all the parameters tweaked. There is always a good deal of calibration needed when setting these things up for the first time. Constant calibration is needed really. If you want good clean and accurate products.

There is also computer programs that will take your cad files and pictures and breaks them down into the machine code or G-code. Creating a list of steps for the system to draw/make the picture/object.

If you want to learn more look into the Reprap project. Particularly the wiki. Lots of great information there for building your own 3D printer.
http://www.reprap.org/wiki/RepRap_Options

It keeps track of all the steps sent to it, if you load it too much, and loses sync, you're stuffed. You have to calibrate your machine by stepping the motor a few steps and measuring the movement. Turning a model into instructions for the cutter is very complicated/