Is this Arduino controlled machine possible

Hi, This sounds basically workable, including a LOT of work from you...

You won't find any shield that will do all you need; think about getting separate Stepper and power control parts, and possibly opto-isolating them from the Arduino.

You;ll have a lot of connections and cabling. Consider a sensor shield like these:
http://arduino-info.wikispaces.com/SensorShield

These are passive, but bring all connections out to easy-to-connect 3-pin connectors. There is also a Mega version (scroll down)..

What are the details of the steppers: power levels etc...??