Check out the interfacing of Processing with an Arduino. Your robotic arm will need driver/control hardware between it and the host PC. There is quite a bit of information about controlling precise movement of servo or stepper motors with Processing and an Arduino microprocessor board. A setup with your Processing application on a PC, communicating with an Arduino, instructing motor drivers could run a suitably-designed robotic arm. We've done quite a bit of motor control in this way, though no robotic arm - but the principles are fundamentally the same.

Thank you for the reply. I guess most industrial robotic arms have their own firmware/hardware protocols for communicating with the computer. I'm just wondering how easy it would be to hack this sort of system so that a Processing/Arduino setup could be hooked up to it. 

You might want to check out this project by Stephan Thiel:

maybe this post will help you