[Alan Anderson]

If you want the arm to move autonomously, you most certainly need to use sensors.

The simplest way to do it is to use a potentiometer to give an indication of where the arm is pointing, and drive the arm's motor in the appropriate direction until the feedback from the pot matches what you want it to be. If the arm has significant inertia or presents a dynamic load due to weight, you'll want to get fancier and use a PID control system (look it up).