Move mechanical arm with mouse

So, I have made an arm with two joints that I can bend with the arrow keys. The arm is attached to my game character so I can move him. The problem is that it's really difficult and I would like to be able to more the arm with the mouse, i.e. the tip of it reaches towards the mouse. I do not want the arm to move to the mouse but simply restrict the mouse movement to the reach length of the arm so the entire character doesn't fly to the mouse position.

Any ideas? Please let me know if my explanation is vague.

Oh yeah, I'm using javascript at the moment.