[dlsmith]

I would suggest trying the accelerometer and see how well it works out, but without any integrating etc. To calculate the angle just use atan2( y, x ) where the two accelerometer axes are in the plane of rotation. Turns out that gravity is a very well-defined "down" vector that will move along the axes. Of course this will only work accurately when the arm is relatively stationary (not experiencing other accelerations relative to g) so you might need to move the arm more slowly when taking measurements. I'll be curious to hear if it works.