I have been thinking to a simpler way to solve your problem, and I came to the conclusion that you should use XY coordinates to trace the point on the arc where your arm moves. Your accellerometer gives you the sin value of the move than you read position zero= X0Y0 and position one = X1Y1 after the move, and so you have the possibility to linearise your data.

You can calculate the XY coordinate with this equation:

X= R * Sin
Y= R * sqr(1-Sin^2)

Where:
R = lenght of your moving arm
Sin = value given by accellerometer.

This is a much simpler way to handle this data with PBP.

Al.