I am Fred - My limbs are proportional to my head. They articulate via a series of ball joints such that the end of a limb is defined by the path of a circle whose radius, r, is the length of the limb.
Theta represents the angle at the origin joint (xo,yo). Given SOH CAH TOA, (x',y') positions on the circular arc are calculated by the equations:
x' = xo + r cos(theta)
y' = yo + r sin(theta)
z' = zo + r cos(Ztheta)
In 2D space Ztheta = 90