Figure 13.

Root-mean-square difference between the PDF of the hinge example and that of the ball joint example. e(χ) denotes the root-mean-square difference between the PDF of the hinge case and that of the ball joint case. It is defined as $e(\chi )=\sqrt{{\int }_0^1{(f_{\mathit{hinge}}(a,\chi )-f_{\mathit{ball}}(a,\chi ))}^{2}da}$. In the case of the rigid chain with a joint in the middle (χ=∞, which is not shown on the plot), e(χ=∞)≈0.55.