\(\begin{equation} \theta_n = \{ \begin{array}{cc} \theta_{ori},\; n \; is \; odd\\ \theta_{free},\; n \; is \; even\\ \end{array} \end{equation}\)
Finally, positions can be obtained as a function of \(\theta_n\) by substituting (1-5) and (10-14).
 
For 2N-module structure, bending angle \(\phi\) can be calculated from end-tip position \(\vec{p_{4N}}\):