\(\begin{equation}
\theta_n = \{
\begin{array}{cc}
\theta_{ori},\; n \; is \; odd\\
\theta_{free},\; n \; is \; even\\
\end{array}
\end{equation}\)
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 \(\vec{p_{4N}}\):