\[\begin{equation}
\vec{p_{4n-3}}=
\vec{p_{4n-4}}+
\left[
\begin{array}{cc}
h_1 \cos{\beta_{2n-1}}\\
h_1 \sin{\beta_{2n-1}}
\end{array}
\right]
\end{equation}\]
\[\begin{equation}
\vec{p_{4n-2}}=
\vec{p_{4n-3}}+
\left[
\begin{array}{cc}
L \cos{\alpha_{2n-1}}\\
L \sin{\alpha_{2n-1}}
\end{array}
\right]
\end{equation}\]
\[\begin{equation}
\vec{p_{4n-1}}=
\vec{p_{4n-2}}+
\left[
\begin{array}{cc}
h_2 \cos{\beta_{2n}}\\
h_2 \sin{\beta_{2n}}
\end{array}
\right]
\end{equation}\]
\[\begin{equation}
\vec{p_{4n}}=
\vec{p_{4n-1}}+
\left[
\begin{array}{cc}
L \cos{\alpha_{2n}}\\
L \sin{\alpha_{2n}}
\end{array}
\right]
\end{equation}\]
For angles \(\alpha_n\) and \(\beta_n\), following relationships can be established:
For n is odd,
\(\begin{equation}
\alpha_{n+1}-\alpha_n = \{
\begin{array}{cc}
2 \theta_n + \pi,\; for \; \alpha_n<0 \;and\; \alpha_{n+1}>0\\
2 \theta_n - \pi,\; else\\
\end{array}
\end{equation}\)
\(\begin{equation}
\beta_{n+1}= \{
\begin{array}{cc}
-\frac{\pi}{2} + \theta_n + \alpha_n + 2 \pi,\; for \; \alpha_n<0 \;and\; \beta_{n+1}>0\\
-\frac{\pi}{2} + \theta_n + \alpha_n,\; else\\
\end{array}
\end{equation}\)
For n is even,