Global Structure

Global Matrix


$$ \begin{bmatrix} R_1 \D \\ R_2 \D \\ R_3 \D \\ R_4 \D \\ R_5 \D \\ R_6 \D \\ \end{bmatrix} = \begin{bmatrix} \color{red}{k_1} + 0 & \color{red}{0} + 0 & \color{red}{-k_1} & \color{red}{0} & 0 & 0 \D \\ \color{red}{0} + 0 & \color{red}{0} + k_2 & \color{red}{0} & \color{red}{0} & 0 & -k_2 \D \\ \color{red}{-k_1} & \color{red}{0} & \color{red}{k_1} + \frac{3}{4}k_3 & \color{red}{0} - \frac{\sqrt{3}}{4}k_3 & -\frac{3}{4}k_3 & \frac{\sqrt{3}}{4}k_3 \D \\ \color{red}{0} & \color{red}{0} & \color{red}{0} -\frac{\sqrt{3}}{4}k_3 & \color{red}{0} + \frac{1}{4}k_3 & \frac{\sqrt{3}}{4}k_3 & -\frac{1}{4}k_3 \D \\ 0 & 0 & -\frac{3}{4}k_3 & \frac{\sqrt{3}}{4}k_3 & 0 + \frac{3}{4}k_3 & 0 -\frac{\sqrt{3}}{4}k_3 \D \\ 0 & -k_2 & \frac{\sqrt{3}}{4}k_3 & -\frac{1}{4}k_3 & 0 -\frac{\sqrt{3}}{4}k_3 & k_2 + \frac{1}{4}k_3 \D \\ \end{bmatrix} \begin{bmatrix} r_1 \D \\ r_2 \D \\ r_3 \D \\ r_4 \D \\ r_5 \D \\ r_6 \D\\ \end{bmatrix} $$ $$ \begin{bmatrix} R_1 \D \\ R_2 \D \\ R_3 \D \\ R_4 \D \\ R_5 \D \\ R_6 \D \\ \end{bmatrix} = \begin{bmatrix} k_1 \color{red}{+ 0} & 0 \color{red}{+ 0} & -k_1 & 0 & \color{red}{0} & \color{red}{0} \D \\ 0 \color{red}{+ 0} & 0 \color{red}{+ k_2} & 0 & 0 & \color{red}{0} & \color{red}{-k_2} \D \\ -k_1 & 0 & k_1 + \frac{3}{4}k_3 & 0 - \frac{\sqrt{3}}{4}k_3 & -\frac{3}{4}k_3 & \frac{\sqrt{3}}{4}k_3 \D \\ 0 & 0 & 0 -\frac{\sqrt{3}}{4}k_3 & 0 + \frac{1}{4}k_3 & \frac{\sqrt{3}}{4}k_3 & -\frac{1}{4}k_3 \D \\ \color{red}{0} & \color{red}{0} & -\frac{3}{4}k_3 & \frac{\sqrt{3}}{4}k_3 & \color{red}{0} + \frac{3}{4}k_3 & \color{red}{0} -\frac{\sqrt{3}}{4}k_3 \D \\ \color{red}{0} & \color{red}{-k_2} & \frac{\sqrt{3}}{4}k_3 & -\frac{1}{4}k_3 & \color{red}{0} -\frac{\sqrt{3}}{4}k_3 & \color{red}{k_2} + \frac{1}{4}k_3 \D \\ \end{bmatrix} \begin{bmatrix} r_1 \D \\ r_2 \D \\ r_3 \D \\ r_4 \D \\ r_5 \D \\ r_6 \D\\ \end{bmatrix} $$ $$ \begin{bmatrix} R_1 \D \\ R_2 \D \\ R_3 \D \\ R_4 \D \\ R_5 \D \\ R_6 \D \\ \end{bmatrix} = \begin{bmatrix} k_1 + 0 & 0 + 0 & -k_1 & 0 & 0 & 0 \D \\ 0 + 0 & 0 + k_2 & 0 & 0 & 0 & -k_2 \D \\ -k_1 & 0 & k_1 \color{red}{+ \frac{3}{4}k_3} & 0 \color{red}{-\frac{\sqrt{3}}{4}k_3} & \color{red}{-\frac{3}{4}k_3} & \color{red}{\frac{\sqrt{3}}{4}k_3} \D \\ 0 & 0 & 0 \color{red}{-\frac{\sqrt{3}}{4}k_3} & 0 \color{red}{+ \frac{1}{4}k_3} & \color{red}{\frac{\sqrt{3}}{4}k_3} & \color{red}{-\frac{1}{4}k_3} \D \\ 0 & 0 & \color{red}{-\frac{3}{4}k_3} & \color{red}{\frac{\sqrt{3}}{4}k_3} & 0 \color{red}{+ \frac{3}{4}k_3} & 0 \color{red}{-\frac{\sqrt{3}}{4}k_3} \D \\ 0 & -k_2 & \color{red}{\frac{\sqrt{3}}{4}k_3} & \color{red}{-\frac{1}{4}k_3} & 0 \color{red}{-\frac{\sqrt{3}}{4}k_3} & k_2 \color{red}{+ \frac{1}{4}k_3} \D \\ \end{bmatrix} \begin{bmatrix} r_1 \D \\ r_2 \D \\ r_3 \D \\ r_4 \D \\ r_5 \D \\ r_6 \D\\ \end{bmatrix} $$

Local Bar

Local Matrix

$$ \begin{bmatrix} P_1 \D \\ P_2 \D \\ P_3 \D \\ P_4 \D \end{bmatrix} = k_1 \begin{bmatrix} 1 & 0 & -1 & 0 \D \\ 0 & 0 & 0 & 0 \D \\ -1 & 0 & 1 & 0 \D \\ 0 & 0 & 0 & 0 \D \\ \end{bmatrix} \begin{bmatrix} \rho_1 \D \\ \rho_2 \D \\ \rho_3 \D \\ \rho_4 \D \end{bmatrix} $$ $$ \begin{bmatrix} P_1 \D \\ P_2 \D \\ P_3 \D \\ P_4 \D \end{bmatrix} = k_2 \begin{bmatrix} 0 & 0 & 0 & 0 \D \\ 0 & 1 & 0 & -1 \D \\ 0 & 0 & 0 & 0 \D \\ 0 & -1 & 0 & 1 \D \\ \end{bmatrix} \begin{bmatrix} \rho_1 \D \\ \rho_2 \D \\ \rho_3 \D \\ \rho_4 \D \end{bmatrix} $$ $$ \begin{bmatrix} P_1 \D \\ P_2 \D \\ P_3 \D \\ P_4 \D \end{bmatrix} = k_3 \begin{bmatrix} \frac{3}{4} & -\frac{\sqrt{3}}{4} & -\frac{3}{4} & \frac{\sqrt{3}}{4} \D \\ -\frac{\sqrt{3}}{4} & \frac{1}{4} & \frac{\sqrt{3}}{4} & -\frac{1}{4} \D \\ -\frac{3}{4} & \frac{\sqrt{3}}{4} & \frac{3}{4} & -\frac{\sqrt{3}}{4} \D \\ \frac{\sqrt{3}}{4} & -\frac{1}{4} & -\frac{\sqrt{3}}{4} & \frac{1}{4} \D \\ \end{bmatrix} \begin{bmatrix} \rho_1 \D \\ \rho_2 \D \\ \rho_3 \D \\ \rho_4 \D \end{bmatrix} $$

Mapping

$$ \scriptsize \begin{array}{c|c} \textbf{Local} & \textbf{Global} \\ \hline 1 & 1 \\ 2 & 2 \\ 3 & 3 \\ 4 & 4 \end{array} $$ $$ \scriptsize \begin{array}{cc} \textbf{Bar Angle} & 0^{\circ} \\ \end{array} $$ $$ \scriptsize \begin{array}{c|c} \textbf{Local} & \textbf{Global} \\ \hline 1 & 1 \\ 2 & 2 \\ 3 & 5 \\ 4 & 6 \end{array} $$ $$ \scriptsize \begin{array}{cc} \textbf{Bar Angle} & 90^{\circ} \\ \end{array} $$ $$ \scriptsize \begin{array}{c|c} \textbf{Local} & \textbf{Global} \\ \hline 1 & 3 \\ 2 & 4 \\ 3 & 5 \\ 4 & 6 \end{array} $$ $$ \scriptsize \begin{array}{cc} \textbf{Bar Angle} & 150^{\circ} \\ \end{array} $$