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\left(\begin{array}{ccc}-\cos\!\left(\theta_{r,1}+
\psi_b\right)&-\sin\!\left(\theta_{r,1}+
\psi_b\right)&x_{b}-\mathrm{L_1}\,
\cos\!\left(\theta_{r,1}+\psi_b\right)+\frac{L_b\,
\cos\!\left(\psi_b\right)}{2}\\\sin\!\left(\theta_{r,1}
+\psi_b\right)&-\cos\!\left(\theta_{r,1}+
\psi_b\right)&y_{b}+\mathrm{L_1}\,
\sin\!\left(\theta_{r,1}+\psi_b\right)-\frac{L_b\,
\sin\!\left(\psi_b\right)}{2}\\0&0&1
\end{array}\right)
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\left(\begin{array}{ccc} - \cos\!\left(\theta_{r,1} + \psi_b\right) & - \sin\!\left(\theta_{r,1} + \psi_b\right) & x_{b} - \mathrm{L_1}\, \cos\!\left(\theta_{r,1} + \psi_b\right) + \frac{L_b\, \cos\!\left(\psi_b\right)}{2}\\ \sin\!\left(\theta_{r,1} + \psi_b\right) & - \cos\!\left(\theta_{r,1} + \psi_b\right) & y_{b} + \mathrm{L_1}\, \sin\!\left(\theta_{r,1} + \psi_b\right) - \frac{L_b\, \sin\!\left(\psi_b\right)}{2}\\ 0 & 0 & 1 \end{array}\right)