Remove two figures
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@ -1167,66 +1167,15 @@ exportFig('figs/test_joints_bend_stiff_hist.pdf', 'width', 'half', 'height', 'no
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#+end_subfigure
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#+end_subfigure
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#+end_figure
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#+end_figure
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#+begin_src matlab :exports results :results value table replace :tangle no :post addhdr(*this*)
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data2orgtable([kRx; kRy]', {'1','2','3','4','5','6','7','8','9','10','11','12','13','14','15','16'}, {'$R_{R_x}$ [Nm/rad]', '$k_{R_y}$ [Nm/rad]'}, ' %.1f ');
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#+end_src
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#+name: tab:test_joints_meas_results_x_dir
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#+caption: Measured bending stiffnesses
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#+attr_latex: :environment tabularx :width 0.6\linewidth :align Xccc
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#+attr_latex: :center t :booktabs t :float t
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#+RESULTS:
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| | $R_{R_x}$ [Nm/rad] | $k_{R_y}$ [Nm/rad] | |
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|----+--------------------+--------------------+---|
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| 1 | 4.4 | 4.6 | X |
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| 2 | 5.0 | 4.8 | X |
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| 3 | 5.0 | 4.8 | X |
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| 4 | 4.7 | 4.6 | X |
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| 5 | 4.6 | 4.7 | X |
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| 6 | 4.6 | 4.7 | X |
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| 7 | 4.7 | 4.3 | |
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| 8 | 4.7 | 4.7 | X |
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| 9 | 4.7 | 4.6 | X |
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| 10 | 4.9 | 4.8 | X |
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| 11 | 4.0 | 3.9 | |
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| 12 | 4.9 | 4.8 | X |
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| 13 | 4.9 | 4.9 | X |
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| 14 | 4.7 | 4.7 | X |
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| 15 | 4.6 | 4.4 | |
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| 16 | 4.9 | 4.3 | |
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#+begin_src matlab :exports none
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load('flex_meas_dim.mat', 'meas_flex');
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figure;
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hold on;
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plot((meas_flex(:,1)+meas_flex(:,2))/2, kRx, 'o', 'DisplayName', '$x$')
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plot((meas_flex(:,3)+meas_flex(:,4))/2, kRy, 'o', 'DisplayName', '$y$')
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hold off;
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xlabel('Flexible Beam Thickness [$\mu m$]');
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ylabel('Bending Stiffness [Nm/rad]');
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legend('location', 'southeast', 'FontSize', 8);
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#+end_src
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#+begin_src matlab :tangle no :exports results :results file replace
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exportFig('figs/test_joints_thickness_stiffness.pdf', 'width', 'wide', 'height', 'normal');
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#+end_src
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#+name: fig:test_joints_thickness_stiffness
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#+caption: Measured bending stiffness as a function of the estimated flexible beam thickness
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#+RESULTS:
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[[file:figs/test_joints_thickness_stiffness.png]]
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** Conclusion
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** Conclusion
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:PROPERTIES:
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:PROPERTIES:
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:UNNUMBERED: t
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:UNNUMBERED: t
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:END:
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:END:
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#+begin_important
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The measured bending stiffness and bending stroke of the flexible joints are very close to the estimated one using a Finite Element Model.
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The measured bending stiffness and bending stroke of the flexible joints are very close to the estimated one using a Finite Element Model.
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The characteristics of all the flexible joints are also quite close to each other.
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The characteristics of all the flexible joints are also quite close to each other.
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This should allow us to model them with unique parameters.
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This should allow us to model them with unique parameters.
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#+end_important
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* Conclusion
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* Conclusion
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<<sec:test_joints_conclusion>>
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<<sec:test_joints_conclusion>>
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@ -1,4 +1,4 @@
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% Created 2024-04-06 Sat 00:18
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% Created 2024-04-06 Sat 00:30
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% Intended LaTeX compiler: pdflatex
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% Intended LaTeX compiler: pdflatex
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\documentclass[a4paper, 10pt, DIV=12, parskip=full, bibliography=totoc]{scrreprt}
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\documentclass[a4paper, 10pt, DIV=12, parskip=full, bibliography=totoc]{scrreprt}
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@ -415,7 +415,7 @@ However, the estimated non-linearity is bellow \(1\,\%\) for forces between \(0.
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\end{center}
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\end{center}
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\subcaption{\label{fig:test_joints_force_sensor_calib_fit}Measured two force and linear fit}
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\subcaption{\label{fig:test_joints_force_sensor_calib_fit}Measured two force and linear fit}
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\end{subfigure}
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\end{subfigure}
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\caption{\label{fig:test_joints_force_sensor_calib}Caption with reference to sub figure (\subref{fig:test_joints_force_sensor_calib_picture}), (\subref{fig:test_joints_force_sensor_calib_fit})}
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\caption{\label{fig:test_joints_force_sensor_calib}Estimation of the load cell accuracy. A picture of the measurement bench is shown in (\subref{fig:test_joints_force_sensor_calib_picture}). Comparison of the two measured forces is made in (\subref{fig:test_joints_force_sensor_calib_fit})}
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\end{figure}
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\end{figure}
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\section{Load Cell Stiffness}
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\section{Load Cell Stiffness}
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The objective of this measurement is to estimate the stiffness \(k_F\) of the force sensor.
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The objective of this measurement is to estimate the stiffness \(k_F\) of the force sensor.
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@ -429,7 +429,7 @@ The load cell stiffness can then be estimated by computing a linear fit, and is
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\begin{center}
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\begin{center}
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\includegraphics[scale=1,height=5.5cm]{figs/test_joints_meas_force_sensor_stiffness_picture.jpg}
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\includegraphics[scale=1,height=5.5cm]{figs/test_joints_meas_force_sensor_stiffness_picture.jpg}
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\end{center}
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\end{center}
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\subcaption{\label{fig:test_joints_meas_force_sensor_stiffness_picture}Picture of the test}
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\subcaption{\label{fig:test_joints_meas_force_sensor_stiffness_picture}Picture of the measurement bench}
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\end{subfigure}
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\end{subfigure}
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\begin{subfigure}{0.49\textwidth}
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\begin{subfigure}{0.49\textwidth}
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\begin{center}
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\begin{center}
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@ -466,7 +466,11 @@ The bending stroke can also be estimated as shown in Figure \ref{fig:test_joints
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\end{figure}
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\end{figure}
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\section{Measured flexible joint stiffnesses}
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\section{Measured flexible joint stiffnesses}
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The same measurement is performed for all the 16 flexible joints, both in the \(x\) and \(y\) directions.
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The same measurement is performed for all the 16 flexible joints, both in the \(x\) and \(y\) directions.
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The measured torque and angular motion are all shown in Figure \ref{fig:test_joints_meas_bending_all_raw_data}.
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The measured angular motion as a function of the applied torque are shown in Figure \ref{fig:test_joints_meas_bending_all_raw_data} for all the 16 flexible joints.
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This gives a first idea of the dispersion of the measured bending stiffnesses (i.e. slope of the linear region) and of the angular stroke.
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An histogram of the measured bending stiffnesses is show in Figure \ref{fig:test_joints_bend_stiff_hist}.
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Most of the bending stiffnesses are between \(4.6\,Nm/rad\) and \(5.0\,Nm/rad\).
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\begin{figure}[htbp]
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\begin{figure}[htbp]
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\begin{subfigure}{0.49\textwidth}
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\begin{subfigure}{0.49\textwidth}
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@ -481,48 +485,13 @@ The measured torque and angular motion are all shown in Figure \ref{fig:test_joi
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\end{center}
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\end{center}
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\subcaption{\label{fig:test_joints_bend_stiff_hist}Histogram of the measured bending stiffness in the x and y directions}
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\subcaption{\label{fig:test_joints_bend_stiff_hist}Histogram of the measured bending stiffness in the x and y directions}
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\end{subfigure}
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\end{subfigure}
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\caption{\label{fig:test_joints_meas_bending_results}Result of measured stiffnesses for all the flexible joints. Raw data are shown in (\subref{fig:test_joints_meas_bending_all_raw_data}). An histogram of the measured stiffnesses is shown in (\subref{fig:test_joints_bend_stiff_hist})}
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\caption{\label{fig:test_joints_meas_bending_results}Result of measured \(k_{R_x}\) and \(k_{R_y}\) stiffnesses for all the 16 flexible joints. Raw data are shown in (\subref{fig:test_joints_meas_bending_all_raw_data}). An histogram of the measured stiffnesses is shown in (\subref{fig:test_joints_bend_stiff_hist})}
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\end{figure}
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\begin{table}[htbp]
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\caption{\label{tab:test_joints_meas_results_x_dir}Measured bending stiffnesses}
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\centering
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\begin{tabularx}{0.6\linewidth}{Xccc}
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\toprule
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& \(R_{R_x}\) {[}Nm/rad] & \(k_{R_y}\) {[}Nm/rad] & \\
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\midrule
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1 & 4.4 & 4.6 & X\\
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2 & 5.0 & 4.8 & X\\
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3 & 5.0 & 4.8 & X\\
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4 & 4.7 & 4.6 & X\\
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5 & 4.6 & 4.7 & X\\
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6 & 4.6 & 4.7 & X\\
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7 & 4.7 & 4.3 & \\
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8 & 4.7 & 4.7 & X\\
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9 & 4.7 & 4.6 & X\\
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10 & 4.9 & 4.8 & X\\
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11 & 4.0 & 3.9 & \\
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12 & 4.9 & 4.8 & X\\
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13 & 4.9 & 4.9 & X\\
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14 & 4.7 & 4.7 & X\\
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15 & 4.6 & 4.4 & \\
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16 & 4.9 & 4.3 & \\
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\bottomrule
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\end{tabularx}
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\end{table}
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\begin{figure}[htbp]
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\centering
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\includegraphics[scale=1]{figs/test_joints_thickness_stiffness.png}
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\caption{\label{fig:test_joints_thickness_stiffness}Measured bending stiffness as a function of the estimated flexible beam thickness}
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\end{figure}
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\end{figure}
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\section*{Conclusion}
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\section*{Conclusion}
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\begin{important}
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The measured bending stiffness and bending stroke of the flexible joints are very close to the estimated one using a Finite Element Model.
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The measured bending stiffness and bending stroke of the flexible joints are very close to the estimated one using a Finite Element Model.
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The characteristics of all the flexible joints are also quite close to each other.
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The characteristics of all the flexible joints are also quite close to each other.
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This should allow us to model them with unique parameters.
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This should allow us to model them with unique parameters.
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\end{important}
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\chapter{Conclusion}
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\chapter{Conclusion}
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\label{sec:test_joints_conclusion}
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\label{sec:test_joints_conclusion}
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\printbibliography[heading=bibintoc,title={Bibliography}]
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\printbibliography[heading=bibintoc,title={Bibliography}]
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