First analysis of stiffness
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19f003e172
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@ -702,9 +702,6 @@ Now we can estimate the stiffness with a linear fit.
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sprintf('Stiffness is %.3f [N/mm]', abs(1e-3*(d\F)))
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#+end_src
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#+RESULTS:
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: Stiffness is 0.039 [N/mm]
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This is very close to the 0.04 [N/mm] written in the [[file:doc/tmp3m0cvmue_7888038c-cdc8-48d8-a837-35de02760685.pdf][Millimar 1318 probe datasheet]].
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And compare the linear fit with the raw measurement data (Figure [[fig:mahr_stiffness_f_d_plot]]).
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@ -735,3 +732,359 @@ The Millimar 1318 probe has a stiffness of $\approx 0.04\,[N/mm]$.
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* Bending Stiffness Measurement
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<<sec:bending_stiffness_meas>>
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** Matlab Init :noexport:ignore:
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#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
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<<matlab-dir>>
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#+end_src
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#+begin_src matlab :exports none :results silent :noweb yes
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<<matlab-init>>
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#+end_src
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#+begin_src matlab :tangle no
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addpath('./matlab/mat/');
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addpath('./matlab/');
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#+end_src
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#+begin_src matlab :eval no
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addpath('./mat/');
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#+end_src
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** Results
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#+begin_src matlab
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load('meas_stiff_flex_12_x.mat', 't', 'd', 'F');
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#+end_src
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#+begin_src matlab
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d = d(t > 5.35 & t < 14.0);
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F = F(t > 5.35 & t < 14.0);
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t = t(t > 5.35 & t < 14.0);
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d = d - d(1);
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F = F - F(1);
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t = t - t(1);
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#+end_src
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#+begin_src matlab :exports none
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%% Time Domain plots
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figure;
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tiledlayout(2, 1, 'TileSpacing', 'None', 'Padding', 'None');
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ax1 = nexttile;
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plot(t, F);
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ylabel('Force [N]'); set(gca, 'XTickLabel',[]);
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ax2 = nexttile;
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plot(t, d);
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xlabel('Time [s]'); ylabel('Displacement [m]');
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#+end_src
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#+begin_src matlab :exports none
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figure;
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hold on;
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plot(F, d, 'DisplayName', 'Raw data');
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% plot(F, F/(d\F), 'DisplayName', 'Linear fit');
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hold off;
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xlabel('Measured Force [N]');
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ylabel('Measured Displacement [m]');
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legend('location', 'southeast');
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#+end_src
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#+begin_src matlab
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ta = [0.05, 1.13];
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tb = [5.75, 7.2];
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d_l = [d(t > ta(1) & t < ta(2)); d(t > tb(1) & t < tb(2))];
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F_l = [F(t > ta(1) & t < ta(2)); F(t > tb(1) & t < tb(2))];
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d_l = d_l - d_l(1);
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F_l = F_l - F_l(1);
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#+end_src
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#+begin_src matlab :exports none
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figure;
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hold on;
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plot(F_l, d_l, '.', 'DisplayName', 'Raw data');
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plot(F_l, F_l/(d_l\F_l), 'DisplayName', 'Linear fit');
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hold off;
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xlabel('Measured Force [N]');
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ylabel('Measured Displacement [m]');
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legend('location', 'southeast');
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#+end_src
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#+begin_src matlab :results value replace :exports results :tangle no
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h = 25e-3;
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sprintf('Stiffness is %.3f [Nm/rad]', abs(h^2*(d_l\F_l)))
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#+end_src
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#+RESULTS:
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: Stiffness is 5.579 [Nm/rad]
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** Results - Y
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#+begin_src matlab
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load('meas_stiff_flex_12_y.mat', 't', 'd', 'F');
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#+end_src
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#+begin_src matlab
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%% Automatic Zero of the force
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F = F - mean(F(t > 0.9 & t < 1.1));
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%% Start measurement at t = 1.0 s
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d = d(t > 1.0);
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F = F(t > 1.0);
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t = t(t > 1.0); t = t - t(1);
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#+end_src
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#+begin_src matlab :exports none
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%% Time Domain plots
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figure;
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tiledlayout(2, 1, 'TileSpacing', 'None', 'Padding', 'None');
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ax1 = nexttile;
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plot(t, F);
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ylabel('Force [N]'); set(gca, 'XTickLabel',[]);
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ax2 = nexttile;
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plot(t, d);
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hold off;
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xlabel('Time [s]'); ylabel('Displacement [m]');
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linkaxes([ax1,ax2],'x');
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#+end_src
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#+begin_src matlab
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t_l = [5.58, 6.75]; % Time of flexible joint's linear region
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t_s = [6.9, 7.24]; % Time of stop's linear region
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#+end_src
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#+begin_src matlab :exports none
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%% Linear Fit
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h = 25e-3;
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F_l = F(t > t_l(1) & t < t_l(2));
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d_l = d(t > t_l(1) & t < t_l(2));
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F_s = F(t > t_s(1) & t < t_s(2));
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d_s = d(t > t_s(1) & t < t_s(2));
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fit_l = polyfit(F_l, d_l, 1);
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fit_s = polyfit(F_s, d_s, 1);
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%% Reset displacement based on fit
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d = d - fit_l(2);
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fit_s(2) = fit_s(2) - fit_l(2);
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fit_l(2) = 0;
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%% Estimated Stroke
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F_max = fit_s(2)/(fit_l(1) - fit_s(1));
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d_max = fit_l(1)*F_max;
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#+end_src
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#+begin_src matlab :exports none
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figure;
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hold on;
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% plot(F_l, d_l, 'k.', 'DisplayName', 'Raw Data');
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% plot(F_s, d_s, 'k.', 'HandleVisibility', 'off');
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plot(F, d, 'k.', 'DisplayName', 'Raw data');
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set(gca,'ColorOrderIndex',1)
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plot(F_l, fit_l(1)*F_l + fit_l(2), '--', 'DisplayName', sprintf('$k_{R_x} = %.1f [Nm/rad]$', (h)^2/fit_l(1)));
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plot(F_s, fit_s(1)*F_s + fit_s(2), '--', 'DisplayName', sprintf('$k_s = %.1f [Nm/rad]$', (h)^2/fit_s(1)));
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plot([0.8*F_max, 1.2*F_max], [d_max, d_max], '--', 'DisplayName', sprintf('$R_{x,max} = %.1f [mrad]$', 1e3*atan2(d_max,h)));
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hold off;
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xlabel('Measured Force [N]');
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ylabel('Measured Displacement [m]');
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legend('location', 'southeast');
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ylim([-1e-4,inf])
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#+end_src
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#+begin_src matlab :results value replace :exports results :tangle no
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sprintf('Bending Stiffness is %.1f [Nm/rad]', (h)^2/fit_l(1))
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#+end_src
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#+RESULTS:
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: Bending Stiffness is 5.5 [Nm/rad]
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#+begin_src matlab :results value replace :exports results :tangle no
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sprintf('Bending Stroke is %.1f [mrad]', 1e3*atan2(d_max,h))
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#+end_src
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#+RESULTS:
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: Bending Stroke is 17.9 [mrad]
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** Results - X
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#+begin_src matlab
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load('meas_stiff_flex_12_x.mat', 't', 'd', 'F');
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#+end_src
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#+begin_src matlab
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%% Automatic Zero of the force
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F = F - mean(F(t > 0.9 & t < 1.1));
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%% Start measurement at t = 1.0 s
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d = d(t > 1.0);
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F = F(t > 1.0);
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t = t(t > 1.0); t = t - t(1);
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#+end_src
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#+begin_src matlab :exports none
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%% Time Domain plots
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figure;
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tiledlayout(2, 1, 'TileSpacing', 'None', 'Padding', 'None');
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ax1 = nexttile;
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plot(t, F);
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ylabel('Force [N]'); set(gca, 'XTickLabel',[]);
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ax2 = nexttile;
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plot(t, d);
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hold off;
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xlabel('Time [s]'); ylabel('Displacement [m]');
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linkaxes([ax1,ax2],'x');
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#+end_src
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#+begin_src matlab
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t_l = [4.365, 5.47]; % Time of flexible joint's linear region
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t_s = [5.65, 6.09]; % Time of stop's linear region
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#+end_src
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#+begin_src matlab :exports none
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%% Linear Fit
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h = 25e-3;
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F_l = F(t > t_l(1) & t < t_l(2));
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d_l = d(t > t_l(1) & t < t_l(2));
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F_s = F(t > t_s(1) & t < t_s(2));
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d_s = d(t > t_s(1) & t < t_s(2));
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fit_l = polyfit(F_l, d_l, 1);
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fit_s = polyfit(F_s, d_s, 1);
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%% Reset displacement based on fit
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d = d - fit_l(2);
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fit_s(2) = fit_s(2) - fit_l(2);
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fit_l(2) = 0;
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%% Estimated Stroke
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F_max = fit_s(2)/(fit_l(1) - fit_s(1));
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d_max = fit_l(1)*F_max;
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#+end_src
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#+begin_src matlab :exports none
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figure;
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hold on;
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plot(F, d, 'k.', 'DisplayName', 'Raw data');
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set(gca,'ColorOrderIndex',1)
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plot(F_l, fit_l(1)*F_l + fit_l(2), '-', 'DisplayName', sprintf('$k_{R_x} = %.1f [Nm/rad]$', (h)^2/fit_l(1)));
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plot(F_s, fit_s(1)*F_s + fit_s(2), '-', 'DisplayName', sprintf('$k_s = %.1f [Nm/rad]$', (h)^2/fit_s(1)));
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plot([0.8*F_max, 1.2*F_max], [d_max, d_max], '-', 'DisplayName', sprintf('$R_{x,max} = %.1f [mrad]$', 1e3*atan2(d_max,h)));
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hold off;
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xlabel('Measured Force [N]');
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ylabel('Measured Displacement [m]');
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legend('location', 'southeast');
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ylim([-1e-4,inf])
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#+end_src
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#+begin_src matlab :results value replace :exports results :tangle no
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sprintf('Bending Stiffness is %.1f [Nm/rad]', (h)^2/fit_l(1))
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#+end_src
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#+RESULTS:
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: Bending Stiffness is 5.7 [Nm/rad]
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#+begin_src matlab :results value replace :exports results :tangle no
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sprintf('Bending Stroke is %.1f [mrad]', 1e3*atan2(d_max,h))
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#+end_src
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#+RESULTS:
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: Bending Stroke is 17.9 [mrad]
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** Results - XY
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#+begin_src matlab
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load('meas_stiff_flex_12_xy.mat', 't', 'd', 'F');
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#+end_src
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#+begin_src matlab
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%% Automatic Zero of the force
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F = F - mean(F(t > 0.9 & t < 1.1));
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%% Start measurement at t = 1.0 s
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d = d(t > 1.0);
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F = F(t > 1.0);
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t = t(t > 1.0); t = t - t(1);
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#+end_src
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#+begin_src matlab :exports none
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%% Time Domain plots
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figure;
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tiledlayout(2, 1, 'TileSpacing', 'None', 'Padding', 'None');
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ax1 = nexttile;
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plot(t, F);
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ylabel('Force [N]'); set(gca, 'XTickLabel',[]);
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ax2 = nexttile;
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plot(t, d);
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hold off;
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xlabel('Time [s]'); ylabel('Displacement [m]');
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linkaxes([ax1,ax2],'x');
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#+end_src
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#+begin_src matlab
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t_l = [4.99, 6.5]; % Time of flexible joint's linear region
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t_s = [6.8, 7.10]; % Time of stop's linear region
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#+end_src
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#+begin_src matlab :exports none
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%% Linear Fit
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h = 25e-3;
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F_l = F(t > t_l(1) & t < t_l(2));
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d_l = d(t > t_l(1) & t < t_l(2));
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F_s = F(t > t_s(1) & t < t_s(2));
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d_s = d(t > t_s(1) & t < t_s(2));
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fit_l = polyfit(F_l, d_l, 1);
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fit_s = polyfit(F_s, d_s, 1);
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%% Reset displacement based on fit
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d = d - fit_l(2);
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fit_s(2) = fit_s(2) - fit_l(2);
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fit_l(2) = 0;
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%% Estimated Stroke
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F_max = fit_s(2)/(fit_l(1) - fit_s(1));
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d_max = fit_l(1)*F_max;
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#+end_src
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#+begin_src matlab :exports none
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figure;
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hold on;
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plot(F, d, 'k.', 'DisplayName', 'Raw data');
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set(gca,'ColorOrderIndex',1)
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plot(F_l, fit_l(1)*F_l + fit_l(2), '-', 'DisplayName', sprintf('$k_{R_x} = %.1f [Nm/rad]$', (h)^2/fit_l(1)));
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plot(F_s, fit_s(1)*F_s + fit_s(2), '-', 'DisplayName', sprintf('$k_s = %.1f [Nm/rad]$', (h)^2/fit_s(1)));
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plot([0.8*F_max, 1.2*F_max], [d_max, d_max], '-', 'DisplayName', sprintf('$R_{x,max} = %.1f [mrad]$', 1e3*atan2(d_max,h)));
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hold off;
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xlabel('Measured Force [N]');
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ylabel('Measured Displacement [m]');
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legend('location', 'southeast');
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ylim([-1e-4,inf])
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#+end_src
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#+begin_src matlab :results value replace :exports results :tangle no
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sprintf('Bending Stiffness is %.1f [Nm/rad]', (h)^2/fit_l(1))
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#+end_src
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#+RESULTS:
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: Bending Stiffness is 5.6 [Nm/rad]
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#+begin_src matlab :results value replace :exports results :tangle no
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sprintf('Bending Stroke is %.1f [mrad]', 1e3*atan2(d_max,h))
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#+end_src
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#+RESULTS:
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: Bending Stroke is 23.1 [mrad]
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