Remove one figure
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@ -655,28 +655,7 @@ The computed bending stiffness will be eqref:eq:test_joints_stiffness_height_err
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k_{R_y, \text{est}} \approx h_{\text{est}}^2 \frac{F_x}{d_x} \approx k_{R_y} \Bigl( 1 + \underbrace{2 \frac{\delta h}{h} + \frac{\delta h ^2}{h^2}}_{\epsilon_h} \Bigl)
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\end{equation}
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The bending stiffness error $\epsilon_h$ due to the height estimation error $\delta h$ is shown in Figure ref:fig:test_joints_effect_height_error.
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The height estimation is foreseen to be reasonably accurate to within $\pm 0.4\,mm$ which should make the bending stiffness error $\epsilon_h < 3.5\,\%$.
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#+begin_src matlab :exports none :results none
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%% Measured stiffness error due to height estimation error
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h_err = [0:0.1:1]*1e-3; % Height error [m]
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epsilon = h_err/h; % Height error in %
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figure;
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plot(1e3*h_err, 100*abs(2*epsilon + epsilon.^2))
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xlabel('Height Error $\delta h$ [mm]');
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ylabel('Error $\epsilon_h$ [$\%$]');
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ylim([0,10]);
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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_effect_height_error.pdf', 'width', 'normal', 'height', 400);
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#+end_src
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#+name: fig:test_joints_effect_height_error
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#+caption: Measured stiffness error due to height estimation error
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#+RESULTS:
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[[file:figs/test_joints_effect_height_error.png]]
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The height estimation is foreseen to be accurate to within $|\delta h| < 0.4\,mm$ which corresponds to a stiffness error $\epsilon_h < 3.5\,\%$.
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**** Estimation error due to force and displacement sensors accuracy
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The maximum error of the measured displacement due the encoder non-linearity is $40\,nm$.
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