From f7510ef5c4e29f7fddee5d71af92af30d6ebb218 Mon Sep 17 00:00:00 2001 From: Thomas Dehaeze Date: Fri, 5 Apr 2024 17:53:53 +0200 Subject: [PATCH] Continuing report --- figs/test_joints_axis.pdf | Bin 6370 -> 0 bytes figs/test_joints_axis.png | Bin 7800 -> 0 bytes figs/test_joints_axis.svg | Bin 171275 -> 0 bytes figs/test_joints_force_sensor_calib_error.pdf | Bin 88876 -> 0 bytes figs/test_joints_force_sensor_calib_error.png | Bin 26088 -> 0 bytes figs/test_joints_force_sensor_calib_fit.pdf | Bin 59150 -> 38532 bytes figs/test_joints_force_sensor_calib_fit.png | Bin 22848 -> 20425 bytes ...est_joints_force_sensor_calib_picture.jpg} | Bin figs/test_joints_force_sensor_calib_time.pdf | Bin 55554 -> 46516 bytes figs/test_joints_force_sensor_calib_time.png | Bin 34798 -> 25127 bytes ...test_joints_force_sensor_stiffness_fit.pdf | Bin 55784 -> 59427 bytes ...test_joints_force_sensor_stiffness_fit.png | Bin 25381 -> 26692 bytes figs/test_joints_meas_F_d.pdf | Bin 422189 -> 0 bytes figs/test_joints_meas_F_d.png | Bin 17737 -> 0 bytes ...est_joints_meas_force_sensor_stiffness.jpg | Bin 368172 -> 0 bytes ...s_meas_force_sensor_stiffness_picture.jpg} | Bin figs/test_joints_profilometer_setup.jpg | Bin 947975 -> 0 bytes test-bench-flexible-joints.org | 194 +++++++----------- test-bench-flexible-joints.pdf | Bin 5392554 -> 5222292 bytes test-bench-flexible-joints.tex | 119 ++++------- 20 files changed, 111 insertions(+), 202 deletions(-) delete mode 100644 figs/test_joints_axis.pdf delete mode 100644 figs/test_joints_axis.png delete mode 100644 figs/test_joints_axis.svg delete mode 100644 figs/test_joints_force_sensor_calib_error.pdf delete mode 100644 figs/test_joints_force_sensor_calib_error.png rename figs/{test_joints_force_sensor_calib.jpg => test_joints_force_sensor_calib_picture.jpg} (100%) delete mode 100644 figs/test_joints_meas_F_d.pdf delete mode 100644 figs/test_joints_meas_F_d.png delete mode 100644 figs/test_joints_meas_force_sensor_stiffness.jpg rename 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zkctn12P;|~V(R%FRw<}|!V?r@r5p_BtDEp~ihIxr5VDjR$KXo6mdZ<-^MT2Vo=fH2 z-msuji2lmerG%=unVhWN9TiVkVPnAjm9;BgoQc+b z7qA%9QMjGaJBQ-ydxR6%XupEHoyuAmh_sMZlOcTEBT0`|~j{Wiec|f5?T}Ms{ zo=3QCWfTq{m^<6FJ~a|0z1Nd~O$3cb0lnv4fQQe~^K6emRDzFJc>(BvOeB+9tCaLI|kOIxJ$>7vV zsvO+6D+E@v7ShKfhNxL7O+r52yqYm9hnRglG9!UFe(rX<0w=BvE~L+%EdKoK@yFkG znfcq(r4Ju%J<{4Z{di~uHJ(_T-p^hHx(+;O7F_vB!m}L99d67thY6P%3TIq_7Nma) z$YZ9!5cFL#GK^ed5VgclJC!7UmS>z#$DeIErwp$qm&Xn{7i#7Ah-i{Sdesn}tBqtQO0uW`aKLR&3e1Q-tI!ME>!< zx)6&5z|Tf4C(FOkIc)01W8LC)?zGOL(pfn|xLn_M?4p`fRi|IuZqL$t!CLEUaE{DJ zYQkmH{v21O>l#1bY=6$+y8DEhFd&p#_&+jn-Iwc?i4J!c3b`|A14RS`2fr+0W~H$+ z_e)dq;Bdh5A;^f{vQm8Kxa_Fs{3&=7t;Iv8cvQ2$sOua$zi&t_bv5fwz;#R zrgxrSLD`Smz1QY_?^dJSGuBfu+{Og<+&_> #+end_src -** Force Sensor Calibration +** Load Cell Calibration In order to estimate the measured errors of the load cell "FC2231", it is compared against another load cell[fn:5]. +The two load cells are measured simultaneously while they are pushed against each other (see Figure ref:fig:test_joints_force_sensor_calib_picture). +The contact between the two load cells is well defined as one has a spherical interface while the other has a flat surface. -There are both specified to have $\pm 1 \%$ of non-linearity over the full range. - -The XFL212R has a spherical interface while the FC2231 has a flat surface. -Therefore, we should have a nice point contact when using the two force sensors as shown in Figure ref:fig:test_joints_force_sensor_calib. - -#+name: fig:test_joints_force_sensor_calib -#+caption: Zoom on the two force sensors in contact -#+attr_latex: :width 0.5\linewidth -[[file:figs/test_joints_force_sensor_calib.jpg]] - -The two force sensors are therefore measuring the exact same force, and we can compare the two measurements. +The measured forces are compared in Figure ref:fig:test_joints_force_sensor_calib_fit. +The gain mismatch between the two load cells is approximately $4\,\%$ which is higher than what was specified in the data-sheets. +However, the estimated non-linearity is bellow $1\,\%$ for forces between $0.5\,N$ and $5\,N$. #+begin_src matlab -%% Load measurement data +%% Force Sensor Calibration +% Load measurement data load('calibration_force_sensor.mat', 't', 'F', 'Fc') -%% We remove any offset such that they are both measuring no force when not in contact. -F = F - mean(F( t > 0.5 & t < 1.0)); -Fc = Fc - mean(Fc(t > 0.5 & t < 1.0)); -#+end_src +% Remove any offset such that they are both measuring no force when not in contact. +F = F - mean(F( t > 0.5 & t < 1.0)); % FC2231 [N] +Fc = Fc - mean(Fc(t > 0.5 & t < 1.0)); % XFL212R [N] -#+begin_src matlab :exports none -%% Measured force using both sensors as a function of time -figure; -hold on; -plot(t, F, 'DisplayName', 'FC2231'); -plot(t, Fc, 'DisplayName', 'XFL212R'); -hold off; -xlabel('Time [s]'); ylabel('Measured Force [N]'); -xlim([0,15]); ylim([0,55]); -legend('location', 'southeast', 'FontSize', 8); -#+end_src +% Only get useful stroke +F = F( t > 1.55 & t < 2.4); +Fc = Fc(t > 1.55 & t < 2.4); -#+begin_src matlab :tangle no :exports results :results file replace -exportFig('figs/test_joints_force_sensor_calib_time.pdf', 'width', 'wide', 'height', 'normal'); -#+end_src - -#+name: fig:test_joints_force_sensor_calib_time -#+caption: Measured force using both sensors as a function of time -#+RESULTS: -[[file:figs/test_joints_force_sensor_calib_time.png]] - -Let's select only the first part from the moment they are in contact until the maximum force is reached. - -#+begin_src matlab -%% Only get the first part until maximum force -F = F( t > 1.55 & t < 4.65); -Fc = Fc(t > 1.55 & t < 4.65); -#+end_src - -Then, let's make a linear fit between the two measured forces. - -#+begin_src matlab -%% Make a line fit +% Make a line fit fit_F = polyfit(Fc, F, 1); + +% Estimate the gain mismatch +F_gain_mismatch = 100*(1 - fit_F(1)); % in % + +% Estimate non-linearity of the sensors +F_non_linearity = 100*(F - (Fc*fit_F(1) + fit_F(2)))./F; % in % #+end_src -The two forces are plotted against each other as well as the linear fit in Figure ref:fig:test_joints_force_sensor_calib_fit. - #+begin_src matlab :exports none +%% Measured two forces and linear fit figure; hold on; -plot(Fc, F, '-', 'DisplayName', 'Raw Data'); +plot(Fc, F, 'k-', 'DisplayName', 'Raw Data'); plot(Fc([1,end]), Fc([1,end])*fit_F(1) + fit_F(2), '--', 'DisplayName', 'Line Fit'); hold off; xlabel('XFL212R [N]'); ylabel('FC2231 [N]'); -xlim([0,50]); ylim([0,50]); +xlim([0.5,5.5]); ylim([0.5,5.5]); legend('location', 'southeast', 'FontSize', 8); #+end_src -#+begin_src matlab :tangle no :exports results :results file replace -exportFig('figs/test_joints_force_sensor_calib_fit.pdf', 'width', 'wide', 'height', 'normal'); +#+begin_src matlab :tangle no :exports results :results file none +exportFig('figs/test_joints_force_sensor_calib_fit.pdf', 'width', 'half', 'height', 'normal'); #+end_src -#+name: fig:test_joints_force_sensor_calib_fit -#+caption: Measured two forces and linear fit -#+RESULTS: -[[file:figs/test_joints_force_sensor_calib_fit.png]] - -The measurement error between the two sensors is shown in Figure ref:fig:test_joints_force_sensor_calib_error. -It is below 0.1N for the full measurement range. - -#+begin_src matlab :exports none -figure; -hold on; -plot(Fc, movmean(100*(F - (Fc*fit_F(1) + fit_F(2)))./F, 100), 'k-'); -hold off; -xlim([5,50]); -xlabel('Measured Force [N]'); -ylabel('Error [N]') -#+end_src - -#+begin_src matlab :tangle no :exports results :results file replace -exportFig('figs/test_joints_force_sensor_calib_error.pdf', 'width', 'wide', 'height', 'normal'); -#+end_src - -#+name: fig:test_joints_force_sensor_calib_error -#+caption: Error in Newtons -#+RESULTS: -[[file:figs/test_joints_force_sensor_calib_error.png]] - -** Force Sensor Stiffness - -The objective of this measurement is to estimate the stiffness of the force sensor. - -To do so, a very stiff element is fixed in front of the force sensor as shown in Figure ref:fig:test_joints_meas_force_sensor_stiffness. - -Then, we apply a force on the stiff element through the force sensor. -We measure the deflection of the force sensor using an encoder. - -Then, having the force and the deflection, we should be able to estimate the stiffness of the force sensor supposing the stiffness of the other elements are much larger. - -#+name: fig:fig_label -#+caption: Caption with reference to sub figure (\subref{fig:fig_label_a}) +#+name: fig:test_joints_force_sensor_calib +#+caption: Caption with reference to sub figure (\subref{fig:test_joints_force_sensor_calib_picture}), (\subref{fig:test_joints_force_sensor_calib_fit}) #+attr_latex: :options [htbp] #+begin_figure -#+attr_latex: :caption \subcaption{\label{fig:test_joints_meas_force_sensor_stiffness}sub caption a} +#+attr_latex: :caption \subcaption{\label{fig:test_joints_force_sensor_calib_picture}Zoom on the two force sensors in contact} #+attr_latex: :options {0.49\textwidth} #+begin_subfigure -#+attr_latex: :width 0.95\linewidth -[[file:figs/test_joints_meas_force_sensor_stiffness-crop.jpg]] +#+attr_latex: :height 5.5cm +[[file:figs/test_joints_force_sensor_calib_picture.jpg]] #+end_subfigure -#+attr_latex: :caption \subcaption{\label{fig:test_joints_force_sensor_stiffness_fit}sub caption b} +#+attr_latex: :caption \subcaption{\label{fig:test_joints_force_sensor_calib_fit}Measured two force and linear fit} #+attr_latex: :options {0.49\textwidth} #+begin_subfigure -#+attr_latex: :width 0.95\linewidth -[[file:figs/test_joints_force_sensor_stiffness_fit.png]] +#+attr_latex: :height 5.5cm +[[file:figs/test_joints_force_sensor_calib_fit.png]] #+end_subfigure #+end_figure -From the documentation, the deflection of the sensor at the maximum load (50N) is 0.05mm, the stiffness is therefore foreseen to be around $1\,N/\mu m$. +** Load Cell Stiffness +The objective of this measurement is to estimate the stiffness $k_F$ of the force sensor. +To do so, a stiff element (much stiffer than the estimated $k_F \approx 1\,N/\mu m$) is fixed in front of the force sensor as shown in Figure ref:fig:test_joints_meas_force_sensor_stiffness_picture. +Then, the force sensor is pushed again this stiff element while the force and the encoder displacement are measured. +Measured displacement as a function of the force is shown in Figure ref:fig:test_joints_force_sensor_stiffness_fit. +The load cell stiffness can then be estimated by computing a linear fit, and is found to be $k_F \approx 0.75\,N/\mu m$. #+begin_src matlab -%% Load measurement data +%% Estimaetd load cell stiffness +% Load measurement data load('force_sensor_stiffness_meas.mat', 't', 'F', 'd') -%% Remove offset +% Remove offset F = F - mean(F(t > 0.5 & t < 1.0)); -%% Select important part of data +% Select important part of data F = F( t > 4.55 & t < 7.24); d = d( t > 4.55 & t < 7.24); d = d - d(1); t = t( t > 4.55 & t < 7.24); -%% Linear fit +% Linear fit fit_k = polyfit(F, d, 1); #+end_src -The displacement as a function of the force as well as the linear fit are shown in Figure ref:fig:test_joints_force_sensor_stiffness_fit. -$k_F \approx 0.75\,N/\mu m$ - #+begin_src matlab :exports none %% Displacement as a function of the measured force figure; hold on; -plot(F, 1e6*d, '-', 'color', colors(2,:), 'DisplayName', 'Raw Data'); -plot(F([1,end]), 1e6*(F([1,end])*fit_k(1) + fit_k(2)), 'k--', 'DisplayName', 'Linear Fit'); +plot(F, 1e6*d, 'k-', 'DisplayName', 'Raw Data'); +plot(F([1,end]), 1e6*(F([1,end])*fit_k(1) + fit_k(2)), '--', 'DisplayName', sprintf('Fit, $k_F \\approx %.2f N/\\mu m$', 1e-6/fit_k(1))); hold off; xlabel('Force [$N$]'); ylabel('Displacement [$\mu m$]'); xlim([0,45]); ylim([0,60]); @@ -901,19 +837,33 @@ legend('location', 'southeast', 'FontSize', 8); exportFig('figs/test_joints_force_sensor_stiffness_fit.pdf', 'width', 'half', 'height', 'normal'); #+end_src -** Analysis of one measurement +#+name: fig:test_joints_meas_force_sensor_stiffness +#+caption: Estimation of the load cell stiffness. Measurement setup is shown in (\subref{fig:test_joints_meas_force_sensor_stiffness_picture}). Measurement results is shown in (\subref{fig:test_joints_meas_force_sensor_stiffness_fit}). +#+attr_latex: :options [htbp] +#+begin_figure +#+attr_latex: :caption \subcaption{\label{fig:test_joints_meas_force_sensor_stiffness_picture}Picture of the test} +#+attr_latex: :options {0.49\textwidth} +#+begin_subfigure +#+attr_latex: :height 5.5cm +[[file:figs/test_joints_meas_force_sensor_stiffness_picture.jpg]] +#+end_subfigure +#+attr_latex: :caption \subcaption{\label{fig:test_joints_force_sensor_stiffness_fit}Measured displacement as a function of the force} +#+attr_latex: :options {0.49\textwidth} +#+begin_subfigure +#+attr_latex: :height 5.5cm +[[file:figs/test_joints_force_sensor_stiffness_fit.png]] +#+end_subfigure +#+end_figure +** Bending Stiffness estimation The actual stiffness measurement in now performed by manually moving the translation stage from a start position where the force sensor is not yet in contact with the flexible joint to a position where flexible joint is on its mechanical stop. The measured force and displacement as a function of time are shown in Figure ref:fig:test_joints_meas_bend_time. +Three regions can be observed: first the force sensor tip is not in contact with the flexible joint and the measured force is zero, then the flexible joint deforms linearly, finally the flexible joint comes in contact with the mechanical stops. -The angular motion $\theta_{y}$ computed from the displacement $d_x$ is displacement as function of the measured torque $T_{y}$ in Figure ref:fig:test_joints_meas_F_d_lin_fit. -The bending stiffness can be estimated by computing the slope of the curve - -The obtained characteristics are: -- Bending Stiffness: $4.4\,Nm/\text{rad}$ -- Bending Stiffness at stop: 144Nm/rad -- Bending Stroke: $20.9\,\text{mrad}$ +The angular motion $\theta_{y}$ computed from the displacement $d_x$ is displacement as function of the measured torque $T_{y}$ in displayed in Figure ref:fig:test_joints_meas_F_d_lin_fit. +The bending stiffness of the flexible joint can be estimated by computing the slope of the curve in the linear regime (red dashed line) and is found to be $k_{R_y} = 4.4\,Nm/\text{rad}$. +The bending stroke can also be estimated as shown in Figure ref:fig:test_joints_meas_F_d_lin_fit and is found to be $\theta_{y,\text{max}} = 20.9\,\text{mrad}$. #+begin_src matlab %% Load Measured Data for first flexible joint @@ -1033,7 +983,7 @@ exportFig('figs/test_joints_meas_F_d_lin_fit.pdf', 'width', 'half', 'height', 'n #+end_src #+name: fig:test_joints_meas_example -#+caption: Caption with reference to sub figure (\subref{fig:fig_label_a}) +#+caption: Results obtained on the first flexible joint. Measured force and displacement are shown in (\subref{fig:test_joints_meas_bend_time}). The estimated angular displacement $\theta_y$ as a function of the estimated applied torque $T_{y}$ is shown in (\subref{fig:test_joints_meas_F_d_lin_fit}). The bending stiffness $k_{R_y}$ of the flexible joint can be estimated by computing a best linear fit (red dashed line). #+attr_latex: :options [htbp] #+begin_figure #+attr_latex: :caption \subcaption{\label{fig:test_joints_meas_bend_time}Force and displacement measured as a function of time} @@ -1050,8 +1000,7 @@ exportFig('figs/test_joints_meas_F_d_lin_fit.pdf', 'width', 'half', 'height', 'n #+end_subfigure #+end_figure -** Bending stiffness and bending stroke of all the flexible joints - +** TODO Comparison of the measured Stiffnesses Now, let's estimate the bending stiffness and stroke for all the flexible joints. #+begin_src matlab :exports none @@ -1214,7 +1163,6 @@ data2orgtable([kRy; kSy; 1e3*Rmy]', {'1','2','3','4','5','6','7','8','9','10','1 | 15 | 5.4 | 241.5 | 17.8 | | 16 | 5.3 | 291.1 | 17.7 | -** Analysis The dispersion of the measured bending stiffness is shown in Figure ref:fig:test_joints_bend_stiff_hist and of the bending stroke in Figure 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