Add inkscape directory

figs/inkscape/convert_svg.sh

@@ -0,0 +1,18 @@
+#!/bin/bash
+
+# Directory containing SVG files
+INPUT_DIR="."
+
+# Loop through all SVG files in the directory
+for svg_file in "$INPUT_DIR"/*.svg; do
+    # Check if there are SVG files in the directory
+    if [ -f "$svg_file" ]; then
+        # Output PDF file name
+        pdf_file="../${svg_file%.svg}.pdf"
+        png_file="../${svg_file%.svg}"
+        
+        # Convert SVG to PDF using Inkscape
+        inkscape "$svg_file" --export-filename="$pdf_file" && \
+            pdftocairo -png -singlefile -cropbox "$pdf_file" "$png_file"
+    fi
+done

matlab/test_struts_1_flexible_modes.m

@@ -11,10 +11,6 @@ addpath('./src/'); % Path for functions
 %% Colors for the figures
 colors = colororder;
 
-% Measured results
-% The obtained frequency response functions for the three configurations (X-bending, Y-bending and Z-torsion) are shown in Figure ref:fig:test_struts_spur_res_frf_no_enc when the encoder is not fixed to the strut and in Figure ref:fig:test_struts_spur_res_frf_enc when the encoder is fixed to the strut.
-
-
 %% Load Data (without the encoder)
 bending_X = load('strut_spur_res_x_bending.mat');
 bending_Y = load('strut_spur_res_y_bending.mat');

matlab/test_struts_2_dynamical_meas.m

@@ -11,10 +11,6 @@ addpath('./src/'); % Path for functions
 %% Colors for the figures
 colors = colororder;
 
-% Effect of the Encoder on the measured dynamics
-% <<ssec:test_struts_effect_encoder>>
-
-
 %% Parameters for Frequency Analysis
 Ts = 1e-4; % Sampling Time [s]
 Nfft = floor(1/Ts); % Number of points for the FFT computation
@@ -61,35 +57,6 @@ iff_with_enc_frf = [frf_sweep(i_lf); frf_noise_hf(i_hf)]; % Combine the FRF
 [frf_noise_hf, ~] = tfestimate(leg_enc_noise_hf.u, leg_enc_noise_hf.de, win, Noverlap, Nfft, 1/Ts);
 enc_frf = [frf_sweep(i_lf); frf_noise_hf(i_hf)]; % Combine the FRF
 
-
-
-% System identification is performed without the encoder fixed to the strut (Figure ref:fig:test_struts_bench_leg_front) and with one encoder fixed to the strut (Figure ref:fig:test_struts_bench_leg_coder).
-
-% #+name: fig:test_struts_bench_leg_with_without_enc
-% #+caption: Struts fixed to the test bench with clamped flexible joints. The coder can be fixed to the struts (\subref{fig:test_struts_bench_leg_coder}) or removed (\subref{fig:test_struts_bench_leg_front})
-% #+attr_latex: :options [htbp]
-% #+begin_figure
-% #+attr_latex: :caption \subcaption{\label{fig:test_struts_bench_leg_coder}Strut with encoder}
-% #+attr_latex: :options {0.5\textwidth}
-% #+begin_subfigure
-% #+attr_latex: :height 6cm
-% [[file:figs/test_struts_bench_leg_coder.jpg]]
-% #+end_subfigure
-% #+attr_latex: :caption \subcaption{\label{fig:test_struts_bench_leg_front}Strut without encoder}
-% #+attr_latex: :options {0.5\textwidth}
-% #+begin_subfigure
-% #+attr_latex: :height 6cm
-% [[file:figs/test_struts_bench_leg_front.jpg]]
-% #+end_subfigure
-% #+end_figure
-
-% The obtained frequency response functions are compared in Figure ref:fig:test_struts_effect_encoder.
-% It is found that the encoder has very little effect on the transfer function from excitation voltage $u$ to the axial motion of the strut $d_a$ as measured by the interferometer (Figure ref:fig:test_struts_effect_encoder_int).
-% This means that the axial motion of the strut is unaffected by the presence of the encoder.
-% Similarly, it has very little effect on the transfer function from $u$ to the sensor stack voltage $V_s$ (Figure ref:fig:test_struts_effect_encoder_iff).
-% This means that the integral force feedback control strategy should be as effective whether the encoders are fixed to the struts or not.
-
-
 %% Plot the FRF from u to da with and without the encoder
 figure;
 tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
@@ -150,18 +117,6 @@ linkaxes([ax1,ax2],'x');
 xlim([10, 2e3]);
 xticks([1e1, 1e2, 1e3]);
 
-% Comparison of the encoder and interferometer
-% <<ssec:test_struts_comp_enc_int>>
-
-% The dynamics as measured by the encoder (i.e. $d_e/u$) and by the interferometers (i.e. $d_a/u$) are compared in Figure ref:fig:test_struts_comp_enc_int.
-% The dynamics from the excitation voltage $u$ to the measured displacement by the encoder $d_e$ presents a behavior that is much more complex than the dynamics to the displacement as measured by the interferometer (comparison made in Figure ref:fig:test_struts_comp_enc_int).
-% Three additional resonance frequencies can be observed at 197Hz, 290Hz and 376Hz.
-% These resonance frequencies are matching the frequencies of the flexible modes that were studied in Section ref:sec:test_struts_flexible_modes.
-
-% The good news is that these resonances are not impacting the axial motion of the strut (which is what is important for the hexapod positioning).
-% However, these resonances are making the use of encoder fixed to the strut difficult from a control perspective.
-
-
 figure;
 tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
 
@@ -195,10 +150,6 @@ linkaxes([ax1,ax2],'x');
 xlim([10, 2e3]);
 xticks([1e1, 1e2, 1e3]);
 
-% Comparison of all the Struts
-% <<ssec:test_struts_comp_all_struts>>
-
-
 %% Numbers of the measured legs
 strut_nums = [1 2 3 4 5];
 
@@ -240,13 +191,6 @@ for i = 1:length(strut_nums)
     iff_frf(:, i) = [frf_lf(i_lf); frf_hf(i_hf)];
 end
 
-
-
-% Then, the dynamics of all the mounted struts (only 5 at the time of the experiment) were all measured using the same test bench.
-% The obtained dynamics from $u$ to $d_a$ are compared in Figure ref:fig:test_struts_comp_interf_plants while is dynamics from $u$ to $V_s$ are compared in Figure ref:fig:test_struts_comp_iff_plants.
-% Very good match can be observed between all the struts.
-
-
 %% Plot the FRF from u to de (interferometer)
 figure;
 tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');

matlab/test_struts_3_simscape_model.m

@@ -31,10 +31,6 @@ io(io_i) = linio([mdl, '/da'], 1, 'openoutput'); io_i = io_i + 1; % Interferomet
 %% Frequency vector [Hz]
 freqs = logspace(1, log10(2000), 1000);
 
-% Model dynamics
-% <<ssec:test_struts_comp_model>>
-
-
 %% Load measured FRF for comparison
 load('meas_struts_frf.mat', 'f', 'enc_frf', 'int_frf', 'iff_frf', 'strut_nums');
 
@@ -64,20 +60,6 @@ Gs_flex = exp(-s*1e-4)*linearize(mdl, io, 0.0, opts);
 Gs_flex.InputName  = {'u'};
 Gs_flex.OutputName = {'Vs', 'de', 'da'};
 
-
-
-% Two models of the APA300ML are used here: a simple two degrees of freedom model and a model using a super element extracted from a finite element model.
-% These two models of the APA300ML were tuned to best match measured frequency response functions of the APA alone.
-% The flexible joints are here modelled with the 4DoF model (axial stiffness, two bending stiffnesses and one torsion stiffness).
-% These two models are compared with the measured frequency responses in Figure ref:fig:test_struts_comp_frf_flexible_model.
-
-% The model dynamics from DAC voltage $u$ to the axial motion of the strut $d_a$ (Figure ref:fig:test_struts_comp_frf_flexible_model_int) and from DAC voltage $u$ to the force sensor voltage $V_s$ (Figure ref:fig:test_struts_comp_frf_flexible_model_iff) are well matching the experimental identification.
-
-% However, the transfer function from $u$ to encoder displacement $d_e$ are not well matching for both models.
-% For the 2DoF model, this is normal as the resonances affecting the dynamics are not modelled at all (the APA300ML is modelled as infinitely rigid in all directions except the translation along it's actuation axis).
-% For the flexible model, it will be shown in the next section that by adding some misalignment between the flexible joints and the APA300ML, this model can better represent the observed dynamics.
-
-
 %% Compare the FRF and identified dynamics from u to Vs and da
 figure;
 tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
@@ -202,36 +184,6 @@ linkaxes([ax1a,ax2a],'x');
 xlim([10, 2e3]);
 xticks([1e1, 1e2, 1e3]);
 
-% Effect of strut misalignment
-% <<ssec:test_struts_effect_misalignment>>
-
-% As was shown in Figure ref:fig:test_struts_comp_enc_plants, the identified dynamics from DAC voltage $u$ to encoder measured displacement $d_e$ are very different from one strut to the other.
-% In this section, it is investigated whether poor alignment of the strut (flexible joints with respect to the APA) can explain such dynamics.
-% For instance, consider Figure ref:fig:test_struts_misalign_schematic where there is a misalignment in the $y$ direction between the two flexible joints (well aligned thanks to the mounting procedure in Section ref:sec:test_struts_mounting) and the APA300ML.
-% In such case, the "x-bending" mode at 200Hz (see Figure ref:fig:test_struts_meas_x_bending) can be expected to have more impact on the dynamics from the actuator to the encoder.
-
-% #+name: fig:test_struts_misalign_schematic
-% #+caption: Mis-alignement between the joints and the APA
-% #+attr_latex: :width 0.8\linewidth
-% [[file:figs/test_struts_misalign_schematic.png]]
-
-% To verify this assumption, the dynamics from output DAC voltage $u$ to the measured displacement by the encoder $d_e$ is computed using the flexible APA Simscape model for several misalignment in the $y$ direction.
-% Obtained dynamics are shown in Figure ref:fig:test_struts_effect_misalignment_y.
-% The alignment of the APA with the flexible joints as a large influence on the dynamics from actuator voltage to measured displacement by the encoder.
-% The misalignment in the $y$ direction mostly influences:
-% - the presence of the flexible mode at 200Hz (see mode shape in Figure ref:fig:test_struts_mode_shapes_1)
-% - the location of the complex conjugate zero between the first two resonances:
-%   - if $d_{y} < 0$: there is no zero between the two resonances and possibly not even between the second and third ones
-%   - if $d_{y} > 0$: there is a complex conjugate zero between the first two resonances
-% - the location of the high frequency complex conjugate zeros at 500Hz (secondary effect, as the axial stiffness of the joint also has large effect on the position of this zero)
-
-% The same can be done for a misalignment in the $x$ direction.
-% The obtained dynamics (Figure ref:fig:test_struts_effect_misalignment_x) are showing that misalignment in the $x$ direction mostly influences the presence of the flexible mode at 300Hz (see mode shape in Figure ref:fig:test_struts_mode_shapes_2).
-
-% Comparing the experimental frequency response functions for all the APA in Figure ref:fig:test_struts_comp_enc_plants with the model dynamics for several $y$ misalignments in Figure ref:fig:test_struts_effect_misalignment_y indicates a clear similarity.
-% This similarity suggests that the identified differences in dynamics are caused by the misalignment.
-
-
 %% Effect of a misalignment in Y-Direction
 % Considered misalignment in the Y direction
 dy_aligns = [-0.5, -0.1, 0.1, 0.5]*1e-3; % [m]
@@ -338,23 +290,6 @@ linkaxes([ax1,ax2],'x');
 xlim([10, 2e3]);
 xticks([1e1, 1e2, 1e3]);
 
-% Measured strut misalignment
-% <<ssec:test_struts_meas_misalignment>>
-
-% During the initial mounting of the struts as presented in Section ref:sec:test_struts_mounting, the positioning pins that are used to position the APA with respect to the flexible joints in the $y$ directions were not used (not received at the time).
-% Therefore, large $y$ misalignments is expected.
-
-% In order to estimate the misalignments between the two flexible joints and the APA:
-% - the struts are fixed horizontally on the mounting bench as shown in Figure ref:fig:test_struts_mounting_step_3 but without the encoder
-% - using a length gauge[fn:2], the height difference from the flexible joints surface and the APA shell surface is measured both for the top and bottom joints and for both sides
-% - as the thickness of the flexible joint is $21\,mm$ and the thickness of the APA shell is $20\,mm$, $0.5\,mm$ of height different should be measured if the two are perfectly aligned
-
-% Large variations in the $y$ misalignment are found from one strut to the other (results are summarized in Table ref:tab:test_struts_meas_y_misalignment).
-
-% To check the validity of the measurement, it can be verified that sum of the measured thickness difference on each side is $1\,mm$ (equal to the thickness difference between the flexible joint and the APA).
-% This thickness differences for all the struts were found to be between $0.94\,mm$ and $1.00\,mm$ which indicate low errors as compared to the misalignments found in Table ref:tab:test_struts_meas_y_misalignment.
-
-
 %% Measurement of the y misalignment between the APA and the flexible joints
 % Mesured struts
 strut_nums = [1, 2, 3, 4, 5];
@@ -376,31 +311,6 @@ thichness_diff_bot = strut_align(:,1) + strut_align(:,2); % [mm]
 dy_bot = (strut_align(:,1) - strut_align(:,2))/2; % [mm]
 dy_top = (strut_align(:,3) - strut_align(:,4))/2; % [mm]
 
-
-
-% #+name: tab:test_struts_meas_y_misalignment
-% #+caption: Measured $y$ misalignment at the top and bottom of the APA. Measurements are in $mm$
-% #+attr_latex: :environment tabularx :width 0.25\linewidth :align ccc
-% #+attr_latex: :center t :booktabs t
-% #+RESULTS:
-% | *Strut* | *Bot* | *Top* |
-% |---------+-------+-------|
-% |       1 |   0.1 |  0.33 |
-% |       2 | -0.19 |  0.14 |
-% |       3 |  0.41 |  0.32 |
-% |       4 | -0.01 |  0.54 |
-% |       5 |  0.15 |  0.02 |
-
-% By using the measured $y$ misalignment in the Simscape model with the flexible APA model, the model dynamics from $u$ to $d_e$ is closer to the measured one as shown in Figure ref:fig:test_struts_comp_dy_tuned_model_frf_enc.
-% Better match in the dynamics can be obtained by fine tuning both the $x$ and $y$ misalignments (yellow curves in Figure ref:fig:test_struts_comp_dy_tuned_model_frf_enc).
-
-% This confirms that the misalignment between the APA and the strut axis (determined by the two flexible joints) is critical and is inducing large variations in the dynamics from DAC voltage $u$ to encoder measured displacement $d_e$.
-% If encoders are fixed to the struts, it is important to precisely align the APA and the flexible joints when mounting the struts.
-
-% In the next section, the struts are re-assembled with a "positioning pin" to better align the APA with the flexible joints.
-% With a better alignment, the amplitude of the spurious resonances are expected to decrease as was shown in Figure ref:fig:test_struts_effect_misalignment_y.
-
-
 %% Idenfity the dynamics from u to de - misalignement estimated from measurement
 Gs_y_align = {zeros(size(strut_align,1), 1)};
 
@@ -496,16 +406,6 @@ xticks([1e1, 1e2, 1e3]);
 linkaxes([ax1,ax2,ax3],'xy');
 xlim([10, 2e3]); ylim([1e-8, 1e-3]);
 
-% Proper struts alignment
-% <<sec:test_struts_meas_all_aligned_struts>>
-
-% After the positioning pins had been received, the struts were mounted again with the positioning pins.
-% This should make the APA better aligned with the two flexible joints.
-
-% This alignment is then estimated using a length gauge as in the previous sections.
-% Measured $y$ alignments are summarized in Table ref:tab:test_struts_meas_y_misalignment_with_pin and are found to be bellow $55\mu m$ for all the struts which is much better than before (see Table ref:tab:test_struts_meas_y_misalignment).
-
-
 %% Measurement of the y misalignment between the APA and the flexible joints after strut better alignment
 
 % Numbers of the measured legs
@@ -529,31 +429,6 @@ thichness_diff_bot = strut_align(:,1) + strut_align(:,2); % [mm]
 dy_bot = (strut_align(:,1) - strut_align(:,2))/2; % [mm]
 dy_top = (strut_align(:,3) - strut_align(:,4))/2; % [mm]
 
-
-
-% #+name: tab:test_struts_meas_y_misalignment_with_pin
-% #+caption: Measured $y$ misalignment at the top and bottom of the APA after realigning the struts using a positioning pin. Measurements are in $mm$.
-% #+attr_latex: :environment tabularx :width 0.25\linewidth :align ccc
-% #+attr_latex: :center t :booktabs t
-% #+RESULTS:
-% | *Strut* |  *Bot* | *Top* |
-% |---------+--------+-------|
-% |       1 |  -0.02 |  0.01 |
-% |       2 |  0.055 |   0.0 |
-% |       3 |   0.01 | -0.02 |
-% |       4 |   0.03 | -0.03 |
-% |       5 |    0.0 |   0.0 |
-% |       6 | -0.005 | 0.055 |
-
-% The dynamics of the re-aligned struts are then measured using the same test bench (Figure ref:fig:test_struts_bench_leg).
-% The comparison of the initial strut dynamics and the dynamics of the re-aligned struts (i.e. with the positioning pin) is made in Figure ref:fig:test_struts_comp_enc_frf_realign.
-% Even though the struts are now much better aligned, not much improvement can be observed.
-% Also, the dynamics of the six aligned struts are quite different from one another.
-
-% Having the encoders fixed to the struts are making the control more challenging.
-% Therefore, the encoders may be fixed to the nano-hexapod plates instead.
-
-
 %% New dynamical identified with re-aligned struts
 % Load the identification data
 leg_noise = {};

test-bench-struts.org

@@ -22,7 +22,7 @@
 # #+BIND: org-latex-bib-compiler "biber"
 
 #+PROPERTY: header-args:matlab  :session *MATLAB*
-#+PROPERTY: header-args:matlab+ :comments org
+#+PROPERTY: header-args:matlab+ :comments no
 #+PROPERTY: header-args:matlab+ :exports none
 #+PROPERTY: header-args:matlab+ :results none
 #+PROPERTY: header-args:matlab+ :eval no-export
@@ -87,7 +87,7 @@
 #+END_SRC
 
 * Notes                                                             :noexport:
-
+** Notes
 Prefix for figures/section/tables =test_struts=
 
 To integrate:
@@ -297,7 +297,7 @@ Using this method, an axial stiffness of $70 N/\mu m$ is found to give good resu
 
 * Introduction                                                        :ignore:
 
-The Nano-Hexapod struts (shown in Figure ref:fig:test_struts_picture_strut) are composed of two flexible joints that are fixed at the two ends of the strut, one acrfull:apa[fn:5] and one optical encoder[fn:6].
+The Nano-Hexapod struts (shown in Figure ref:fig:test_struts_picture_strut) are composed of two flexible joints that are fixed at the two ends of the strut, one Amplified Piezeolectric Actuator [fn:test_struts_5] and one optical encoder[fn:test_struts_6].
 
 #+name: fig:test_struts_picture_strut
 #+caption: One strut including two flexible joints, an amplified piezoelectric actuator and an encoder
@@ -319,19 +319,8 @@ The model dynamics from the acrshort:dac voltage to the axial motion of the stru
 However, this is not the case for the dynamics from acrshort:dac voltage to the encoder displacement.
 It is found that the complex dynamics is due to a misalignment between the flexible joints and the acrshort:apa.
 
-# #+name: tab:test_struts_section_matlab_code
-# #+caption: Report sections and corresponding Matlab files
-# #+attr_latex: :environment tabularx :width 0.6\linewidth :align lX
-# #+attr_latex: :center t :booktabs t
-# | *Sections*                                 | *Matlab File*                    |
-# |--------------------------------------------+----------------------------------|
-# | Section ref:sec:test_struts_flexible_modes | =test_struts_1_flexible_modes.m= |
-# | Section ref:sec:test_struts_dynamical_meas | =test_struts_2_dynamical_meas.m= |
-# | Section ref:sec:test_struts_simscape       | =test_struts_3_simscape_model’m= |
-
 * Mounting Procedure
 <<sec:test_struts_mounting>>
-** Introduction                                                      :ignore:
 
 A mounting bench was developed to ensure:
 - Good coaxial alignment between the interfaces (cylinders) of the flexible joints.
@@ -340,13 +329,11 @@ A mounting bench was developed to ensure:
 - Precise alignment of the APA with the two flexible joints
 - Reproducible and consistent assembly between all struts
 
-** Mounting Bench
-
 A CAD view of the mounting bench is shown in Figure ref:fig:test_struts_mounting_bench_first_concept.
 It consists of a "main frame" (Figure ref:fig:test_struts_mounting_step_0) precisely machined to ensure both correct strut length and strut coaxiality.
 The coaxiality is ensured by good flatness (specified at $20\,\mu m$) between surfaces A and B and between surfaces C and D.
-Such flatness was checked using a Faro arm[fn:1] (see Figure ref:fig:test_struts_check_dimensions_bench) and was found to comply with the requirements.
-The strut length (defined by the distance between the rotation points of the two flexible joints) was ensured by using precisely machines dowel holes.
+Such flatness was checked using a FARO arm[fn:test_struts_1] (see Figure ref:fig:test_struts_check_dimensions_bench) and was found to comply with the requirements.
+The strut length (defined by the distance between the rotation points of the two flexible joints) was ensured by using precisely machined dowel holes.
 
 
 #+name: fig:test_struts_mounting
@@ -413,8 +400,6 @@ These "sleeves" have one dowel groove (that are fitted to the dowel holes shown
 #+end_subfigure
 #+end_figure
 
-** Mounting Procedure
-
 The "sleeves" were mounted to the main element as shown in Figure ref:fig:test_struts_mounting_step_0.
 The left sleeve has a thigh fit such that its orientation is fixed (it is roughly aligned horizontally), while the right sleeve has a loose fit such that it can rotate (it will get the same orientation as the fixed one when tightening the screws).
 
@@ -464,11 +449,10 @@ Thanks to this mounting procedure, the coaxiality and length between the two fle
 :header-args:matlab+: :tangle matlab/test_struts_1_flexible_modes.m
 :END:
 <<sec:test_struts_flexible_modes>>
-** Introduction
 
-A Finite Element Model[fn:3] of the struts is developed and is used to estimate the flexible modes.
+A Finite Element Model[fn:test_struts_3] of the struts is developed and is used to estimate the flexible modes.
 The inertia of the encoder (estimated at $15\,g$) is considered.
-The two cylindrical interfaces were fixed, and the first three flexible modes were computed.
+The two cylindrical interfaces were fixed (boundary conditions), and the first three flexible modes were computed.
 The mode shapes are displayed in Figure ref:fig:test_struts_mode_shapes: an "X-bending" mode at 189Hz, a "Y-bending" mode at 285Hz and a "Z-torsion" mode at 400Hz.
 
 #+name: fig:test_struts_mode_shapes
@@ -495,7 +479,6 @@ The mode shapes are displayed in Figure ref:fig:test_struts_mode_shapes: an "X-b
 #+end_subfigure
 #+end_figure
 
-** Matlab Init                                              :noexport:ignore:
 #+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
 <<matlab-dir>>
 #+end_src
@@ -516,9 +499,7 @@ The mode shapes are displayed in Figure ref:fig:test_struts_mode_shapes: an "X-b
 <<m-init-other>>
 #+end_src
 
-** Measurement Setup
-
-To experimentally measure these mode shapes, a Laser vibrometer[fn:7] was used.
+To experimentally measure these mode shapes, a Laser vibrometer[fn:test_struts_7] was used.
 It measures the difference of motion between two beam path (red points in Figure ref:fig:test_struts_meas_modes).
 The strut is then excited by an instrumented hammer, and the transfer function from the hammer to the measured rotation is computed.
 
@@ -550,7 +531,6 @@ These tests were performed with and without the encoder being fixed to the strut
 #+end_subfigure
 #+end_figure
 
-** Measured results
 The obtained frequency response functions for the three configurations (X-bending, Y-bending and Z-torsion) are shown in Figure ref:fig:test_struts_spur_res_frf_no_enc when the encoder is not fixed to the strut and in Figure ref:fig:test_struts_spur_res_frf_enc when the encoder is fixed to the strut.
 
 #+begin_src matlab :exports none
@@ -659,7 +639,7 @@ In order to measure the dynamics of the strut, the test bench used to measure th
 
 The strut mounted on the bench is shown in Figure ref:fig:test_struts_bench_leg_overview
 A schematic of the bench and the associated signals are shown in Figure ref:fig:test_struts_bench_schematic.
-A fiber interferometer[fn:4] is used to measure the motion of the granite (i.e. the axial motion of the strut).
+A fiber interferometer[fn:test_struts_4] is used to measure the motion of the granite (i.e. the axial motion of the strut).
 
 #+name: fig:test_struts_bench_leg
 #+caption: Experimental setup used to measure the dynamics of the struts.
@@ -1122,6 +1102,7 @@ The same comparison is made for the transfer function from $u$ to $d_e$ (encoder
 In this study, large dynamics differences were observed between the 5 struts.
 Although the same resonance frequencies were seen for all of the struts (95Hz, 200Hz, 300Hz and 400Hz), the amplitude of the peaks were not the same.
 In addition, the location or even presence of complex conjugate zeros changes from one strut to another.
+The reason for this variability will be studied in the next section thanks to the strut model.
 
 #+begin_src matlab :tangle no :exports none
 %% Save the estimated FRF for further analysis
@@ -1133,15 +1114,6 @@ save('./matlab/mat/meas_struts_frf.mat', 'f', 'enc_frf', 'int_frf', 'iff_frf', '
 save('./mat/meas_struts_frf.mat', 'f', 'enc_frf', 'int_frf', 'iff_frf', 'strut_nums');
 #+end_src
 
-** Conclusion
-:PROPERTIES:
-:UNNUMBERED: t
-:END:
-
-All the struts exhibit very consistent behavior from the excitation voltage $u$ to the force sensor generated voltage $V_s$ and to the interferometer measured displacement $d_a$.
-However, the dynamics from $u$ to the encoder measurement $d_e$ is much more complex and vary from one strut to the another.
-The reason for this variability will be studied in the next section thanks to the strut model.
-
 * Strut Model
 :PROPERTIES:
 :header-args:matlab+: :tangle matlab/test_struts_3_simscape_model.m
@@ -1149,7 +1121,7 @@ The reason for this variability will be studied in the next section thanks to th
 <<sec:test_struts_simscape>>
 ** Introduction                                                      :ignore:
 
-The Simscape model of the strut was included in the Simscape model of the test bench (see Figure ref:fig:test_struts_simscape_model).
+The multi-body model of the strut was included in the multi-body model of the test bench (see Figure ref:fig:test_struts_simscape_model).
 The obtained model was first used to compare the measured FRF with the existing model (Section ref:ssec:test_struts_comp_model).
 
 Using a flexible APA model (extracted from a acrshort:fem), the effect of a misalignment of the APA with respect to flexible joints is studied (Section ref:ssec:test_struts_effect_misalignment).
@@ -1158,7 +1130,7 @@ This misalignment is estimated and measured in Section ref:ssec:test_struts_meas
 The struts were then disassembled and reassemble a second time to optimize alignment (Section ref:sec:test_struts_meas_all_aligned_struts).
 
 #+name: fig:test_struts_simscape_model
-#+caption: Screenshot of the Simscape model of the strut fixed to the bench
+#+caption: Screenshot of the multi-body model of the strut fixed to the bench
 #+attr_latex: :width 0.65\linewidth
 [[file:figs/test_struts_simscape_model.png]]
 
@@ -1393,7 +1365,7 @@ exportFig('figs/test_struts_comp_frf_flexible_model_iff.pdf', 'width', 400, 'hei
 #+end_src
 
 #+name: fig:test_struts_comp_frf_flexible_model
-#+caption: Comparison of the measured frequency response functions, the Simscape model using the 2 DoF APA model, and using the "flexible" APA300ML model (Super-Element extracted from a Finite Element Model).
+#+caption: Comparison of the measured frequency response functions, the multi-body model using the 2 DoF APA model, and using the "flexible" APA300ML model (Super-Element extracted from a Finite Element Model).
 #+attr_latex: :options [htbp]
 #+begin_figure
 #+attr_latex: :caption \subcaption{\label{fig:test_struts_comp_frf_flexible_model_int}$u$ to $d_a$}
@@ -1429,7 +1401,7 @@ In this case, the "x-bending" mode at 200Hz (see Figure ref:fig:test_struts_meas
 #+attr_latex: :width 0.8\linewidth
 [[file:figs/test_struts_misalign_schematic.png]]
 
-To verify this assumption, the dynamics from the output DAC voltage $u$ to the measured displacement by the encoder $d_e$ is computed using the flexible APA Simscape model for several misalignments in the $y$ direction.
+To verify this assumption, the dynamics from the output DAC voltage $u$ to the measured displacement by the encoder $d_e$ is computed using the flexible APA model for several misalignments in the $y$ direction.
 The obtained dynamics are shown in Figure ref:fig:test_struts_effect_misalignment_y.
 The alignment of the APA with the flexible joints has a large influence on the dynamics from actuator voltage to the measured displacement by the encoder.
 The misalignment in the $y$ direction mostly influences:
@@ -1591,7 +1563,7 @@ Therefore, large $y$ misalignments are expected.
 
 To estimate the misalignments between the two flexible joints and the APA:
 - the struts were fixed horizontally on the mounting bench, as shown in Figure ref:fig:test_struts_mounting_step_3 but without the encoder
-- using a length gauge[fn:2], the height difference between the flexible joints surface and the APA shell surface was measured for both the top and bottom joints and for both sides
+- using a length gauge[fn:test_struts_2], the height difference between the flexible joints surface and the APA shell surface was measured for both the top and bottom joints and for both sides
 - as the thickness of the flexible joint is $21\,mm$ and the thickness of the APA shell is $20\,mm$, $0.5\,mm$ of height difference should be measured if the two are perfectly aligned
 
 Large variations in the $y$ misalignment are found from one strut to the other (results are summarized in Table ref:tab:test_struts_meas_y_misalignment).
@@ -1639,7 +1611,7 @@ data2orgtable([dy_bot, dy_top] , {'1', '2', '3', '4', '5'}, {'*Strut*', '*Bot*',
 |       4 | -0.01 |  0.54 |
 |       5 |  0.15 |  0.02 |
 
-By using the measured $y$ misalignment in the Simscape model with the flexible APA model, the model dynamics from $u$ to $d_e$ is closer to the measured dynamics, as shown in Figure ref:fig:test_struts_comp_dy_tuned_model_frf_enc.
+By using the measured $y$ misalignment in the model with the flexible APA model, the model dynamics from $u$ to $d_e$ is closer to the measured dynamics, as shown in Figure ref:fig:test_struts_comp_dy_tuned_model_frf_enc.
 A better match in the dynamics can be obtained by fine-tuning both the $x$ and $y$ misalignments (yellow curves in Figure ref:fig:test_struts_comp_dy_tuned_model_frf_enc).
 
 This confirms that misalignment between the APA and the strut axis (determined by the two flexible joints) is critical and inducing large variations in the dynamics from DAC voltage $u$ to encoder measured displacement $d_e$.
@@ -1875,6 +1847,9 @@ exportFig('figs/test_struts_comp_enc_frf_realign.pdf', 'width', 'wide', 'height'
 [[file:figs/test_struts_comp_enc_frf_realign.png]]
 
 * Conclusion
+:PROPERTIES:
+:UNNUMBERED: t
+:END:
 <<sec:test_struts_conclusion>>
 
 The Hano-Hexapod struts are a key component of the developed acrfull:nass.
@@ -2288,10 +2263,10 @@ actuator.cs = args.cs; % Damping of one stack [N/m]
 
 * Footnotes
 
-[fn:7] OFV-3001 controller and OFV512 sensor head from Polytec
-[fn:6] Vionic from Renishaw
-[fn:5] APA300ML from Cedrat Technologies
-[fn:4] Two fiber intereferometers were used: an IDS3010 from Attocube and a quDIS from QuTools
-[fn:3] Using Ansys\textsuperscript{\textregistered}. Flexible Joints and APA Shell are made of a stainless steel allow called /17-4 PH/. Encoder and ruler support material is aluminium.
-[fn:2] Heidenhain MT25, specified accuracy of $\pm 0.5\,\mu m$
-[fn:1] Faro Arm Platinum 4ft, specified accuracy of $\pm 13\mu m$
+[fn:test_struts_7] OFV-3001 controller and OFV512 sensor head from Polytec
+[fn:test_struts_6] Vionic from Renishaw
+[fn:test_struts_5] APA300ML from Cedrat Technologies
+[fn:test_struts_4] Two fiber intereferometers were used: an IDS3010 from Attocube and a quDIS from QuTools
+[fn:test_struts_3] Using Ansys\textsuperscript{\textregistered}. Flexible Joints and APA Shell are made of a stainless steel allow called /17-4 PH/. Encoder and ruler support material is aluminium.
+[fn:test_struts_2] Heidenhain MT25, specified accuracy of $\pm 0.5\,\mu m$
+[fn:test_struts_1] FARO Arm Platinum 4ft, specified accuracy of $\pm 13\mu m$

test-bench-struts.tex

@@ -1,4 +1,4 @@
-% Created 2024-10-25 Fri 17:22
+% Created 2025-04-03 Thu 22:09
 % Intended LaTeX compiler: pdflatex
 \documentclass[a4paper, 10pt, DIV=12, parskip=full, bibliography=totoc]{scrreprt}
 
@@ -11,13 +11,6 @@
 \author{Dehaeze Thomas}
 \date{\today}
 \title{Test Bench - Nano-Hexapod Struts}
-\hypersetup{
- pdfauthor={Dehaeze Thomas},
- pdftitle={Test Bench - Nano-Hexapod Struts},
- pdfkeywords={},
- pdfsubject={},
- pdfcreator={Emacs 29.4 (Org mode 9.6)}, 
- pdflang={English}}
 \usepackage{biblatex}
 
 \begin{document}
@@ -26,8 +19,7 @@
 \tableofcontents
 
 \clearpage
-
-The Nano-Hexapod struts (shown in Figure \ref{fig:test_struts_picture_strut}) are composed of two flexible joints that are fixed at the two ends of the strut, one \acrfull{apa}\footnote{APA300ML from Cedrat Technologies} and one optical encoder\footnote{Vionic from Renishaw}.
+The Nano-Hexapod struts (shown in Figure \ref{fig:test_struts_picture_strut}) are composed of two flexible joints that are fixed at the two ends of the strut, one Amplified Piezeolectric Actuator \footnote{APA300ML from Cedrat Technologies} and one optical encoder\footnote{Vionic from Renishaw}.
 
 \begin{figure}[htbp]
 \centering
@@ -49,10 +41,9 @@ The strut models were then compared with the measured dynamics (Section \ref{sec
 The model dynamics from the \acrshort{dac} voltage to the axial motion of the strut (measured by an interferometer) and to the force sensor voltage well match the experimental results.
 However, this is not the case for the dynamics from \acrshort{dac} voltage to the encoder displacement.
 It is found that the complex dynamics is due to a misalignment between the flexible joints and the \acrshort{apa}.
-
-
 \chapter{Mounting Procedure}
 \label{sec:test_struts_mounting}
+
 A mounting bench was developed to ensure:
 \begin{itemize}
 \item Good coaxial alignment between the interfaces (cylinders) of the flexible joints.
@@ -61,13 +52,12 @@ This is important not to loose to much angular stroke during their mounting into
 \item Precise alignment of the APA with the two flexible joints
 \item Reproducible and consistent assembly between all struts
 \end{itemize}
-\section{Mounting Bench}
 
 A CAD view of the mounting bench is shown in Figure \ref{fig:test_struts_mounting_bench_first_concept}.
 It consists of a ``main frame'' (Figure \ref{fig:test_struts_mounting_step_0}) precisely machined to ensure both correct strut length and strut coaxiality.
 The coaxiality is ensured by good flatness (specified at \(20\,\mu m\)) between surfaces A and B and between surfaces C and D.
-Such flatness was checked using a Faro arm\footnote{Faro Arm Platinum 4ft, specified accuracy of \(\pm 13\mu m\)} (see Figure \ref{fig:test_struts_check_dimensions_bench}) and was found to comply with the requirements.
-The strut length (defined by the distance between the rotation points of the two flexible joints) was ensured by using precisely machines dowel holes.
+Such flatness was checked using a FARO arm\footnote{FARO Arm Platinum 4ft, specified accuracy of \(\pm 13\mu m\)} (see Figure \ref{fig:test_struts_check_dimensions_bench}) and was found to comply with the requirements.
+The strut length (defined by the distance between the rotation points of the two flexible joints) was ensured by using precisely machined dowel holes.
 
 
 \begin{figure}[htbp]
@@ -128,8 +118,6 @@ These ``sleeves'' have one dowel groove (that are fitted to the dowel holes show
 \caption{\label{fig:test_struts_cylindrical_mounting}Preparation of the flexible joints by fixing them in their cylindrical ``sleeve''}
 \end{figure}
 
-\section{Mounting Procedure}
-
 The ``sleeves'' were mounted to the main element as shown in Figure \ref{fig:test_struts_mounting_step_0}.
 The left sleeve has a thigh fit such that its orientation is fixed (it is roughly aligned horizontally), while the right sleeve has a loose fit such that it can rotate (it will get the same orientation as the fixed one when tightening the screws).
 
@@ -171,14 +159,12 @@ Thanks to this mounting procedure, the coaxiality and length between the two fle
 \end{subfigure}
 \caption{\label{fig:test_struts_mounting_steps}Steps for mounting the struts.}
 \end{figure}
-
 \chapter{Measurement of flexible modes}
 \label{sec:test_struts_flexible_modes}
-\section{Introduction}
 
 A Finite Element Model\footnote{Using Ansys\textsuperscript{\textregistered}. Flexible Joints and APA Shell are made of a stainless steel allow called \emph{17-4 PH}. Encoder and ruler support material is aluminium.} of the struts is developed and is used to estimate the flexible modes.
 The inertia of the encoder (estimated at \(15\,g\)) is considered.
-The two cylindrical interfaces were fixed, and the first three flexible modes were computed.
+The two cylindrical interfaces were fixed (boundary conditions), and the first three flexible modes were computed.
 The mode shapes are displayed in Figure \ref{fig:test_struts_mode_shapes}: an ``X-bending'' mode at 189Hz, a ``Y-bending'' mode at 285Hz and a ``Z-torsion'' mode at 400Hz.
 
 \begin{figure}[htbp]
@@ -203,8 +189,6 @@ The mode shapes are displayed in Figure \ref{fig:test_struts_mode_shapes}: an ``
 \caption{\label{fig:test_struts_mode_shapes}Spurious resonances of the struts estimated from a Finite Element Model}
 \end{figure}
 
-\section{Measurement Setup}
-
 To experimentally measure these mode shapes, a Laser vibrometer\footnote{OFV-3001 controller and OFV512 sensor head from Polytec} was used.
 It measures the difference of motion between two beam path (red points in Figure \ref{fig:test_struts_meas_modes}).
 The strut is then excited by an instrumented hammer, and the transfer function from the hammer to the measured rotation is computed.
@@ -235,7 +219,6 @@ These tests were performed with and without the encoder being fixed to the strut
 \caption{\label{fig:test_struts_meas_modes}Measurement of strut flexible modes}
 \end{figure}
 
-\section{Measured results}
 The obtained frequency response functions for the three configurations (X-bending, Y-bending and Z-torsion) are shown in Figure \ref{fig:test_struts_spur_res_frf_no_enc} when the encoder is not fixed to the strut and in Figure \ref{fig:test_struts_spur_res_frf_enc} when the encoder is fixed to the strut.
 
 \begin{figure}[htbp]
@@ -260,7 +243,6 @@ In addition, the computed resonance frequencies from the \acrshort{fem} are very
 This validates the quality of the \acrshort{fem}.
 
 \begin{table}[htbp]
-\caption{\label{tab:test_struts_spur_mode_freqs}Measured frequency of the flexible modes of the strut}
 \centering
 \begin{tabularx}{0.9\linewidth}{Xccc}
 \toprule
@@ -271,8 +253,9 @@ Y-Bending & 285Hz & 293Hz & 337Hz\\
 Z-Torsion & 400Hz & 381Hz & 398Hz\\
 \bottomrule
 \end{tabularx}
-\end{table}
+\caption{\label{tab:test_struts_spur_mode_freqs}Measured frequency of the flexible modes of the strut}
 
+\end{table}
 \chapter{Dynamical measurements}
 \label{sec:test_struts_dynamical_meas}
 In order to measure the dynamics of the strut, the test bench used to measure the APA300ML dynamics is being used again.
@@ -348,7 +331,6 @@ This means that the encoder should have little effect on the effectiveness of th
 \end{subfigure}
 \caption{\label{fig:test_struts_effect_encoder}Effect of having the encoder fixed to the struts on the measured dynamics from \(u\) to \(d_a\) (\subref{fig:test_struts_effect_encoder_int}) and from \(u\) to \(V_s\) (\subref{fig:test_struts_effect_encoder_iff}). Comparison of the observed dynamics by the encoder and interferometers (\subref{fig:test_struts_comp_enc_int})}
 \end{figure}
-
 \section{Comparison of the encoder and interferometer}
 \label{ssec:test_struts_comp_enc_int}
 
@@ -359,7 +341,6 @@ These resonance frequencies match the frequencies of the flexible modes studied
 
 The good news is that these resonances are not impacting the axial motion of the strut (which is what is important for the hexapod positioning).
 However, these resonances make the use of an encoder fixed to the strut difficult from a control perspective.
-
 \section{Comparison of all the Struts}
 \label{ssec:test_struts_comp_all_struts}
 
@@ -393,15 +374,10 @@ The same comparison is made for the transfer function from \(u\) to \(d_e\) (enc
 In this study, large dynamics differences were observed between the 5 struts.
 Although the same resonance frequencies were seen for all of the struts (95Hz, 200Hz, 300Hz and 400Hz), the amplitude of the peaks were not the same.
 In addition, the location or even presence of complex conjugate zeros changes from one strut to another.
-
-\section*{Conclusion}
-All the struts exhibit very consistent behavior from the excitation voltage \(u\) to the force sensor generated voltage \(V_s\) and to the interferometer measured displacement \(d_a\).
-However, the dynamics from \(u\) to the encoder measurement \(d_e\) is much more complex and vary from one strut to the another.
 The reason for this variability will be studied in the next section thanks to the strut model.
-
 \chapter{Strut Model}
 \label{sec:test_struts_simscape}
-The Simscape model of the strut was included in the Simscape model of the test bench (see Figure \ref{fig:test_struts_simscape_model}).
+The multi-body model of the strut was included in the multi-body model of the test bench (see Figure \ref{fig:test_struts_simscape_model}).
 The obtained model was first used to compare the measured FRF with the existing model (Section \ref{ssec:test_struts_comp_model}).
 
 Using a flexible APA model (extracted from a \acrshort{fem}), the effect of a misalignment of the APA with respect to flexible joints is studied (Section \ref{ssec:test_struts_effect_misalignment}).
@@ -412,7 +388,7 @@ The struts were then disassembled and reassemble a second time to optimize align
 \begin{figure}[htbp]
 \centering
 \includegraphics[scale=1,width=0.65\linewidth]{figs/test_struts_simscape_model.png}
-\caption{\label{fig:test_struts_simscape_model}Screenshot of the Simscape model of the strut fixed to the bench}
+\caption{\label{fig:test_struts_simscape_model}Screenshot of the multi-body model of the strut fixed to the bench}
 \end{figure}
 \section{Model dynamics}
 \label{ssec:test_struts_comp_model}
@@ -447,9 +423,8 @@ For the flexible model, it will be shown in the next section that by adding some
 \end{center}
 \subcaption{\label{fig:test_struts_comp_frf_flexible_model_iff}$u$ to $V_s$}
 \end{subfigure}
-\caption{\label{fig:test_struts_comp_frf_flexible_model}Comparison of the measured frequency response functions, the Simscape model using the 2 DoF APA model, and using the ``flexible'' APA300ML model (Super-Element extracted from a Finite Element Model).}
+\caption{\label{fig:test_struts_comp_frf_flexible_model}Comparison of the measured frequency response functions, the multi-body model using the 2 DoF APA model, and using the ``flexible'' APA300ML model (Super-Element extracted from a Finite Element Model).}
 \end{figure}
-
 \section{Effect of strut misalignment}
 \label{ssec:test_struts_effect_misalignment}
 
@@ -464,7 +439,7 @@ In this case, the ``x-bending'' mode at 200Hz (see Figure \ref{fig:test_struts_m
 \caption{\label{fig:test_struts_misalign_schematic}Mis-alignement between the joints and the APA}
 \end{figure}
 
-To verify this assumption, the dynamics from the output DAC voltage \(u\) to the measured displacement by the encoder \(d_e\) is computed using the flexible APA Simscape model for several misalignments in the \(y\) direction.
+To verify this assumption, the dynamics from the output DAC voltage \(u\) to the measured displacement by the encoder \(d_e\) is computed using the flexible APA model for several misalignments in the \(y\) direction.
 The obtained dynamics are shown in Figure \ref{fig:test_struts_effect_misalignment_y}.
 The alignment of the APA with the flexible joints has a large influence on the dynamics from actuator voltage to the measured displacement by the encoder.
 The misalignment in the \(y\) direction mostly influences:
@@ -499,7 +474,6 @@ This similarity suggests that the identified differences in dynamics are caused
 \end{subfigure}
 \caption{\label{fig:test_struts_effect_misalignment}Effect of a misalignment between the flexible joints and the APA300ML in the \(y\) direction (\subref{fig:test_struts_effect_misalignment_y}) and in the \(x\) direction (\subref{fig:test_struts_effect_misalignment_x})}
 \end{figure}
-
 \section{Measured strut misalignment}
 \label{ssec:test_struts_meas_misalignment}
 
@@ -519,7 +493,6 @@ To check the validity of the measurement, it can be verified that the sum of the
 Thickness differences for all the struts were found to be between \(0.94\,mm\) and \(1.00\,mm\) which indicate low errors compared to the misalignments found in Table \ref{tab:test_struts_meas_y_misalignment}.
 
 \begin{table}[htbp]
-\caption{\label{tab:test_struts_meas_y_misalignment}Measured \(y\) misalignment at the top and bottom of the APA. Measurements are in \(mm\)}
 \centering
 \begin{tabularx}{0.25\linewidth}{ccc}
 \toprule
@@ -532,9 +505,11 @@ Thickness differences for all the struts were found to be between \(0.94\,mm\) a
 5 & 0.15 & 0.02\\
 \bottomrule
 \end{tabularx}
+\caption{\label{tab:test_struts_meas_y_misalignment}Measured \(y\) misalignment at the top and bottom of the APA. Measurements are in \(mm\)}
+
 \end{table}
 
-By using the measured \(y\) misalignment in the Simscape model with the flexible APA model, the model dynamics from \(u\) to \(d_e\) is closer to the measured dynamics, as shown in Figure \ref{fig:test_struts_comp_dy_tuned_model_frf_enc}.
+By using the measured \(y\) misalignment in the model with the flexible APA model, the model dynamics from \(u\) to \(d_e\) is closer to the measured dynamics, as shown in Figure \ref{fig:test_struts_comp_dy_tuned_model_frf_enc}.
 A better match in the dynamics can be obtained by fine-tuning both the \(x\) and \(y\) misalignments (yellow curves in Figure \ref{fig:test_struts_comp_dy_tuned_model_frf_enc}).
 
 This confirms that misalignment between the APA and the strut axis (determined by the two flexible joints) is critical and inducing large variations in the dynamics from DAC voltage \(u\) to encoder measured displacement \(d_e\).
@@ -548,7 +523,6 @@ With a better alignment, the amplitude of the spurious resonances is expected to
 \includegraphics[scale=1]{figs/test_struts_comp_dy_tuned_model_frf_enc.png}
 \caption{\label{fig:test_struts_comp_dy_tuned_model_frf_enc}Comparison of the frequency response functions from DAC voltage \(u\) to measured displacement \(d_e\) by the encoders for the three struts. In blue, the measured dynamics is represted, in red the dynamics extracted from the model with the \(y\) misalignment estimated from measurements, and in yellow, the dynamics extracted from the model when both the \(x\) and \(y\) misalignments are tuned}
 \end{figure}
-
 \section{Proper struts alignment}
 \label{sec:test_struts_meas_all_aligned_struts}
 
@@ -559,7 +533,6 @@ The alignment is then estimated using a length gauge, as described in the previo
 Measured \(y\) alignments are summarized in Table \ref{tab:test_struts_meas_y_misalignment_with_pin} and are found to be bellow \(55\mu m\) for all the struts, which is much better than before (see Table \ref{tab:test_struts_meas_y_misalignment}).
 
 \begin{table}[htbp]
-\caption{\label{tab:test_struts_meas_y_misalignment_with_pin}Measured \(y\) misalignment at the top and bottom of the APA after realigning the struts using a positioning pin. Measurements are in \(mm\).}
 \centering
 \begin{tabularx}{0.25\linewidth}{ccc}
 \toprule
@@ -573,6 +546,8 @@ Measured \(y\) alignments are summarized in Table \ref{tab:test_struts_meas_y_mi
 6 & -0.005 & 0.055\\
 \bottomrule
 \end{tabularx}
+\caption{\label{tab:test_struts_meas_y_misalignment_with_pin}Measured \(y\) misalignment at the top and bottom of the APA after realigning the struts using a positioning pin. Measurements are in \(mm\).}
+
 \end{table}
 
 The dynamics of the re-aligned struts were then measured on the same test bench (Figure \ref{fig:test_struts_bench_leg}).
@@ -588,8 +563,7 @@ Therefore, fixing the encoders to the nano-hexapod plates instead may be an inte
 \includegraphics[scale=1]{figs/test_struts_comp_enc_frf_realign.png}
 \caption{\label{fig:test_struts_comp_enc_frf_realign}Comparison of the dynamics from \(u\) to \(d_e\) before and after proper alignment using the dowel pins}
 \end{figure}
-
-\chapter{Conclusion}
+\chapter*{Conclusion}
 \label{sec:test_struts_conclusion}
 
 The Hano-Hexapod struts are a key component of the developed \acrfull{nass}.
@@ -600,6 +574,5 @@ Thanks to a \acrshort{fem} and experimental measurements, the modes inducing thi
 The variability in the dynamics was attributed to the poor alignment of the \acrshort{apa} with respect to the flexible joints.
 Even with better alignment using dowel pins, the observed dynamics by the encoder remained problematic.
 Therefore, the encoders will be fixed directly to the nano-hexapod plates rather than being fixed to the struts.
-
 \printglossaries
 \end{document}