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Thomas Dehaeze 2025-04-21 16:48:59 +02:00
parent 26680faf56
commit feff6cb5dd
55 changed files with 9411 additions and 188 deletions
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mat/
figures/
ltximg/
slprj/
matlab/slprj/

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nass-design.org
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@ -15,13 +15,14 @@
#+LaTeX_CLASS: scrreprt
#+LaTeX_CLASS_OPTIONS: [a4paper, 10pt, DIV=12, parskip=full, bibliography=totoc]
#+LaTeX_HEADER_EXTRA: \input{preamble.tex}
#+LATEX_HEADER: \input{preamble.tex}
#+LATEX_HEADER_EXTRA: \input{preamble_extra.tex}
#+LATEX_HEADER_EXTRA: \bibliography{nass-design.bib}
#+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
@ -44,12 +45,6 @@
#+PROPERTY: header-args:latex+ :post pdf2svg(file=*this*, ext="png")
:END:
#+begin_export html
<hr>
<p>This report is also available as a <a href="./nass-design.pdf">pdf</a>.</p>
<hr>
#+end_export
#+latex: \clearpage
* Build :noexport:
@ -96,59 +91,416 @@
#+END_SRC
* Notes :noexport:
** Notes
Prefix is =detail_design=
- [ ] Look [[https://gitlab.esrf.fr/dehaeze/nass-fem/-/tree/master?ref_type=heads][here]] for the struts, encoder support, etc...
- [ ] file:~/Cloud/work-projects/ID31-NASS/matlab/nass-simscape/org/nano_hexapod.org
- [ ] Design of the flexible joints
- [ ] Nice pictures: file:/home/thomas/Cloud/work-projects/ID31-NASS/nano-hexapod
- [ ] Mounting of struts is explained later in file:~/Cloud/work-projects/ID31-NASS/phd-thesis-chapters/C3-test-bench-struts/test-bench-struts.org
- [ ] Mounting of hexapod is explained in file:~/Cloud/work-projects/ID31-NASS/phd-thesis-chapters/C4-test-bench-nano-hexapod/test-bench-nano-hexapod.org
*Outline*:
- Design goals:
- Position =bi= and =si=
- Maximum height of 95mm
- As close as possible to "perfect" stewart platform: flexible modes at high frequency
- Summary of specifications
- Easy mounting, easy change of strut in case of failure
- Plates:
- Maximize frequency of flexible modes (show FEM)
- Good tolerances for interfaces with flexible joints
Positioning of =bi= and orientation =si=
- Flexible joints:
- Strut mounting (later described)
- Encoder support:
- Possible to fix them to the struts or to the plates
** TODO [#C] Summary of the specifications
Flexible joints:
- Axial Stiffness
- Bending Stiffness
- Stroke
APA:
- Axial stiffness
Encoders:
- Stroke, Noise
Plates:
- Maximize flexible modes
- Correct positioning of bi and si => precisely know the Jacobian matrix
** TODO [#C] Explain the good wanted flatness for the APA
#+begin_quote
Sur le plan on a une co-planéitée de 0.08mm entre les 2 interfaces (ce
qui est pas très exigent avant la découpe intérieure au fil, mais qui
est pas si évidente que ça si la matière a des contraintes interne). En
plus, ça peut évoluer après collage des piezos (c'est probablement ce
qu'on regardait sur ta photo.)
Je pense qu'on avait demandé ça pour ne pas consommer la course des flex
seulement pour compenser les défauts d'usinage/collage. 20um c’était
vraiment du bon boulot.
Le plans que Damien avait fait du corps de l'APA est en pj si tu veux
illustrer.
#+end_quote
** TODO [#C] Understand why hexapod stiffness (maximizing suspension modes) is often the main design goal
See for instance cite:afzali-far16_vibrat_dynam_isotr_hexap_analy_studies.
Possible reasons:
- ease of designing a controller with bandwidth < first suspension mode
- when controlling <6DoF, above the resonance the "off-axis" motion may be very large even though the "on-axis" is controlled.
Not the case for the following references (control bandwidth > suspension mode):
- cite:hanieh03_activ_stewar
Example of claims that resonances impose limitation to control bandwidth:
From cite:babakhani12_activ_dampin_vibrat_high_precis_motion_system (page i)
#+begin_quote
Speed and accuracy in motion systems can be attained by implementing a high-bandwidth motion controller.
The resonances in the plant transfer impose a limit on the achievable bandwidth of such a controller.
#+end_quote
** DONE [#B] Put all the figure in the document
CLOSED: [2025-04-21 Mon 14:21]
*Design*:
- [X] Overview
[[file:figs/detail_design_nano_hexapod_elements.png]]
- [X] Final design of struts
[[file:figs/detail_design_strut_without_enc.jpg]]
[[file:figs/detail_design_strut_with_enc.jpg]]
- [X] Modification of APA300ML for easier mounting purposes
[[file:figs/detail_design_apa_mod.jpg]]
- [X] Plate design
[[file:figs/detail_design_top_plate.jpg]]
- [X] Design of plates for positioning struts
[[file:figs/detail_design_fixation_flexible_joints.png]]
[[file:figs/detail_design_location_bot_flex.png]]
[[file:figs/detail_design_location_top_flexible_joints.png]]
- [X] Design of Flexible joints for fixation to the plates / precise positioning of center of rotation
[[file:figs/detail_design_specifications_flexible_joints.png]]
- [X] Encoder on plates
[[file:figs/detail_design_encoders_plates.jpg]]
[[file:figs/detail_design_enc_plates.jpg]]
- [X] Encoder on struts
[[file:figs/detail_design_enc_struts.jpg]]
*FEM*:
- [X] FEM of nano-hexapod: rigid body modes
[[file:figs/detail_design_fem_rigid_body_mode.jpg]]
- [X] FEM of struts => maybe issue with encoder => several options
[[file:figs/detail_design_fem_strut_mode.jpg]]
- [X] FEM of plates
[[file:figs/detail_design_fem_plate_mode.jpg]]
- [X] FEM of encoder support
[[file:figs/detail_design_fem_encoder_fix.png]]
*Multi-Body Model*:
- [X] Joint Model
[[file:figs/detail_design_simscape_model_flexible_joint.png]]
- [X] Encoder model
[[file:figs/detail_design_simscape_encoder.png]]
[[file:figs/detail_design_simscape_encoder_disp.png]]
- [X] Screenshot of Simscape Model
[[file:figs/detail_design_simscape_encoder_plates.png]]
[[file:figs/detail_design_simscape_encoder_struts.png]]
20 figures
** DONE [#A] Make detailed outline
CLOSED: [2025-04-21 Mon 14:13]
- *Design goals*:
- Position =bi= and =si=
- Maximum height of 95mm
- As close as possible to "perfect" stewart platform: flexible modes at high frequency
- Easy mounting, easy change of strut in case of failure
- *Mechanical Design*
- Struts:
- Flexible joints: interface with plates, etc..
- APA: modification for better mounting
- Encoder support:
- Plates:
- Maximize frequency of flexible modes (show FEM)
- Good tolerances for interfaces with flexible joints
Positioning of =bi= and orientation =si=
- Obtained design:
- FEM of complete system
- Show modes of the struts
- Alternative encoder position: on the plates
- *Multi body Model*:
- Complete model: two plates, 6 joints, 6 actuators, 6 encoders
- Joint Model
- APA Model
- Encoder model
- Say that obtained dynamics was considered good + possible to perform simulations of tomography experiments with same performance as during the conceptual design
* Introduction :ignore:
#+name: fig:detail_design_nano_hexapod_elements
#+caption: Obtained mechanical design of the Active platform, the "nano-hexapod"
#+attr_latex: :width 0.95\linewidth
[[file:figs/detail_design_nano_hexapod_elements.png]]
*Design goals*:
- Position =bi= and =si=
- Maximum height of 95mm
- As close as possible to "perfect" stewart platform: flexible modes at high frequency
- Easy mounting, easy change of strut in case of failure
Presentation of the obtained design:
- Fixation
- Section on: Complete strut
- Cable management
- Plates design
- FEM results
- Table some pictures from here: [[file:~/Cloud/work-projects/ID31-NASS/matlab/nass-nano-hexapod-assembly/nass-nano-hexapod-assembly.org][nass-nano-hexapod-assembly]]
- Explain again the different specifications in terms of space, payload, etc..
- CAD view of the nano-hexapod
- Chosen geometry, materials, ease of mounting, cabling, ...
- Validation on Simscape with accurate model?
#+name: tab:nass_design_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:nass_design_ | =nass_design_1_.m= |
* Mechanical Design
<<sec:detail_design_mechanics>>
** Struts
**** Introduction :ignore:
#+name: fig:detail_design_strut
#+caption: Design of the Nano-Hexapod struts. Before (\subref{fig:detail_design_strut_without_enc}) and after (\subref{fig:detail_design_strut_with_enc}) encoder integration.
#+attr_latex: :options [htbp]
#+begin_figure
#+attr_latex: :caption \subcaption{\label{fig:detail_design_strut_without_enc}Before encoder integration}
#+attr_latex: :options {0.49\textwidth}
#+begin_subfigure
#+attr_latex: :width 0.95\linewidth
[[file:figs/detail_design_strut_without_enc.jpg]]
#+end_subfigure
#+attr_latex: :caption \subcaption{\label{fig:detail_design_strut_with_enc}With the mounted encoder}
#+attr_latex: :options {0.49\textwidth}
#+begin_subfigure
#+attr_latex: :width 0.95\linewidth
[[file:figs/detail_design_strut_with_enc.jpg]]
#+end_subfigure
#+end_figure
**** Flexible joints
Flexible joints: X5CrNiCuNb16-4 (F16Ph)
- high yield strength: specified >1GPa using heat treatment
- high fatigue resistance
#+name: fig:detail_design_apa_joints
#+caption: Two main components of the struts: the amplified piezoelectric actuator (\subref{fig:detail_design_apa}) and the flexible joint (\subref{fig:detail_design_flexible_joint}).
#+attr_latex: :options [htbp]
#+begin_figure
#+attr_latex: :caption \subcaption{\label{fig:detail_design_apa}Amplified Piezoelectric Actuator}
#+attr_latex: :options {0.49\textwidth}
#+begin_subfigure
#+attr_latex: :scale 1
[[file:figs/detail_design_apa.png]]
#+end_subfigure
#+attr_latex: :caption \subcaption{\label{fig:detail_design_flexible_joint}Flexible joint}
#+attr_latex: :options {0.49\textwidth}
#+begin_subfigure
#+attr_latex: :scale 1
[[file:figs/detail_design_flexible_joint.png]]
#+end_subfigure
#+end_figure
**** Piezoelectric Amplified Actuators
APA: modification for better mounting
**** Encoder support
All other parts are made of aluminum.
** Plates
Plates: X30Cr13
- high hardness to not deform
* Amplified Piezoelectric Design
- Maximize frequency of flexible modes (show FEM)
- Good tolerances for interfaces with flexible joints
Positioning of =bi= and orientation =si=
#+name: fig:detail_design_top_plate
#+caption: The mechanical design for the top platform incorporates precisely positioned V-grooves for the joint interfaces (displayed in red). The purpose of the encoder interface (shown in green) is detailed later.
#+attr_latex: :scale 1
[[file:figs/detail_design_top_plate.png]]
The cylindrical component is located (or constrained) within the V-groove via two distinct line contacts.
#+name: fig:detail_design_fixation_flexible_joints
#+caption: Fixation of the flexible points to the nano-hexapod plates. Both top and bottom flexible joints are clamped to the plates as shown in (\subref{fig:detail_design_fixation_flexible_joints}). While the top flexible joint is in contact with the top plate for precise positioning of its center of rotation (\subref{fig:detail_design_location_top_flexible_joints}), the bottom joint is just oriented (\subref{fig:detail_design_location_bot_flex}).
#+begin_figure
#+attr_latex: :caption \subcaption{\label{fig:detail_design_fixation_flexible_joints}Flexible Joint Clamping}
#+attr_latex: :options {0.33\textwidth}
#+begin_subfigure
#+attr_latex: :width 0.99\linewidth
[[file:figs/detail_design_fixation_flexible_joints.png]]
#+end_subfigure
#+attr_latex: :caption \subcaption{\label{fig:detail_design_location_top_flexible_joints}Top positioning}
#+attr_latex: :options {0.33\textwidth}
#+begin_subfigure
#+attr_latex: :width 0.99\linewidth
[[file:figs/detail_design_location_top_flexible_joints.png]]
#+end_subfigure
#+attr_latex: :caption \subcaption{\label{fig:detail_design_location_bot_flex}Bottom Positioning}
#+attr_latex: :options {0.33\textwidth}
#+begin_subfigure
#+attr_latex: :width 0.99\linewidth
[[file:figs/detail_design_location_bot_flex.png]]
#+end_subfigure
#+end_figure
** Finite Element Analysis
#+name: fig:detail_design_enc_struts
#+caption: Obtained Nano-Hexapod design
#+attr_latex: :width 0.9\linewidth
[[file:figs/detail_design_enc_struts.jpg]]
- FEM of complete system
- Show modes of the struts
#+name: fig:detail_design_fem_nano_hexapod
#+caption: Measurement of strut flexible modes. First six modes are "suspension" modes in which the top plate behaves as a rigid body (\subref{fig:detail_design_fem_rigid_body_mode}). Then modes of the struts have natural frequencies from $205\,\text{Hz}$ to $420\,\text{Hz}$ (\subref{fig:detail_design_fem_strut_mode}). Finally, the first flexible mode of the top plate is at $650\,\text{Hz}$ (\subref{fig:detail_design_fem_plate_mode})
#+attr_latex: :options [htbp]
#+begin_figure
#+attr_latex: :caption \subcaption{\label{fig:detail_design_fem_rigid_body_mode}Suspension modes}
#+attr_latex: :options {0.33\textwidth}
#+begin_subfigure
#+attr_latex: :width 0.9\linewidth
[[file:figs/detail_design_fem_rigid_body_mode.jpg]]
#+end_subfigure
#+attr_latex: :caption \subcaption{\label{fig:detail_design_fem_strut_mode}Strut - Local modes}
#+attr_latex: :options {0.33\textwidth}
#+begin_subfigure
#+attr_latex: :width 0.9\linewidth
[[file:figs/detail_design_fem_strut_mode.jpg]]
#+end_subfigure
#+attr_latex: :caption \subcaption{\label{fig:detail_design_fem_plate_mode}Top plate modes}
#+attr_latex: :options {0.33\textwidth}
#+begin_subfigure
#+attr_latex: :width 0.9\linewidth
[[file:figs/detail_design_fem_plate_mode.jpg]]
#+end_subfigure
#+end_figure
** Obtained Design
- Alternative encoder position: on the plates
- Support made of aluminum
#+name: fig:detail_design_enc_plates_design
#+caption: Alternative way of using the encoders: they are fixed directly to the plates.
#+attr_latex: :options [htbp]
#+begin_figure
#+attr_latex: :caption \subcaption{\label{fig:detail_design_enc_plates}Nano-Hexapod with encoders fixed to the plates}
#+attr_latex: :options {0.59\textwidth}
#+begin_subfigure
#+attr_latex: :height 5cm
[[file:figs/detail_design_enc_plates.jpg]]
#+end_subfigure
#+attr_latex: :caption \subcaption{\label{fig:detail_design_encoders_plates}Zoom on encoder fixation}
#+attr_latex: :options {0.39\textwidth}
#+begin_subfigure
#+attr_latex: :height 5cm
[[file:figs/detail_design_encoders_plates.jpg]]
#+end_subfigure
#+end_figure
#+name: fig:detail_design_fem_encoder_fix
#+caption: Finite Element Analysis of the encoder supports. Encoder inertia was taken into account.
[[file:figs/detail_design_fem_encoder_fix.png]]
* Multi-Body Model
:PROPERTIES:
:HEADER-ARGS:matlab+: :tangle matlab/nass_design_1_.m
:HEADER-ARGS:matlab+: :tangle matlab/detail_design_1_model.m
:END:
<<sec:nass_design_mechanics>>
<<sec:detail_design_model>>
*Multi body Model*:
- Complete model: two plates, 6 joints, 6 actuators, 6 encoders
- Joint Model
- APA Model
- Encoder model
- Say that obtained dynamics was considered good + possible to perform simulations of tomography experiments with same performance as during the conceptual design
** Introduction :ignore:
** 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
Two configurations:
- Encoders fixed to the struts
- Encoders fixed to the plates
#+begin_src matlab :exports none :results silent :noweb yes
<<matlab-init>>
#+end_src
#+name: fig:detail_design_simscape_encoder
#+caption: 3D representation of the multi-body model. There are two configurations: encoders fixed to the struts (\subref{fig:detail_design_simscape_encoder_struts}) and encoders fixed to the plates (\subref{fig:detail_design_simscape_encoder_plates}).
#+attr_latex: :options [htbp]
#+begin_figure
#+attr_latex: :caption \subcaption{\label{fig:detail_design_simscape_encoder_struts}Encoders fixed to the struts}
#+attr_latex: :options {0.49\textwidth}
#+begin_subfigure
#+attr_latex: :width 0.95\linewidth
[[file:figs/detail_design_simscape_encoder_struts.png]]
#+end_subfigure
#+attr_latex: :caption \subcaption{\label{fig:detail_design_simscape_encoder_plates}Encoders fixed to the plates}
#+attr_latex: :options {0.49\textwidth}
#+begin_subfigure
#+attr_latex: :width 0.95\linewidth
[[file:figs/detail_design_simscape_encoder_plates.png]]
#+end_subfigure
#+end_figure
#+begin_src matlab :tangle no :noweb yes
<<m-init-path>>
#+end_src
#+begin_src matlab :eval no :noweb yes
<<m-init-path-tangle>>
#+end_src
** Flexible Joints
#+name: fig:detail_design_simscape_model_flexible_joint
#+caption: Multi-Body (using the Simscape software) model of the flexible joints. A 4-DoFs model is shown.
#+attr_latex: :scale 1
[[file:figs/detail_design_simscape_model_flexible_joint.png]]
** Amplified Piezoelectric Actuators
** Encoders
#+name: fig:detail_design_simscape_encoder_model
#+caption: Representation of the encoder model in the multi-body model. Measurement $d_i$ corresponds to the $x$ position of the encoder frame $\{E\}$ expresssed in the ruller frame $\{R\}$ (\subref{fig:detail_design_simscape_encoder}). A rotation of the encoder therefore induces a measured displacement (\subref{fig:detail_design_simscape_encoder_disp}).
#+attr_latex: :options [htbp]
#+begin_figure
#+attr_latex: :caption \subcaption{\label{fig:detail_design_simscape_encoder}Aligned encoder and ruler}
#+attr_latex: :options {0.49\textwidth}
#+begin_subfigure
#+attr_latex: :scale 1
[[file:figs/detail_design_simscape_encoder.png]]
#+end_subfigure
#+attr_latex: :caption \subcaption{\label{fig:detail_design_simscape_encoder_disp}Rotation of the encoder head}
#+attr_latex: :options {0.49\textwidth}
#+begin_subfigure
#+attr_latex: :scale 1
[[file:figs/detail_design_simscape_encoder_disp.png]]
#+end_subfigure
#+end_figure
#+begin_src matlab :noweb yes
<<m-init-other>>
#+end_src
* Conclusion
<<sec:nass_design_conclusion>>
<<sec:detail_design_conclusion>>
* Bibliography :ignore:
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% Created 2024-03-19 Tue 11:13
% Created 2025-04-21 Mon 16:49
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\author{Dehaeze Thomas}
\date{\today}
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pdftitle={Nano Hexapod - Obtained Design},
pdfkeywords={},
pdfsubject={},
pdfcreator={Emacs 29.2 (Org mode 9.7)},
pdfcreator={Emacs 30.1 (Org mode 9.7.26)},
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\tableofcontents
\clearpage
\begin{figure}[htbp]
\centering
\includegraphics[scale=1,width=0.95\linewidth]{figs/detail_design_nano_hexapod_elements.png}
\caption{\label{fig:detail_design_nano_hexapod_elements}Obtained mechanical design of the Active platform, the ``nano-hexapod''}
\end{figure}
\textbf{Design goals}:
\begin{itemize}
\item Position \texttt{bi} and \texttt{si}
\item Maximum height of 95mm
\item As close as possible to ``perfect'' stewart platform: flexible modes at high frequency
\item Easy mounting, easy change of strut in case of failure
\end{itemize}
Presentation of the obtained design:
\begin{itemize}
\item Fixation
\item Section on: Complete strut
\item Cable management
\item Plates design
\item FEM results
\item Table some pictures from here: \href{file:///home/thomas/Cloud/work-projects/ID31-NASS/matlab/nass-nano-hexapod-assembly/nass-nano-hexapod-assembly.org}{nass-nano-hexapod-assembly}
\item Explain again the different specifications in terms of space, payload, etc..
\item CAD view of the nano-hexapod
\item Chosen geometry, materials, ease of mounting, cabling, \ldots{}
\item Validation on Simscape with accurate model?
\end{itemize}
\chapter{Mechanical Design}
\label{sec:detail_design_mechanics}
\section{Struts}
\begin{figure}[htbp]
\begin{subfigure}{0.49\textwidth}
\begin{center}
\includegraphics[scale=1,width=0.95\linewidth]{figs/detail_design_strut_without_enc.jpg}
\end{center}
\subcaption{\label{fig:detail_design_strut_without_enc}Before encoder integration}
\end{subfigure}
\begin{subfigure}{0.49\textwidth}
\begin{center}
\includegraphics[scale=1,width=0.95\linewidth]{figs/detail_design_strut_with_enc.jpg}
\end{center}
\subcaption{\label{fig:detail_design_strut_with_enc}With the mounted encoder}
\end{subfigure}
\caption{\label{fig:detail_design_strut}Design of the Nano-Hexapod struts. Before (\subref{fig:detail_design_strut_without_enc}) and after (\subref{fig:detail_design_strut_with_enc}) encoder integration.}
\end{figure}
\subsubsection{Flexible joints}
\begin{table}[htbp]
\caption{\label{tab:nass_design_section_matlab_code}Report sections and corresponding Matlab files}
Flexible joints: X5CrNiCuNb16-4 (F16Ph)
\begin{itemize}
\item high yield strength: specified >1GPa using heat treatment
\item high fatigue resistance
\end{itemize}
\begin{figure}[htbp]
\begin{subfigure}{0.49\textwidth}
\begin{center}
\includegraphics[scale=1,scale=1]{figs/detail_design_apa.png}
\end{center}
\subcaption{\label{fig:detail_design_apa}Amplified Piezoelectric Actuator}
\end{subfigure}
\begin{subfigure}{0.49\textwidth}
\begin{center}
\includegraphics[scale=1,scale=1]{figs/detail_design_flexible_joint.png}
\end{center}
\subcaption{\label{fig:detail_design_flexible_joint}Flexible joint}
\end{subfigure}
\caption{\label{fig:detail_design_apa_joints}Two main components of the struts: the amplified piezoelectric actuator (\subref{fig:detail_design_apa}) and the flexible joint (\subref{fig:detail_design_flexible_joint}).}
\end{figure}
\subsubsection{Piezoelectric Amplified Actuators}
APA: modification for better mounting
\subsubsection{Encoder support}
All other parts are made of aluminum.
\section{Plates}
Plates: X30Cr13
\begin{itemize}
\item high hardness to not deform
\end{itemize}
\begin{itemize}
\item Maximize frequency of flexible modes (show FEM)
\item Good tolerances for interfaces with flexible joints
Positioning of \texttt{bi} and orientation \texttt{si}
\end{itemize}
\begin{figure}[htbp]
\centering
\begin{tabularx}{0.6\linewidth}{lX}
\toprule
\textbf{Sections} & \textbf{Matlab File}\\
\midrule
Section \ref{sec:nass_design}\_ & \texttt{nass\_design\_1\_.m}\\
\bottomrule
\end{tabularx}
\end{table}
\chapter{Amplified Piezoelectric Design}
\label{sec:nass_design_mechanics}
\includegraphics[scale=1,scale=1]{figs/detail_design_top_plate.png}
\caption{\label{fig:detail_design_top_plate}The mechanical design for the top platform incorporates precisely positioned V-grooves for the joint interfaces (displayed in red). The purpose of the encoder interface (shown in green) is detailed later.}
\end{figure}
The cylindrical component is located (or constrained) within the V-groove via two distinct line contacts.
\begin{figure}
\begin{subfigure}{0.33\textwidth}
\begin{center}
\includegraphics[scale=1,width=0.99\linewidth]{figs/detail_design_fixation_flexible_joints.png}
\end{center}
\subcaption{\label{fig:detail_design_fixation_flexible_joints}Flexible Joint Clamping}
\end{subfigure}
\begin{subfigure}{0.33\textwidth}
\begin{center}
\includegraphics[scale=1,width=0.99\linewidth]{figs/detail_design_location_top_flexible_joints.png}
\end{center}
\subcaption{\label{fig:detail_design_location_top_flexible_joints}Top positioning}
\end{subfigure}
\begin{subfigure}{0.33\textwidth}
\begin{center}
\includegraphics[scale=1,width=0.99\linewidth]{figs/detail_design_location_bot_flex.png}
\end{center}
\subcaption{\label{fig:detail_design_location_bot_flex}Bottom Positioning}
\end{subfigure}
\caption{\label{fig:detail_design_fixation_flexible_joints}Fixation of the flexible points to the nano-hexapod plates. Both top and bottom flexible joints are clamped to the plates as shown in (\subref{fig:detail_design_fixation_flexible_joints}). While the top flexible joint is in contact with the top plate for precise positioning of its center of rotation (\subref{fig:detail_design_location_top_flexible_joints}), the bottom joint is just oriented (\subref{fig:detail_design_location_bot_flex}).}
\end{figure}
\section{Finite Element Analysis}
\begin{figure}[htbp]
\centering
\includegraphics[scale=1,width=0.9\linewidth]{figs/detail_design_enc_struts.jpg}
\caption{\label{fig:detail_design_enc_struts}Obtained Nano-Hexapod design}
\end{figure}
\begin{itemize}
\item FEM of complete system
\item Show modes of the struts
\end{itemize}
\begin{figure}[htbp]
\begin{subfigure}{0.33\textwidth}
\begin{center}
\includegraphics[scale=1,width=0.9\linewidth]{figs/detail_design_fem_rigid_body_mode.jpg}
\end{center}
\subcaption{\label{fig:detail_design_fem_rigid_body_mode}Suspension modes}
\end{subfigure}
\begin{subfigure}{0.33\textwidth}
\begin{center}
\includegraphics[scale=1,width=0.9\linewidth]{figs/detail_design_fem_strut_mode.jpg}
\end{center}
\subcaption{\label{fig:detail_design_fem_strut_mode}Strut - Local modes}
\end{subfigure}
\begin{subfigure}{0.33\textwidth}
\begin{center}
\includegraphics[scale=1,width=0.9\linewidth]{figs/detail_design_fem_plate_mode.jpg}
\end{center}
\subcaption{\label{fig:detail_design_fem_plate_mode}Top plate modes}
\end{subfigure}
\caption{\label{fig:detail_design_fem_nano_hexapod}Measurement of strut flexible modes. First six modes are ``suspension'' modes in which the top plate behaves as a rigid body (\subref{fig:detail_design_fem_rigid_body_mode}). Then modes of the struts have natural frequencies from \(205\,\text{Hz}\) to \(420\,\text{Hz}\) (\subref{fig:detail_design_fem_strut_mode}). Finally, the first flexible mode of the top plate is at \(650\,\text{Hz}\) (\subref{fig:detail_design_fem_plate_mode})}
\end{figure}
\section{Obtained Design}
\begin{itemize}
\item Alternative encoder position: on the plates
\item Support made of aluminum
\end{itemize}
\begin{figure}[htbp]
\begin{subfigure}{0.59\textwidth}
\begin{center}
\includegraphics[scale=1,height=5cm]{figs/detail_design_enc_plates.jpg}
\end{center}
\subcaption{\label{fig:detail_design_enc_plates}Nano-Hexapod with encoders fixed to the plates}
\end{subfigure}
\begin{subfigure}{0.39\textwidth}
\begin{center}
\includegraphics[scale=1,height=5cm]{figs/detail_design_encoders_plates.jpg}
\end{center}
\subcaption{\label{fig:detail_design_encoders_plates}Zoom on encoder fixation}
\end{subfigure}
\caption{\label{fig:detail_design_enc_plates_design}Alternative way of using the encoders: they are fixed directly to the plates.}
\end{figure}
\begin{figure}[htbp]
\centering
\includegraphics[scale=1]{figs/detail_design_fem_encoder_fix.png}
\caption{\label{fig:detail_design_fem_encoder_fix}Finite Element Analysis of the encoder supports. Encoder inertia was taken into account.}
\end{figure}
\chapter{Multi-Body Model}
\label{sec:detail_design_model}
\textbf{Multi body Model}:
\begin{itemize}
\item Complete model: two plates, 6 joints, 6 actuators, 6 encoders
\item Joint Model
\item APA Model
\item Encoder model
\item Say that obtained dynamics was considered good + possible to perform simulations of tomography experiments with same performance as during the conceptual design
\end{itemize}
Two configurations:
\begin{itemize}
\item Encoders fixed to the struts
\item Encoders fixed to the plates
\end{itemize}
\begin{figure}[htbp]
\begin{subfigure}{0.49\textwidth}
\begin{center}
\includegraphics[scale=1,width=0.95\linewidth]{figs/detail_design_simscape_encoder_struts.png}
\end{center}
\subcaption{\label{fig:detail_design_simscape_encoder_struts}Encoders fixed to the struts}
\end{subfigure}
\begin{subfigure}{0.49\textwidth}
\begin{center}
\includegraphics[scale=1,width=0.95\linewidth]{figs/detail_design_simscape_encoder_plates.png}
\end{center}
\subcaption{\label{fig:detail_design_simscape_encoder_plates}Encoders fixed to the plates}
\end{subfigure}
\caption{\label{fig:detail_design_simscape_encoder}3D representation of the multi-body model. There are two configurations: encoders fixed to the struts (\subref{fig:detail_design_simscape_encoder_struts}) and encoders fixed to the plates (\subref{fig:detail_design_simscape_encoder_plates}).}
\end{figure}
\section{Flexible Joints}
\begin{figure}[htbp]
\centering
\includegraphics[scale=1,scale=1]{figs/detail_design_simscape_model_flexible_joint.png}
\caption{\label{fig:detail_design_simscape_model_flexible_joint}Multi-Body (using the Simscape software) model of the flexible joints. A 4-DoFs model is shown.}
\end{figure}
\section{Amplified Piezoelectric Actuators}
\section{Encoders}
\begin{figure}[htbp]
\begin{subfigure}{0.49\textwidth}
\begin{center}
\includegraphics[scale=1,scale=1]{figs/detail_design_simscape_encoder.png}
\end{center}
\subcaption{\label{fig:detail_design_simscape_encoder}Aligned encoder and ruler}
\end{subfigure}
\begin{subfigure}{0.49\textwidth}
\begin{center}
\includegraphics[scale=1,scale=1]{figs/detail_design_simscape_encoder_disp.png}
\end{center}
\subcaption{\label{fig:detail_design_simscape_encoder_disp}Rotation of the encoder head}
\end{subfigure}
\caption{\label{fig:detail_design_simscape_encoder_model}Representation of the encoder model in the multi-body model. Measurement \(d_i\) corresponds to the \(x\) position of the encoder frame \(\{E\}\) expresssed in the ruller frame \(\{R\}\) (\subref{fig:detail_design_simscape_encoder}). A rotation of the encoder therefore induces a measured displacement (\subref{fig:detail_design_simscape_encoder_disp}).}
\end{figure}
\chapter{Conclusion}
\label{sec:nass_design_conclusion}
\label{sec:detail_design_conclusion}
\printbibliography[heading=bibintoc,title={Bibliography}]
\end{document}

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