#+TITLE: Nano Hexapod - Obtained Design
:DRAWER:
#+LANGUAGE: en
#+EMAIL: dehaeze.thomas@gmail.com
#+AUTHOR: Dehaeze Thomas

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* 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]]


Detail design phase:
- key elements were optimized such as: actuator and flexible joints
- relative motion sensor (an encoder) was also selected
- specific kinematics of the Stewart platform (i.e. position of joints and orientation of struts) was not found to be too critical for this application.
  Yet, the geometry was fixed in Section [...]

In this section, the mechanical design of the active platform, shown in Figure ref:fig:detail_design_nano_hexapod_elements, is detailed.

The main design objectives are:
- Well defined kinematics: Good positioning of the top flexible joint rotation point $\bm{b}_i$ and correct orientation of the struts $\hat{\bm{s}}_i$.
  The goal is to have a well defined geometry such that the Jacobian matrix is well defined.
- Space constrains: it should fit within a cylinder with radius of $120\,\text{mm}$ and height of $95\,\text{mm}$
- As good performances were obtained with the multi-body model.
  The final design should behave as close as possible to "perfect" stewart platform.
  This means that the frequency of flexible modes that could be problematic for control must be made as high as possible.
- Easy mounting and alignment.
- Easy maintenance: the struts should be easily changed in case for failure.

* Mechanical Design
<<sec:detail_design_mechanics>>
**** Introduction                                                  :ignore:
**** Struts

The strut design is shown in Figure ref:fig:detail_design_strut.

The design of the struts was driven by:
- having stiff interface between the amplified piezoelectric actuator and the two flexible joints
- having stiff interface between the flexible joints and the two places (discussed afterwards)
- Because the angular stroke of the flexible joints is fairly limited, it is important to be able to mount the strut such that the two cylindrical interfaces are coaxial.
  Do to so:
  - A mounting bench was designed
    The mounting procedure will be described in Section [...]
    # TODO - Add link to section
  - Cylindrical washers, shown in Figure ref:fig:detail_design_strut_without_enc, were integrated to allow for adjustments.
    The issue was that the flatness between the two interface planes of the APA shown in Figure ref:fig:detail_design_apa could not be guaranteed.
    With the added cylindrical washers and the mounting tool, it should be possible to well align the struts even in the presence of machining inaccuracies.
- Possibility to fix the encoder parallel to the strut, as shown in Figure ref:fig:detail_design_strut_with_enc

#+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: :scale 0.9
[[file:figs/detail_design_strut_without_enc.png]]
#+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: :scale 0.9
[[file:figs/detail_design_strut_with_enc.png]]
#+end_subfigure
#+end_figure

The flexible joints are manufactured using wire-cut electrical discharge machining, allowing for:
- very tight tolerances:
  - allowing good location of the center of rotation with respect to the plate interfaces (red surfaces shown in Figure ref:fig:detail_design_flexible_joint)
  - allowing correct neck dimension to have the wanted properties (stiffness and angular stroke)
- Such part is fragile, mainly due to its small "neck" dimension of only $0.25\,\text{mm}$
  Such machining technique has little to no cutting forces.

The flexible joints are made from a stainless steel referenced as "X5CrNiCuNb16-4" (also called "F16Ph").
This material is chosen for:
- its high yield strength: specified >1GPa using heat treatment.
- its high fatigue resistance

Figure ref:fig:detail_design_flexible_joint
- Interface with the APA has a cylindrical shape to allow the use of cylindrical washers
  A slotted hole has been added to align the flexible joint with the APA using a dowel pin.
- Two threaded holes on the sides can be used to mount the encoders
- The interface with the plate will be latter described.

The amplified piezoelectric actuators are APA300ML.
Modification of the mechanical interfaces were asked to the manufacturer.
Two planes surfaces and a dowel hole were used, as shown in Figure ref:fig:detail_design_apa.
The amplifying structure, is also made of stainless steel.

#+name: fig:detail_design_apa_joints
#+caption: Two main components of the struts: the flexible joint (\subref{fig:detail_design_flexible_joint}) and the amplified piezoelectric actuator (\subref{fig:detail_design_apa}).
#+attr_latex: :options [htbp]
#+begin_figure
#+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
#+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
#+end_figure

To correctly measure the relative motion of each strut, the encoders need to measure the relative motion between the two flexible joint's rotational centers.
Two interface parts, made of aluminum, are used to fix the encoder and ruler to the two fleible joints as shown in Figure ref:fig:detail_design_strut_with_enc.

**** Plates

The two plates of the active platform were designed to:
- Maximize the frequency of flexible modes
- have good positioning of the top flexible joints, and good/known orientation of the struts.

To maximize the flexible joints, finite element analysis were used iteratively.
While topology optimization could have been used, a network of reinforcing ribs was used as shown in Figure ref:fig:detail_design_top_plate.

#+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 fixation interface for the joints and "V-grooves".
The cylindrical part of the flexible joint is located (or constrained) within the V-groove via two distinct line contacts (Figure ref:fig:detail_design_fixation_flexible_joints).
Therefore, these grooves are defining the initial strut orientation
High machining accuracy is required, such that during the mounting of the active platform, the flexible joints are that "rest" position

The "flat" interface of each top flexible joint is also in contact with the top platform, as shown in Figure ref:fig:detail_design_location_top_flexible_joints, such that the center of rotation of the top flexible joints $\bm{b}_i$ are well located with respect to the top platform.

The bottom flexible joints are not Figure ref:fig:detail_design_location_bot_flex

The two plates are made with a martensitic stainless steel "X30Cr13":
- It has high hardness, such that the reference surfaces to not deform when fixing the flexible joints
- This should allow to assemble and disassemble the struts many times if necessary

#+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

# TODO - Maybe this picture is not necessary
# #+name: fig:detail_design_enc_struts
# #+caption: Obtained Nano-Hexapod design
# #+attr_latex: :width 0.9\linewidth
# [[file:figs/detail_design_enc_struts.jpg]]

Finite element analysis of the complete active platform was performed to identify problematic modes (Figure ref:fig:detail_design_fem_nano_hexapod):
- First six modes were found to be "suspension" modes were the top plate moves as a rigid body, and the six struts are only moving axially (Figure ref:fig:detail_design_fem_rigid_body_mode)
- Then, between $205\,\text{Hz}$ and $420\,\text{Hz}$ many "local" modes of the struts were observed.
  On is represented in Figure ref:fig:detail_design_fem_strut_mode.
  While these modes seem not to induce any motion of the top platform, it induces a relative displacement of the encoder with respect to the ruler.
  Therefore, when controlling the position of the active platform using the encoders, such modes could be problematic.
  Whether these modes are problematic is difficult to estimate at this point as:
  - it is not known if the APA will "excite" these modes
  - theoretically, if the struts are well aligned, these modes should not be observed
  Then, flexible modes of the top plate are appearing above $650\,\text{Hz}$ (Figure ref:fig:detail_design_fem_plate_mode)

#+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 mode}
#+attr_latex: :options {0.36\textwidth}
#+begin_subfigure
#+attr_latex: :width 0.95\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 mode}
#+attr_latex: :options {0.36\textwidth}
#+begin_subfigure
#+attr_latex: :width 0.95\linewidth
[[file:figs/detail_design_fem_strut_mode.jpg]]
#+end_subfigure
#+attr_latex: :caption \subcaption{\label{fig:detail_design_fem_plate_mode}Top plate mode}
#+attr_latex: :options {0.26\textwidth}
#+begin_subfigure
#+attr_latex: :width 0.95\linewidth
[[file:figs/detail_design_fem_plate_mode.jpg]]
#+end_subfigure
#+end_figure

**** Alternative Encoder Placement

To anticipate potential issue with local modes of the struts, an alternative fixation for the encoder is planned:
- Instead of being fixed to the struts, the encoders are fixed to the plates instead, as shown in Figure ref:fig:detail_design_enc_plates_design.
- The support are made of aluminum, and it is verified that the natural modes are at high enough frequency (Figure ref:fig:detail_design_enc_support_modes).
- The positioning of the encoders are made using pockets in both plates as shown in Figure ref:fig:detail_design_top_plate.
- The encoders are aligned parallel to the struts, but yet they don't exactly measure the relative motion of each strut.
- This means that if relative motion of the active platform is performed based on the encoders, the accuracy of the motion may be affected.
  The issue is that the Kinematics may not be correct.

#+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_enc_support_modes
#+caption: Finite Element Analysis of the encoder supports. Encoder inertia was taken into account.
#+attr_latex: :options [htbp]
#+begin_figure
#+attr_latex: :caption \subcaption{\label{fig:detail_design_enc_support_mode_1}$1^{\text{st}}$ mode at $1120\,\text{Hz}$}
#+attr_latex: :options {0.33\textwidth}
#+begin_subfigure
#+attr_latex: :scale 0.5
[[file:figs/detail_design_enc_support_mode_1.jpg]]
#+end_subfigure
#+attr_latex: :caption \subcaption{\label{fig:detail_design_enc_support_mode_2}$2^{\text{nd}}$ mode at $2020\,\text{Hz}$}
#+attr_latex: :options {0.33\textwidth}
#+begin_subfigure
#+attr_latex: :scale 0.5
[[file:figs/detail_design_enc_support_mode_2.jpg]]
#+end_subfigure
#+attr_latex: :caption \subcaption{\label{fig:detail_design_enc_support_mode_3}$3^{\text{rd}}$ mode at $2080\,\text{Hz}$}
#+attr_latex: :options {0.33\textwidth}
#+begin_subfigure
#+attr_latex: :scale 0.5
[[file:figs/detail_design_enc_support_mode_3.jpg]]
#+end_subfigure
#+end_figure

* Multi-Body Model
<<sec:detail_design_model>>
**** Introduction                                                  :ignore:

Before all the mechanical parts were ordered, the multi-body model of the active platform was refined using the design parts.

Two configurations, displayed in Figure ref:fig:detail_design_simscape_encoder, were considered:
- Encoders fixed to the struts
- Encoders fixed to the plates

Plates were modelled as rigid bodies, with inertia computed from the 3D shape.

#+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

**** Flexible Joints

Different models of the flexible joints where considered:
- 2DoF: only bending stiffnesses
- 3DoF: added torsional stiffness
- 4DoF: added axial stiffness

The multi-body model for the 4DoF configuration is shown in Figure ref:fig:detail_design_simscape_model_flexible_joint.
It is composed of three solid bodies connected by joints whose stiffnesses are computed from the finite element model.

#+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

The amplified piezoelectric actuators are modelled as explained in Section [..].
# Add link to section
Two different models can be used in the multi-body model:
- a 2DoF "axial" model
- a "super-element" extracted from the finite element model

**** Encoders

Up to now, relative displacement sensors were implemented as a relative distance measurement between $\bm{a}_i$ and $\bm{b}_i$.

As shown in the previous section, flexible modes of the struts may negatively impact the encoder signal.
It was therefore necessary to better model the encoder.

The optical encoder works:
- Encoder heads contains a light source shine on the ruler, and a photo-diode.
  This is represented by frame $\{E\}$ in Figure ref:fig:detail_design_simscape_encoder.
- ruler or scale with a grating (here with a $20\,\mu m$ pitch). A reference frame is indicated by $\{R\}$

Therefore, the measured displacement is the relative position of $\{E\}$ (i.e. there the light "hits" the scale) with respect to frame $\{R\}$, in the direction of the scale.


In that case, a rotation of the encoder, as shown in figure ref:fig:detail_design_simscape_encoder_disp induces a measured displacement.

#+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

**** Simulation

Based on this refined model:
- the active platform could be integrated on top of the micro-station's model.
- the obtained dynamics was considered good
- simulations of tomography experiments were performed, and similar performance were obtained as during the conceptual design
- this is not presented here as results are very similar to the simulations performed in Section [...]
  # Add link to section

* Conclusion
<<sec:detail_design_conclusion>>

* Bibliography                                                        :ignore:
#+latex: \printbibliography[heading=bibintoc,title={Bibliography}]