438 lines
24 KiB
Org Mode
438 lines
24 KiB
Org Mode
#+TITLE: Nano Hexapod - Optimal Geometry
|
|
:DRAWER:
|
|
#+LANGUAGE: en
|
|
#+EMAIL: dehaeze.thomas@gmail.com
|
|
#+AUTHOR: Dehaeze Thomas
|
|
|
|
#+HTML_LINK_HOME: ../index.html
|
|
#+HTML_LINK_UP: ../index.html
|
|
|
|
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="https://research.tdehaeze.xyz/css/style.css"/>
|
|
#+HTML_HEAD: <script type="text/javascript" src="https://research.tdehaeze.xyz/js/script.js"></script>
|
|
|
|
#+BIND: org-latex-image-default-option "scale=1"
|
|
#+BIND: org-latex-image-default-width ""
|
|
|
|
#+LaTeX_CLASS: scrreprt
|
|
#+LaTeX_CLASS_OPTIONS: [a4paper, 10pt, DIV=12, parskip=full, bibliography=totoc]
|
|
#+LATEX_HEADER: \input{preamble.tex}
|
|
#+LATEX_HEADER_EXTRA: \input{preamble_extra.tex}
|
|
#+LATEX_HEADER_EXTRA: \bibliography{nass-geometry.bib}
|
|
|
|
#+BIND: org-latex-bib-compiler "biber"
|
|
|
|
#+PROPERTY: header-args:matlab :session *MATLAB*
|
|
#+PROPERTY: header-args:matlab+ :comments org
|
|
#+PROPERTY: header-args:matlab+ :exports none
|
|
#+PROPERTY: header-args:matlab+ :results none
|
|
#+PROPERTY: header-args:matlab+ :eval no-export
|
|
#+PROPERTY: header-args:matlab+ :noweb yes
|
|
#+PROPERTY: header-args:matlab+ :mkdirp yes
|
|
#+PROPERTY: header-args:matlab+ :output-dir figs
|
|
#+PROPERTY: header-args:matlab+ :tangle no
|
|
|
|
#+PROPERTY: header-args:latex :headers '("\\usepackage{tikz}" "\\usepackage{import}" "\\import{$HOME/Cloud/tikz/org/}{config.tex}")
|
|
#+PROPERTY: header-args:latex+ :imagemagick t :fit yes
|
|
#+PROPERTY: header-args:latex+ :iminoptions -scale 100% -density 150
|
|
#+PROPERTY: header-args:latex+ :imoutoptions -quality 100
|
|
#+PROPERTY: header-args:latex+ :results file raw replace
|
|
#+PROPERTY: header-args:latex+ :buffer no
|
|
#+PROPERTY: header-args:latex+ :tangle no
|
|
#+PROPERTY: header-args:latex+ :eval no-export
|
|
#+PROPERTY: header-args:latex+ :exports results
|
|
#+PROPERTY: header-args:latex+ :mkdirp yes
|
|
#+PROPERTY: header-args:latex+ :output-dir figs
|
|
#+PROPERTY: header-args:latex+ :post pdf2svg(file=*this*, ext="png")
|
|
:END:
|
|
|
|
#+latex: \clearpage
|
|
|
|
* Build :noexport:
|
|
#+NAME: startblock
|
|
#+BEGIN_SRC emacs-lisp :results none :tangle no
|
|
(add-to-list 'org-latex-classes
|
|
'("scrreprt"
|
|
"\\documentclass{scrreprt}"
|
|
("\\chapter{%s}" . "\\chapter*{%s}")
|
|
("\\section{%s}" . "\\section*{%s}")
|
|
("\\subsection{%s}" . "\\subsection*{%s}")
|
|
("\\paragraph{%s}" . "\\paragraph*{%s}")
|
|
))
|
|
|
|
;; Remove automatic org heading labels
|
|
(defun my-latex-filter-removeOrgAutoLabels (text backend info)
|
|
"Org-mode automatically generates labels for headings despite explicit use of `#+LABEL`. This filter forcibly removes all automatically generated org-labels in headings."
|
|
(when (org-export-derived-backend-p backend 'latex)
|
|
(replace-regexp-in-string "\\\\label{sec:org[a-f0-9]+}\n" "" text)))
|
|
(add-to-list 'org-export-filter-headline-functions
|
|
'my-latex-filter-removeOrgAutoLabels)
|
|
|
|
;; Remove all org comments in the output LaTeX file
|
|
(defun delete-org-comments (backend)
|
|
(loop for comment in (reverse (org-element-map (org-element-parse-buffer)
|
|
'comment 'identity))
|
|
do
|
|
(setf (buffer-substring (org-element-property :begin comment)
|
|
(org-element-property :end comment))
|
|
"")))
|
|
(add-hook 'org-export-before-processing-hook 'delete-org-comments)
|
|
|
|
;; Use no package by default
|
|
(setq org-latex-packages-alist nil)
|
|
(setq org-latex-default-packages-alist nil)
|
|
|
|
;; Do not include the subtitle inside the title
|
|
(setq org-latex-subtitle-separate t)
|
|
(setq org-latex-subtitle-format "\\subtitle{%s}")
|
|
|
|
(setq org-export-before-parsing-hook '(org-ref-glossary-before-parsing
|
|
org-ref-acronyms-before-parsing))
|
|
#+END_SRC
|
|
|
|
* Notes :noexport:
|
|
** Notes
|
|
Prefix is =detail_kinematics=
|
|
|
|
Talk about the optimization of the nano-hexapod: geometry, stiffness, etc...
|
|
- [ ] [[file:~/Cloud/work-projects/ID31-NASS/documents/state-of-thesis-2020/index.org::*Optimal Nano-Hexapod Design][Optimal Nano-Hexapod Design]]
|
|
- [X] file:~/Cloud/work-projects/ID31-NASS/matlab/stewart-simscape/org/kinematic-study.org
|
|
- [X] file:~/Cloud/work-projects/ID31-NASS/matlab/stewart-simscape/org/flexible-stewart-platform.org
|
|
Not so interesting
|
|
|
|
- [ ] Talk about what will influence the dynamics
|
|
It will influence the mechanical design.
|
|
For instance we want to precisely position =bi= with respect to the top platform
|
|
|
|
Optimal geometry?
|
|
- [ ] *Cubic architecture*?
|
|
Cubic configuration file:~/Cloud/work-projects/ID31-NASS/matlab/stewart-simscape/org/cubic-configuration.org
|
|
https://tdehaeze.github.io/stewart-simscape/cubic-configuration.html
|
|
- [ ] Kinematics
|
|
- [ ] Trade-off for the strut orientation
|
|
- [ ] Requirements in terms of positioning of the joints
|
|
- [ ] Not a lot of differences, no specificity of cubic architecture, no specific positioning
|
|
|
|
|
|
- [ ] https://research.tdehaeze.xyz/stewart-simscape/docs/bibliography.html
|
|
- [ ] [[file:~/Cloud/work-projects/ID31-NASS/matlab/stewart-simscape/org/kinematic-study.org::*Estimated required actuator stroke from specified platform mobility][Estimated required actuator stroke from specified platform mobility]]
|
|
- [ ] [[file:~/Cloud/work-projects/ID31-NASS/matlab/stewart-simscape/org/kinematic-study.org::*Estimation of the Joint required Stroke][Estimation of the Joint required Stroke]]
|
|
|
|
** TODO [#A] Copy relevant parts of reports
|
|
|
|
** TODO [#A] Structure the review of Stewart platforms
|
|
|
|
Focus on short stroke (<1 mm) stewart platforms with flexible joints.
|
|
|
|
- Actuators: voice coil, piezo
|
|
- Flexible joints
|
|
- Geometry:
|
|
- Cubic, non cubic, ...
|
|
- Control ? Maybe in the control section ?
|
|
|
|
** DONE [#A] Make table for review of Stewart platforms
|
|
CLOSED: [2025-03-19 Wed 18:25]
|
|
|
|
[[file:~/Cloud/work-projects/ID31-NASS/matlab/stewart-simscape/org/bibliography.org::*Built Stewart PLatforms][Built Stewart PLatforms]]
|
|
|
|
Link to figures.
|
|
|
|
In figure legend: link to references, mention the university and the application.
|
|
|
|
** TODO [#C] Create a function to plot the mobility of the Stewart platform
|
|
|
|
Arguments:
|
|
- choose to fix the orientation with ${}^{B}R_{A}$
|
|
- maximum stroke of each actuator (may be included in the Stewart object)
|
|
|
|
* Introduction :ignore:
|
|
|
|
- In the conceptual design phase, the geometry of the Stewart platform was not optimized
|
|
- In the detail design phase, we want to see if the geometry can be optimized to improve the overall performances
|
|
- Optimization criteria: mobility, stiffness, dynamical decoupling, more performance / bandwidth
|
|
|
|
Outline:
|
|
- Review of Stewart platform: Section ref:sec:detail_kinematics_stewart_review
|
|
Geometry, Actuators, Sensors, Joints
|
|
- Effect of geometry on the Stewart platform characteristics ref:sec:detail_kinematics_geometry
|
|
- Cubic configuration: benefits? ref:sec:detail_kinematics_cubic
|
|
|
|
* Review of Stewart platforms
|
|
<<sec:detail_kinematics_stewart_review>>
|
|
** Introduction :ignore:
|
|
|
|
- as was explained in the conceptual phase, Stewart platform have the following key elements:
|
|
- two plates
|
|
- flexible joints
|
|
- actuators
|
|
- sensors
|
|
- the geometry
|
|
- This results in various designs as shown in Table ref:tab:detail_kinematics_stewart_review
|
|
- The focus is here made on Stewart platforms for nano-positioning of vibration control.
|
|
Not on long stroke stewart platforms.
|
|
- All presented Stewart platforms are using flexible joints, as it is a prerequisites for nano-positioning capabilities.
|
|
- Most of stewart platforms are using voice coil actuators or piezoelectric actuators.
|
|
The actuators used for the Stewart platform will be chosen in the next section.
|
|
# TODO - Add reference to the section
|
|
- Depending on the application, various sensors are integrated in the struts or on the plates.
|
|
The choice of sensor for the nano-hexapod will be described in the next section.
|
|
# TODO - Add reference to the section
|
|
|
|
- [ ] Only keep integrated sensor and not external metrology
|
|
- [ ] Check for missing information
|
|
|
|
#+name: fig:detail_kinematics_stewart_examples_cubic
|
|
#+caption: Some examples of developped Stewart platform with Cubic geometry. (\subref{fig:detail_kinematics_jpl}), (\subref{fig:detail_kinematics_uw_gsp}), (\subref{fig:detail_kinematics_ulb_pz}), (\subref{fig:detail_kinematics_uqp})
|
|
#+attr_latex: :options [htbp]
|
|
#+begin_figure
|
|
#+attr_latex: :caption \subcaption{\label{fig:detail_kinematics_jpl}California Institute of Technology - USA}
|
|
#+attr_latex: :options {0.48\textwidth}
|
|
#+begin_subfigure
|
|
#+attr_latex: :width 0.95\linewidth
|
|
[[file:figs/detail_kinematics_jpl.jpg]]
|
|
#+end_subfigure
|
|
#+attr_latex: :caption \subcaption{\label{fig:detail_kinematics_uw_gsp}University of Wyoming - USA}
|
|
#+attr_latex: :options {0.48\textwidth}
|
|
#+begin_subfigure
|
|
#+attr_latex: :width 0.95\linewidth
|
|
[[file:figs/detail_kinematics_uw_gsp.jpg]]
|
|
#+end_subfigure
|
|
|
|
\bigskip
|
|
#+attr_latex: :caption \subcaption{\label{fig:detail_kinematics_ulb_pz}ULB - Belgium}
|
|
#+attr_latex: :options {0.53\textwidth}
|
|
#+begin_subfigure
|
|
#+attr_latex: :width 0.95\linewidth
|
|
[[file:figs/detail_kinematics_ulb_pz.jpg]]
|
|
#+end_subfigure
|
|
#+attr_latex: :caption \subcaption{\label{fig:detail_kinematics_uqp}Naval Postgraduate School - USA}
|
|
#+attr_latex: :options {0.43\textwidth}
|
|
#+begin_subfigure
|
|
#+attr_latex: :width 0.95\linewidth
|
|
[[file:figs/detail_kinematics_uqp.jpg]]
|
|
#+end_subfigure
|
|
#+end_figure
|
|
|
|
#+name: fig:detail_kinematics_stewart_examples_non_cubic
|
|
#+caption: Some examples of developped Stewart platform with non-cubic geometry. (\subref{fig:detail_kinematics_pph}), (\subref{fig:detail_kinematics_zhang11}), (\subref{fig:detail_kinematics_yang19}), (\subref{fig:detail_kinematics_naves})
|
|
#+attr_latex: :options [htbp]
|
|
#+begin_figure
|
|
#+attr_latex: :caption \subcaption{\label{fig:detail_kinematics_pph}Naval Postgraduate School - USA}
|
|
#+attr_latex: :options {0.48\textwidth}
|
|
#+begin_subfigure
|
|
#+attr_latex: :height 5cm
|
|
[[file:figs/detail_kinematics_pph.jpg]]
|
|
#+end_subfigure
|
|
#+attr_latex: :caption \subcaption{\label{fig:detail_kinematics_zhang11}Beihang University - China}
|
|
#+attr_latex: :options {0.48\textwidth}
|
|
#+begin_subfigure
|
|
#+attr_latex: :height 5cm
|
|
[[file:figs/detail_kinematics_zhang11.jpg]]
|
|
#+end_subfigure
|
|
|
|
\bigskip
|
|
#+attr_latex: :caption \subcaption{\label{fig:detail_kinematics_yang19}Nanjing University - China}
|
|
#+attr_latex: :options {0.43\textwidth}
|
|
#+begin_subfigure
|
|
#+attr_latex: :height 5cm
|
|
[[file:figs/detail_kinematics_yang19.jpg]]
|
|
#+end_subfigure
|
|
#+attr_latex: :caption \subcaption{\label{fig:detail_kinematics_naves}University of Twente - Netherlands}
|
|
#+attr_latex: :options {0.53\textwidth}
|
|
#+begin_subfigure
|
|
#+attr_latex: :height 5cm
|
|
[[file:figs/detail_kinematics_naves.jpg]]
|
|
#+end_subfigure
|
|
#+end_figure
|
|
|
|
#+name: tab:detail_kinematics_stewart_review
|
|
#+caption: Examples of Stewart platform developed. When not specifically indicated, sensors are included in the struts. All presented Stewart platforms are using flexible joints. The table is sorted by "date"
|
|
#+attr_latex: :environment tabularx :width \linewidth :align llllX
|
|
#+attr_latex: :center t :booktabs t :font \scriptsize
|
|
| | *Geometry* | *Actuators* | *Sensors* | *Reference* |
|
|
|------------------------------------------+-------------------+------------------------------+------------------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
|
|
| | Cubic (6-UPU) | Magnetostrictive | Force (collocated), Accelerometers | [[cite:&geng93_six_degree_of_freed_activ;&geng94_six_degree_of_freed_activ;&geng95_intel_contr_system_multip_degree]] |
|
|
| Figure ref:fig:detail_kinematics_jpl | Cubic | Voice Coil (0.5 mm) | Force (collocated) | [[cite:&spanos95_soft_activ_vibrat_isolat;&rahman98_multiax]] |
|
|
| | Cubic | Voice Coil (10 mm) | Force, LVDT, Geophones | [[cite:&thayer98_stewar;&thayer02_six_axis_vibrat_isolat_system;&hauge04_sensor_contr_space_based_six]] |
|
|
| Figure ref:fig:detail_kinematics_uw_gsp | Cubic (CoM=CoK) | Voice Coil | Force | [[cite:&mcinroy99_dynam;&mcinroy99_precis_fault_toler_point_using_stewar_platf;&mcinroy00_desig_contr_flexur_joint_hexap;&li01_simul_vibrat_isolat_point_contr;&jafari03_orthog_gough_stewar_platf_microm]] |
|
|
| | Cubic | Piezoelectric ($25\,\mu m$) | Piezo force sensors | [[cite:&defendini00_techn]] |
|
|
| Figure ref:fig:detail_kinematics_ulb_pz | Cubic | APA ($50\,\mu m$) | Force sensor | [[cite:&abu02_stiff_soft_stewar_platf_activ]] |
|
|
| Figure ref:fig:detail_kinematics_pph | Non-Cubic | Voice Coil | Accelerometers | [[cite:&chen03_payload_point_activ_vibrat_isolat]] |
|
|
| | Cubic | Voice Coil | Force | [[cite:&hanieh03_activ_stewar;&preumont07_six_axis_singl_stage_activ]] |
|
|
| Figure ref:fig:detail_kinematics_uqp | Cubic | Piezoelectric ($50\,\mu m$) | Geophone aligned with the strut | [[cite:&agrawal04_algor_activ_vibrat_isolat_spacec]] |
|
|
| | Non-Cubic | Piezoelectric ($16\,\mu m$) | Eddy Current | [[cite:&furutani04_nanom_cuttin_machin_using_stewar]] |
|
|
| | Cubic | Piezoelectric ($120\,\mu m$) | External capacitive | [[cite:&ting06_desig_stewar_nanos_platf;&ting13_compos_contr_desig_stewar_nanos_platf]] |
|
|
| | Non-Cubic | Piezoelectric ($160\,\mu m$) | External capacitive (LION) | [[cite:&ting07_measur_calib_stewar_microm_system]] |
|
|
| Figure ref:fig:detail_kinematics_zhang11 | Non-cubic | Magnetostrictive | Inertial | [[cite:&zhang11_six_dof]] |
|
|
| | 6-SPS (Optimized) | Piezoelectric | Strain Gauge | [[cite:&du14_piezo_actuat_high_precis_flexib]] |
|
|
| | Cubic | Voice Coil | Accelerometer in each leg | [[cite:&chi15_desig_exper_study_vcm_based;&tang18_decen_vibrat_contr_voice_coil;&jiao18_dynam_model_exper_analy_stewar]] |
|
|
| | Cubic | Piezoelectric | Force Sensor + Accelerometer | [[cite:&wang16_inves_activ_vibrat_isolat_stewar]] |
|
|
| | Almost cubic | Voice Coil | Force Sensor + Accelerometer | [[cite:&beijen18_self_tunin_mimo_distur_feedf;&tjepkema12_activ_ph]] |
|
|
| Figure ref:fig:detail_kinematics_yang19 | 6-UPS (Cubic?) | Piezoelectric | Force, Position | [[cite:&yang19_dynam_model_decoup_contr_flexib]] |
|
|
| Figure ref:fig:detail_kinematics_naves | Non-Cubic | 3-phase rotary motor | Rotary Encoders | [[cite:&naves20_desig;&naves20_t_flex]] |
|
|
|
|
- [ ] https://research.tdehaeze.xyz/stewart-simscape/docs/bibliography.html
|
|
- [ ] Joints and actuators are optimized in the next section
|
|
|
|
* Effect of geometry on Stewart platform properties
|
|
<<sec:detail_kinematics_geometry>>
|
|
** Introduction :ignore:
|
|
|
|
- Remind that the choice of frames (independently of the physical geometry) impacts the obtained stiffness matrix (as it is defined as forces/motion evaluated at the chosen frame)
|
|
- Important: bi (join position w.r.t top platform) and si (orientation of struts)
|
|
|
|
For the nano-hexapod:
|
|
- Size requirements: Maximum height, maximum radius
|
|
|
|
** 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
|
|
|
|
#+begin_src matlab :exports none :results silent :noweb yes
|
|
<<matlab-init>>
|
|
#+end_src
|
|
|
|
#+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
|
|
|
|
#+begin_src matlab :noweb yes
|
|
<<m-init-other>>
|
|
#+end_src
|
|
|
|
** Stiffness
|
|
|
|
- Give some examples:
|
|
- struts further apart: higher angular stiffness, same linear stiffness
|
|
- orientation: more vertical => increase vertical stiffness, decrease horizontal stiffness
|
|
|
|
** Mobility and required joint and actuator stroke
|
|
|
|
- Comparison of the XYZ mobility (fixed orientation) for two geometry (or maybe only in the XY or YZ plane to see more clearly the differences)
|
|
|
|
- [ ] [[file:~/Cloud/work-projects/ID31-NASS/matlab/stewart-simscape/org/kinematic-study.org::*Estimated required actuator stroke from specified platform mobility][Estimated required actuator stroke from specified platform mobility]]
|
|
Will be useful to choose the actuators
|
|
- [ ] [[file:~/Cloud/work-projects/ID31-NASS/matlab/stewart-simscape/org/kinematic-study.org::*Estimation of the Joint required Stroke][Estimation of the Joint required Stroke]]
|
|
Will be useful to design the flexible joints
|
|
|
|
** Conclusion
|
|
:PROPERTIES:
|
|
:UNNUMBERED: t
|
|
:END:
|
|
|
|
- [ ] Table that summarize the findings
|
|
[[file:~/Cloud/work-projects/ID31-NASS/documents/state-of-thesis-2020/index.org::*Optimal Nano-Hexapod Geometry][Optimal Nano-Hexapod Geometry]]
|
|
|
|
* The Cubic Architecture
|
|
:PROPERTIES:
|
|
:HEADER-ARGS:matlab+: :tangle matlab/detail_kinematics_1_.m
|
|
:END:
|
|
<<sec:detail_kinematics_cubic>>
|
|
** Introduction :ignore:
|
|
|
|
Cubic configuration file:~/Cloud/work-projects/ID31-NASS/matlab/stewart-simscape/org/cubic-configuration.org
|
|
|
|
** 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
|
|
|
|
#+begin_src matlab :exports none :results silent :noweb yes
|
|
<<matlab-init>>
|
|
#+end_src
|
|
|
|
#+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
|
|
|
|
#+begin_src matlab :noweb yes
|
|
<<m-init-other>>
|
|
#+end_src
|
|
|
|
** The Cubic Architecture
|
|
|
|
From [[cite:&geng94_six_degree_of_freed_activ]], 7 properties of cubic configuration:
|
|
1) Uniformity in control capability in all directions
|
|
2) Uniformity in stiffness in all directions
|
|
3) Minimum cross coupling force effect among actuators
|
|
4) Facilitate collocated sensor-actuator control system design
|
|
5) Simple kinematics relationships
|
|
6) Simple dynamic analysis
|
|
7) Simple mechanical design
|
|
|
|
|
|
|
|
- Principle
|
|
- Examples of Stewart platform with Cubic architecture
|
|
- Different options?
|
|
Center of the cube above the top platform?
|
|
Where to mention that ? With examples
|
|
|
|
|
|
|
|
** Static Properties
|
|
|
|
Explain that we get diagonal K matrix => static decoupling in the cartesian frame.
|
|
Uniform mobility in X,Y,Z directions
|
|
|
|
** Dynamical Properties?
|
|
|
|
[[cite:&mcinroy00_desig_contr_flexur_joint_hexap]]
|
|
|
|
[[cite:&afzali-far16_vibrat_dynam_isotr_hexap_analy_studies]]:
|
|
- proposes an architecture where the CoM can be above the top platform
|
|
- "*Dynamic isotropy*, leading to equal eigenfrequencies, is a powerful optimization measure."
|
|
|
|
|
|
|
|
- Show examples where the dynamics can indeed be decoupled in the cartesian frame (i.e. decoupled K and M matrices)
|
|
- Better decoupling between the struts? not sure...
|
|
Compute the coupling between the struts for a cubic and non-cubic architecture
|
|
- Same resonance frequencies for suspension modes?
|
|
Maybe in one case: sphere at the CoM?
|
|
Could be nice to show that.
|
|
Say that this can be nice for optimal damping for instance (link to paper explaining that)
|
|
|
|
* Conclusion
|
|
<<sec:detail_kinematics_conclusion>>
|
|
|
|
Inertia used for experiments will be very broad => difficult to optimize the dynamics
|
|
Specific geometry is not found to have a huge impact on performances.
|
|
Practical implementation is important.
|
|
|
|
Geometry impacts the static and dynamical characteristics of the Stewart platform.
|
|
Considering the design constrains, the slight change of geometry will not significantly impact the obtained results.
|
|
|
|
* Bibliography :ignore:
|
|
#+latex: \printbibliography[heading=bibintoc,title={Bibliography}]
|
|
|
|
* Helping Functions :noexport:
|
|
** Initialize Path
|
|
#+NAME: m-init-path
|
|
#+BEGIN_SRC matlab
|
|
%% Path for functions, data and scripts
|
|
addpath('./matlab/mat/'); % Path for data
|
|
addpath('./matlab/'); % Path for scripts
|
|
#+END_SRC
|
|
|
|
#+NAME: m-init-path-tangle
|
|
#+BEGIN_SRC matlab
|
|
%% Path for functions, data and scripts
|
|
addpath('./mat/'); % Path for data
|
|
#+END_SRC
|
|
|
|
** Initialize other elements
|
|
#+NAME: m-init-other
|
|
#+BEGIN_SRC matlab
|
|
%% Colors for the figures
|
|
colors = colororder;
|
|
#+END_SRC
|