First version
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@@ -1,32 +1,26 @@
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#+TITLE: Decoupling Properties of the Cubic Architecture
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:DRAWER:
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#+LANGUAGE: en
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#+EMAIL: dehaeze.thomas@gmail.com
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#+AUTHOR: Dehaeze Thomas
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#+BIND: org-latex-image-default-option "scale=1"
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#+BIND: org-latex-image-default-width ""
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#+LaTeX_CLASS: scrreprt
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#+LaTeX_CLASS_OPTIONS: [a4paper, 10pt, DIV=12, parskip=full, bibliography=totoc]
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#+OPTIONS: toc:nil date:nil
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#+LaTeX_CLASS: asmejour
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#+LaTeX_CLASS_OPTIONS: [balance,nocopyright,nolists]
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#+LATEX_HEADER: \input{preamble.tex}
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#+LATEX_HEADER_EXTRA: \input{preamble_extra.tex}
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#+LATEX_HEADER_EXTRA: \bibliography{dehaeze26_cubic_architecture.bib}
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#+BIND: org-latex-bib-compiler "biber"
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#+LATEX_HEADER_EXTRA: \usepackage[square,numbers]{natbib}
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#+LATEX_HEADER_EXTRA: \JourName{Journal of Mechanical Design}
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:END:
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#+latex: \clearpage
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* Build :noexport:
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#+NAME: startblock
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#+BEGIN_SRC emacs-lisp :results none :tangle no
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(add-to-list 'org-latex-classes
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'("scrreprt"
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"\\documentclass{scrreprt}"
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("\\chapter{%s}" . "\\chapter*{%s}")
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'("asmejour"
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"\\documentclass{asmejour}"
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("\\section{%s}" . "\\section*{%s}")
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("\\subsection{%s}" . "\\subsection*{%s}")
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("\\subsubsection{%s}" . "\\subsubsection*{%s}")
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("\\paragraph{%s}" . "\\paragraph*{%s}")
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))
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@@ -52,12 +46,27 @@
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(setq org-latex-packages-alist nil)
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(setq org-latex-default-packages-alist nil)
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;; Do not include the subtitle inside the title
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(setq org-latex-subtitle-separate t)
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(setq org-latex-subtitle-format "\\subtitle{%s}")
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;; Remove empty title as it is manually placed after "/begin{document}"
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(defun my-org-latex-remove-title (str)
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(replace-regexp-in-string "^\\\\title{}$" "" str))
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(setq org-export-before-parsing-hook '(org-ref-glossary-before-parsing
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org-ref-acronyms-before-parsing))
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(advice-add 'org-latex-template :filter-return 'my-org-latex-remove-title)
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;; Remove empty date
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(defun my-org-latex-remove-date (str)
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(replace-regexp-in-string "^\\\\date{}$" "" str))
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(advice-add 'org-latex-template :filter-return 'my-org-latex-remove-date)
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;; Remove Automatic add of \usepackage{biblatex}
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(defun my-org-remove-biblatex-final (output backend info)
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"Remove any \\usepackage[...]{biblatex} line from final LaTeX output."
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(when (eq backend 'latex)
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(replace-regexp-in-string
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"\\\\usepackage\\(\\[[^]]*\\]\\)?{biblatex}[ \t]*\\(\n\\|$\\)" "" output)))
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(add-hook 'org-export-filter-final-output-functions
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#'my-org-remove-biblatex-final)
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#+END_SRC
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* Notes :noexport:
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@@ -70,13 +79,105 @@ Guide: https://www.asme.org/publications-submissions/journals/information-for-au
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Research papers undergo full peer review. Authors are encouraged to prepare concise manuscripts that convey clearly the significance of the work. Research Papers do not have a specified length but are usually 8,000 to 12,000 words with 5-8 figures or tables.
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#+end_quote
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12000 words should be equivalent to 25 pages.
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** LaTeX Template
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%% * Option to color the vertical bar in the title block [barcolor = colorname]
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%% * where colorname is any name def'd by xcolor package; omit barcolor option to get black
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%%
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%% * Option to omit the list of figures and list of tables at the end [nolists]
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%%
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%% * Option to include line numbers [lineno]. You must run *twice* for proper placement of the
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%% * line numbers. The lineno package does not number tables, footnotes, or captions.
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%% * This option will disable balancing of the column heights on final page.
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%%
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%% * Option to balance column heights on final page [balance]. This option sometimes
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%% * misbehaves, so use it with an awareness that it can create unexpected problems.
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%% * This option is not compatible with line numbering.
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%%
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%% * Options for copyright notices:
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%% * Omit the ASME copyright from the footer [nocopyright]
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%% * Copyright footnote if all authors are government employees [govt]
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%% * Copyright footnote if some authors are government employees [govtsome]
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%% * Copyright footnote for government contractors [contractor]
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%%
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%% * Option to omit all ASME text fields from the footer [nofoot].
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%%
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%% * Option for single column formatting [singlecolumn].
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%%
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%% * Option for upright integrals [upint]
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%%
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%% * Additional math options from M. Sharpe's newtxmath package (pdfTeX only):
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%% * [varvw] for v and w that are better distinguished from Greek nu; fine
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%% * adjustments to subscripts [subscriptcorrection]; and various other options
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%% * such as [smallerops, varg, slantedGreek, frenchmath, varbb, cmbraces].
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%%
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%% * Support for the unicode-math package and its math options (LuaLaTeX only)
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%%
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%% * Options for the typewriter font:
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%% * [var0] replace default slashed zero by an unslashed zero
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%% * [mono] force interword separation to be monospaced
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%% * [hyphenate] allow hyphenation (pdfTeX only). Typewriter fonts usually are not hyphenated.
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%%
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%% * Options for the babel package to support passages in other languages (such as a translated
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%% * abstract in an appendix), e.g. [german]. The main language will default to English
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%% * unless a different main language is selected, e.g. [main=spanish]. See Appendix B for details.
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%%
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%% * PDF/A archivability compliance. Since 2022, LaTeX has included integrated support for PDF/A,
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%% * through the \DocumentMetadata{..} command. This works with both pdfTeX and luaLaTeX.
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%% * The legacy PDF/A class options have been dropped as of mid-2025.
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** DONE [#B] Setup the template for the journal
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CLOSED: [2025-11-27 Thu 17:30] SCHEDULED: <2025-11-26 Wed>
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** TODO [#B] Add more content from the PhD thesis?
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Maybe add:
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- [[file:~/Cloud/work-projects/ID31-NASS/phd-thesis-chapters/B1-nass-geometry/nass-geometry.org::*Review of Stewart platforms][Review of Stewart platforms]]
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- [[file:~/Cloud/work-projects/ID31-NASS/phd-thesis-chapters/B1-nass-geometry/nass-geometry.org::*Effect of geometry on Stewart platform properties][Effect of geometry on Stewart platform properties]]
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- [ ] [[file:~/Cloud/work-projects/ID31-NASS/phd-thesis-chapters/A5-simscape-nano-hexapod/simscape-nano-hexapod.org::*The Stewart platform][The Stewart platform]]
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For the equations of motion, definition of the geometry, Jacobian matrix, etc...
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- [ ] [[file:~/Cloud/work-projects/ID31-NASS/phd-thesis-chapters/B1-nass-geometry/nass-geometry.org::*Review of Stewart platforms][Review of Stewart platforms]]
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- [ ] [[file:~/Cloud/work-projects/ID31-NASS/phd-thesis-chapters/B1-nass-geometry/nass-geometry.org::*Effect of geometry on Stewart platform properties][Effect of geometry on Stewart platform properties]]
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* Introduction :ignore:
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* Title and Abstract :ignore:
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#+begin_export latex
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\SetAuthorBlock{Thomas Dehaeze\CorrespondingAuthor}{%
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ESRF, The European Synchrotron\\
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Grenoble, France\\
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email: thomas.dehaeze@esrf.fr
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}
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\SetAuthorBlock{Christophe Collette}{%
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Precision Mechatronics Laboratory\\
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University of Li\`{e}ge, Belgium\\
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email: christophe.collette@uliege.be
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}
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%%% Change to your paper title. Can insert line breaks if you wish (otherwise breaks are selected automatically).
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\title{Decoupling Properties of the Cubic Architecture}
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#+end_export
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# less than 150 words and is normally in italics
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#+begin_export latex
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\begin{abstract}
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{\it This is the abstract.
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This article illustrates preparation of ASME paper using
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Please use this template to test how your figures will look on the printed journal page of the Journal of Mechanical Design. The Journal will no longer publish papers that contain errors in figure resolution. These usually consist of unreadable or fuzzy text, and pixilation or rasterization of lines. This template identifies the specifications used by JMD some of which may not be easily duplicated; for example, ASME actually uses Helvetica Condensed Bold, but this is not generally available so for the purpose of this exercise Helvetica is adequate. However, reproduction of the journal page is not the goal, instead this exercise is to verify the quality of your figures. Notice that this abstract is to be set in 9pt Times Italic, single spaced and right justified.
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}
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\end{abstract}
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#+end_export
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#+begin_export latex
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\date{Version \versionno, \today}%% You can modify this information as desired.
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%% Putting \date{} will suppress any date.
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%% If this command is omitted, date defaults to \today
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%% This command must come somewhere before \maketitle
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\maketitle %% This command creates the author/title/abstract block. Essential!
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#+end_export
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* Introduction
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The Cubic configuration for the Stewart platform was first proposed by Dr. Gough in a comment to the original paper by Dr. Stewart [[cite:&stewart65_platf_with_six_degrees_freed]].
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This configuration is characterized by active struts arranged in a mutually orthogonal configuration connecting the corners of a cube, as shown in Figure ref:fig:detail_kinematics_cubic_architecture_example.
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@@ -90,15 +191,15 @@ It is also possible to implement designs with strut lengths smaller than the cub
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#+attr_latex: :options [htbp]
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#+begin_figure
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#+attr_latex: :caption \subcaption{\label{fig:detail_kinematics_cubic_architecture_example}Classical Cubic architecture}
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#+attr_latex: :options {0.49\textwidth}
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#+attr_latex: :options {\linewidth}
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#+begin_subfigure
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#+attr_latex: :scale 1
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#+attr_latex: :scale 0.7
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[[file:figs/detail_kinematics_cubic_architecture_example.png]]
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#+end_subfigure
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#+attr_latex: :caption \subcaption{\label{fig:detail_kinematics_cubic_architecture_example_small}Alternative configuration}
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#+attr_latex: :options {0.49\textwidth}
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#+attr_latex: :options {\linewidth}
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#+begin_subfigure
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#+attr_latex: :scale 1
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#+attr_latex: :scale 0.7
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[[file:figs/detail_kinematics_cubic_architecture_example_small.png]]
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#+end_subfigure
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#+end_figure
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@@ -121,12 +222,14 @@ Consider the cubic architecture shown in Figure ref:fig:detail_kinematics_cubic_
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The unit vectors corresponding to the edges of the cube are described by equation eqref:eq:detail_kinematics_cubic_s.
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\begin{equation}\label{eq:detail_kinematics_cubic_s}
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\hat{\bm{s}}_1 = \begin{bmatrix} \frac{\sqrt{2}}{\sqrt{3}} \\ 0 \\ \frac{1}{\sqrt{3}} \end{bmatrix} \quad
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\hat{\bm{s}}_2 = \begin{bmatrix} \frac{-1}{\sqrt{6}} \\ \frac{-1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} \end{bmatrix} \quad
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\hat{\bm{s}}_3 = \begin{bmatrix} \frac{-1}{\sqrt{6}} \\ \frac{ 1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} \end{bmatrix} \quad
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\hat{\bm{s}}_4 = \begin{bmatrix} \frac{\sqrt{2}}{\sqrt{3}} \\ 0 \\ \frac{1}{\sqrt{3}} \end{bmatrix} \quad
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\hat{\bm{s}}_5 = \begin{bmatrix} \frac{-1}{\sqrt{6}} \\ \frac{-1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} \end{bmatrix} \quad
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\hat{\bm{s}}_6 = \begin{bmatrix} \frac{-1}{\sqrt{6}} \\ \frac{ 1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} \end{bmatrix}
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\begin{align*}
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\hat{\bm{s}}_1 = \begin{bmatrix} \frac{\sqrt{2}}{\sqrt{3}} \\ 0 \\ \frac{1}{\sqrt{3}} \end{bmatrix} \quad
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\hat{\bm{s}}_2 = \begin{bmatrix} \frac{-1}{\sqrt{6}} \\ \frac{-1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} \end{bmatrix} \quad
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\hat{\bm{s}}_3 = \begin{bmatrix} \frac{-1}{\sqrt{6}} \\ \frac{ 1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} \end{bmatrix} \\
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\hat{\bm{s}}_4 = \begin{bmatrix} \frac{\sqrt{2}}{\sqrt{3}} \\ 0 \\ \frac{1}{\sqrt{3}} \end{bmatrix} \quad
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\hat{\bm{s}}_5 = \begin{bmatrix} \frac{-1}{\sqrt{6}} \\ \frac{-1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} \end{bmatrix} \quad
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\hat{\bm{s}}_6 = \begin{bmatrix} \frac{-1}{\sqrt{6}} \\ \frac{ 1}{\sqrt{2}} \\ \frac{1}{\sqrt{3}} \end{bmatrix}
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\end{align*}
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\end{equation}
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#+name: fig:detail_kinematics_cubic_schematic_cases
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@@ -134,15 +237,15 @@ The unit vectors corresponding to the edges of the cube are described by equatio
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#+attr_latex: :options [htbp]
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#+begin_figure
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#+attr_latex: :caption \subcaption{\label{fig:detail_kinematics_cubic_schematic_full}Full cube}
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#+attr_latex: :options {0.48\textwidth}
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#+attr_latex: :options {\linewidth}
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#+begin_subfigure
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#+attr_latex: :scale 0.9
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#+attr_latex: :scale 0.8
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[[file:figs/detail_kinematics_cubic_schematic_full.png]]
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#+end_subfigure
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#+attr_latex: :caption \subcaption{\label{fig:detail_kinematics_cubic_schematic}Cube's portion}
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#+attr_latex: :options {0.48\textwidth}
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#+attr_latex: :options {\linewidth}
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#+begin_subfigure
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#+attr_latex: :scale 0.9
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#+attr_latex: :scale 0.8
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[[file:figs/detail_kinematics_cubic_schematic.png]]
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#+end_subfigure
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#+end_figure
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@@ -150,16 +253,18 @@ The unit vectors corresponding to the edges of the cube are described by equatio
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Coordinates of the cube's vertices relevant for the top joints, expressed with respect to the cube's center, are shown in equation eqref:eq:detail_kinematics_cubic_vertices.
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\begin{equation}\label{eq:detail_kinematics_cubic_vertices}
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\tilde{\bm{b}}_1 = \tilde{\bm{b}}_2 = H_c \begin{bmatrix} \frac{1}{\sqrt{2}} \\ \frac{-\sqrt{3}}{\sqrt{2}} \\ \frac{1}{2} \end{bmatrix}, \quad
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\tilde{\bm{b}}_3 = \tilde{\bm{b}}_4 = H_c \begin{bmatrix} \frac{1}{\sqrt{2}} \\ \frac{ \sqrt{3}}{\sqrt{2}} \\ \frac{1}{2} \end{bmatrix}, \quad
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\tilde{\bm{b}}_5 = \tilde{\bm{b}}_6 = H_c \begin{bmatrix} \frac{-2}{\sqrt{2}} \\ 0 \\ \frac{1}{2} \end{bmatrix}
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\begin{align*}
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\tilde{\bm{b}}_1 &= \tilde{\bm{b}}_2 = H_c \begin{bmatrix} \frac{1}{\sqrt{2}} \\ \frac{-\sqrt{3}}{\sqrt{2}} \\ \frac{1}{2} \end{bmatrix}, \quad
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\tilde{\bm{b}}_3 = \tilde{\bm{b}}_4 = H_c \begin{bmatrix} \frac{1}{\sqrt{2}} \\ \frac{ \sqrt{3}}{\sqrt{2}} \\ \frac{1}{2} \end{bmatrix}, \\
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\tilde{\bm{b}}_5 &= \tilde{\bm{b}}_6 = H_c \begin{bmatrix} \frac{-2}{\sqrt{2}} \\ 0 \\ \frac{1}{2} \end{bmatrix}
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\end{align*}
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\end{equation}
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In the case where top joints are positioned at the cube's vertices, a diagonal stiffness matrix is obtained as shown in equation eqref:eq:detail_kinematics_cubic_stiffness.
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Translation stiffness is twice the stiffness of the struts, and rotational stiffness is proportional to the square of the cube's size $H_c$.
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\begin{equation}\label{eq:detail_kinematics_cubic_stiffness}
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\bm{K}_{\{B\} = \{C\}} = k \begin{bmatrix}
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\bm{K} = k \begin{bmatrix}
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2 & 0 & 0 & 0 & 0 & 0 \\
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0 & 2 & 0 & 0 & 0 & 0 \\
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0 & 0 & 2 & 0 & 0 & 0 \\
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@@ -189,14 +294,15 @@ Considering a vertical shift as shown in Figure ref:fig:detail_kinematics_cubic_
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Off-diagonal elements increase proportionally with the height difference between the cube's center and the considered $\{B\}$ frame.
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\begin{equation}\label{eq:detail_kinematics_cubic_stiffness_off_centered}
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\bm{K}_{\{B\} \neq \{C\}} = k \begin{bmatrix}
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\bm{K} = k \\
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{\footnotesize \begin{bmatrix}
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2 & 0 & 0 & 0 & -2 H & 0 \\
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0 & 2 & 0 & 2 H & 0 & 0 \\
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0 & 0 & 2 & 0 & 0 & 0 \\
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0 & 2 H & 0 & \frac{3}{2} H_c^2 + 2 H^2 & 0 & 0 \\
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-2 H & 0 & 0 & 0 & \frac{3}{2} H_c^2 + 2 H^2 & 0 \\
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0 & 0 & 0 & 0 & 0 & 6 H_c^2 \\
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\end{bmatrix}
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\end{bmatrix}}
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\end{equation}
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This stiffness matrix structure is characteristic of Stewart platforms exhibiting symmetry, and is not an exclusive property of cubic architectures.
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@@ -224,15 +330,15 @@ Furthermore, an inverse relationship exists between the cube's dimension and rot
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#+attr_latex: :options [htbp]
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#+begin_figure
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#+attr_latex: :caption \subcaption{\label{fig:detail_kinematics_cubic_mobility_translations}Mobility in translation}
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#+attr_latex: :options {0.48\textwidth}
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#+attr_latex: :options {\linewidth}
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#+begin_subfigure
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#+attr_latex: :scale 1
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#+attr_latex: :scale 0.8
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[[file:figs/detail_kinematics_cubic_mobility_translations.png]]
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#+end_subfigure
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#+attr_latex: :caption \subcaption{\label{fig:detail_kinematics_cubic_mobility_rotations}Mobility in rotation}
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#+attr_latex: :options {0.48\textwidth}
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#+attr_latex: :options {\linewidth}
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#+begin_subfigure
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#+attr_latex: :scale 1
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#+attr_latex: :scale 0.8
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[[file:figs/detail_kinematics_cubic_mobility_rotations.png]]
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#+end_subfigure
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#+end_figure
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@@ -269,7 +375,7 @@ To achieve a diagonal mass matrix, the center of mass of the mobile components m
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#+name: fig:detail_kinematics_cubic_payload
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#+caption: Cubic stewart platform with top cylindrical payload
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#+attr_latex: :width 0.6\linewidth
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#+attr_latex: :width 0.7\linewidth
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[[file:figs/detail_kinematics_cubic_payload.png]]
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To verify these properties, a cubic Stewart platform with a cylindrical payload was analyzed (Figure ref:fig:detail_kinematics_cubic_payload).
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@@ -282,15 +388,15 @@ Conversely, when positioned at the center of stiffness, coupling occurred at hig
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#+attr_latex: :options [htbp]
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#+begin_figure
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#+attr_latex: :caption \subcaption{\label{fig:detail_kinematics_cubic_cart_coupling_com}$\{B\}$ at the center of mass}
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#+attr_latex: :options {0.48\textwidth}
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#+attr_latex: :options {\linewidth}
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#+begin_subfigure
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#+attr_latex: :width 0.95\linewidth
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#+attr_latex: :scale 0.8
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[[file:figs/detail_kinematics_cubic_cart_coupling_com.png]]
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#+end_subfigure
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#+attr_latex: :caption \subcaption{\label{fig:detail_kinematics_cubic_cart_coupling_cok}$\{B\}$ at the cube's center}
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#+attr_latex: :options {0.48\textwidth}
|
||||
#+attr_latex: :options {\linewidth}
|
||||
#+begin_subfigure
|
||||
#+attr_latex: :width 0.95\linewidth
|
||||
#+attr_latex: :scale 0.8
|
||||
[[file:figs/detail_kinematics_cubic_cart_coupling_cok.png]]
|
||||
#+end_subfigure
|
||||
#+end_figure
|
||||
@@ -299,7 +405,7 @@ Conversely, when positioned at the center of stiffness, coupling occurred at hig
|
||||
|
||||
An effective strategy for improving dynamical performances involves aligning the cube's center (center of stiffness) with the center of mass of the moving components [[cite:&li01_simul_fault_vibrat_isolat_point]].
|
||||
This can be achieved by positioning the payload below the top platform, such that the center of mass of the moving body coincides with the cube's center (Figure ref:fig:detail_kinematics_cubic_centered_payload).
|
||||
This approach was physically implemented in several studies [[cite:&mcinroy99_dynam;&jafari03_orthog_gough_stewar_platf_microm]], as shown in Figure ref:fig:detail_kinematics_uw_gsp.
|
||||
This approach was physically implemented in several studies [[cite:&mcinroy99_dynam;&jafari03_orthog_gough_stewar_platf_microm]].
|
||||
The resulting dynamics are indeed well-decoupled (Figure ref:fig:detail_kinematics_cubic_cart_coupling_com_cok), taking advantage from diagonal stiffness and mass matrices.
|
||||
The primary limitation of this approach is that, for many applications including the nano-hexapod, the payload must be positioned above the top platform.
|
||||
If a design similar to Figure ref:fig:detail_kinematics_cubic_centered_payload were employed for the nano-hexapod, the X-ray beam would intersect with the struts during spindle rotation.
|
||||
@@ -309,15 +415,15 @@ If a design similar to Figure ref:fig:detail_kinematics_cubic_centered_payload w
|
||||
#+attr_latex: :options [htbp]
|
||||
#+begin_figure
|
||||
#+attr_latex: :caption \subcaption{\label{fig:detail_kinematics_cubic_centered_payload}Payload at the cube's center}
|
||||
#+attr_latex: :options {0.49\textwidth}
|
||||
#+attr_latex: :options {\linewidth}
|
||||
#+begin_subfigure
|
||||
#+attr_latex: :width 0.95\linewidth
|
||||
#+attr_latex: :width 0.7\linewidth
|
||||
[[file:figs/detail_kinematics_cubic_centered_payload.png]]
|
||||
#+end_subfigure
|
||||
#+attr_latex: :caption \subcaption{\label{fig:detail_kinematics_cubic_cart_coupling_com_cok}Fully decoupled cartesian plant}
|
||||
#+attr_latex: :options {0.49\textwidth}
|
||||
#+attr_latex: :options {\linewidth}
|
||||
#+begin_subfigure
|
||||
#+attr_latex: :width 0.95\linewidth
|
||||
#+attr_latex: :scale 0.8
|
||||
[[file:figs/detail_kinematics_cubic_cart_coupling_com_cok.png]]
|
||||
#+end_subfigure
|
||||
#+end_figure
|
||||
@@ -348,7 +454,7 @@ The second uses a non-cubic Stewart platform shown in Figure ref:fig:detail_kine
|
||||
|
||||
#+name: fig:detail_kinematics_non_cubic_payload
|
||||
#+caption: Stewart platform with non-cubic architecture
|
||||
#+attr_latex: :width 0.6\linewidth
|
||||
#+attr_latex: :width 0.7\linewidth
|
||||
[[file:figs/detail_kinematics_non_cubic_payload.png]]
|
||||
|
||||
** Relative Displacement Sensors
|
||||
@@ -365,15 +471,15 @@ The resonance frequencies differ between the two cases because the more vertical
|
||||
#+attr_latex: :options [htbp]
|
||||
#+begin_figure
|
||||
#+attr_latex: :caption \subcaption{\label{fig:detail_kinematics_non_cubic_decentralized_dL}Non cubic architecture}
|
||||
#+attr_latex: :options {0.48\textwidth}
|
||||
#+attr_latex: :options {\linewidth}
|
||||
#+begin_subfigure
|
||||
#+attr_latex: :width 0.95\linewidth
|
||||
#+attr_latex: :scale 0.8
|
||||
[[file:figs/detail_kinematics_non_cubic_decentralized_dL.png]]
|
||||
#+end_subfigure
|
||||
#+attr_latex: :caption \subcaption{\label{fig:detail_kinematics_cubic_decentralized_dL}Cubic architecture}
|
||||
#+attr_latex: :options {0.48\textwidth}
|
||||
#+attr_latex: :options {\linewidth}
|
||||
#+begin_subfigure
|
||||
#+attr_latex: :width 0.95\linewidth
|
||||
#+attr_latex: :scale 0.8
|
||||
[[file:figs/detail_kinematics_cubic_decentralized_dL.png]]
|
||||
#+end_subfigure
|
||||
#+end_figure
|
||||
@@ -389,15 +495,15 @@ The system demonstrates good decoupling at high frequency in both cases, with no
|
||||
#+attr_latex: :options [htbp]
|
||||
#+begin_figure
|
||||
#+attr_latex: :caption \subcaption{\label{fig:detail_kinematics_non_cubic_decentralized_fn}Non cubic architecture}
|
||||
#+attr_latex: :options {0.48\textwidth}
|
||||
#+attr_latex: :options {\linewidth}
|
||||
#+begin_subfigure
|
||||
#+attr_latex: :width 0.95\linewidth
|
||||
#+attr_latex: :scale 0.8
|
||||
[[file:figs/detail_kinematics_non_cubic_decentralized_fn.png]]
|
||||
#+end_subfigure
|
||||
#+attr_latex: :caption \subcaption{\label{fig:detail_kinematics_cubic_decentralized_fn}Cubic architecture}
|
||||
#+attr_latex: :options {0.48\textwidth}
|
||||
#+attr_latex: :options {\linewidth}
|
||||
#+begin_subfigure
|
||||
#+attr_latex: :width 0.95\linewidth
|
||||
#+attr_latex: :scale 0.8
|
||||
[[file:figs/detail_kinematics_cubic_decentralized_fn.png]]
|
||||
#+end_subfigure
|
||||
#+end_figure
|
||||
@@ -441,21 +547,21 @@ This approach yields a compact architecture, but the small cube size may result
|
||||
#+attr_latex: :options [htbp]
|
||||
#+begin_figure
|
||||
#+attr_latex: :caption \subcaption{\label{fig:detail_kinematics_cubic_above_small_iso}Isometric view}
|
||||
#+attr_latex: :options {0.36\textwidth}
|
||||
#+attr_latex: :options {\linewidth}
|
||||
#+begin_subfigure
|
||||
#+attr_latex: :width 0.9\linewidth
|
||||
#+attr_latex: :scale 0.7
|
||||
[[file:figs/detail_kinematics_cubic_above_small_iso.png]]
|
||||
#+end_subfigure
|
||||
#+attr_latex: :caption \subcaption{\label{fig:detail_kinematics_cubic_above_small_side}Side view}
|
||||
#+attr_latex: :options {0.30\textwidth}
|
||||
#+attr_latex: :options {\linewidth}
|
||||
#+begin_subfigure
|
||||
#+attr_latex: :width 0.9\linewidth
|
||||
#+attr_latex: :scale 0.7
|
||||
[[file:figs/detail_kinematics_cubic_above_small_side.png]]
|
||||
#+end_subfigure
|
||||
#+attr_latex: :caption \subcaption{\label{fig:detail_kinematics_cubic_above_small_top}Top view}
|
||||
#+attr_latex: :options {0.30\textwidth}
|
||||
#+attr_latex: :options {\linewidth}
|
||||
#+begin_subfigure
|
||||
#+attr_latex: :width 0.9\linewidth
|
||||
#+attr_latex: :scale 0.7
|
||||
[[file:figs/detail_kinematics_cubic_above_small_top.png]]
|
||||
#+end_subfigure
|
||||
#+end_figure
|
||||
@@ -468,28 +574,28 @@ Increasing the cube's size such that eqref:eq:detail_kinematics_cube_medium is v
|
||||
2 H_{CoM} < H_c < 2 (H_{CoM} + H)
|
||||
\end{equation}
|
||||
|
||||
This configuration resembles the design proposed in [[cite:&yang19_dynam_model_decoup_contr_flexib]] (Figure ref:fig:detail_kinematics_yang19), although their design is not strictly cubic.
|
||||
This configuration resembles the design proposed in [[cite:&yang19_dynam_model_decoup_contr_flexib]], although their design is not strictly cubic.
|
||||
|
||||
#+name: fig:detail_kinematics_cubic_above_medium
|
||||
#+caption: Cubic architecture with cube's center above the top platform. A cube height of 140mm is used.
|
||||
#+attr_latex: :options [htbp]
|
||||
#+begin_figure
|
||||
#+attr_latex: :caption \subcaption{\label{fig:detail_kinematics_cubic_above_medium_iso}Isometric view}
|
||||
#+attr_latex: :options {0.36\textwidth}
|
||||
#+attr_latex: :options {\linewidth}
|
||||
#+begin_subfigure
|
||||
#+attr_latex: :width 0.9\linewidth
|
||||
#+attr_latex: :scale 0.7
|
||||
[[file:figs/detail_kinematics_cubic_above_medium_iso.png]]
|
||||
#+end_subfigure
|
||||
#+attr_latex: :caption \subcaption{\label{fig:detail_kinematics_cubic_above_medium_side}Side view}
|
||||
#+attr_latex: :options {0.30\textwidth}
|
||||
#+attr_latex: :options {\linewidth}
|
||||
#+begin_subfigure
|
||||
#+attr_latex: :width 0.9\linewidth
|
||||
#+attr_latex: :scale 0.7
|
||||
[[file:figs/detail_kinematics_cubic_above_medium_side.png]]
|
||||
#+end_subfigure
|
||||
#+attr_latex: :caption \subcaption{\label{fig:detail_kinematics_cubic_above_medium_top}Top view}
|
||||
#+attr_latex: :options {0.30\textwidth}
|
||||
#+attr_latex: :options {\linewidth}
|
||||
#+begin_subfigure
|
||||
#+attr_latex: :width 0.9\linewidth
|
||||
#+attr_latex: :scale 0.7
|
||||
[[file:figs/detail_kinematics_cubic_above_medium_top.png]]
|
||||
#+end_subfigure
|
||||
#+end_figure
|
||||
@@ -507,21 +613,21 @@ When the cube's height exceeds twice the sum of the platform height and CoM heig
|
||||
#+attr_latex: :options [htbp]
|
||||
#+begin_figure
|
||||
#+attr_latex: :caption \subcaption{\label{fig:detail_kinematics_cubic_above_large_iso}Isometric view}
|
||||
#+attr_latex: :options {0.36\textwidth}
|
||||
#+attr_latex: :options {\linewidth}
|
||||
#+begin_subfigure
|
||||
#+attr_latex: :width 0.9\linewidth
|
||||
#+attr_latex: :scale 0.7
|
||||
[[file:figs/detail_kinematics_cubic_above_large_iso.png]]
|
||||
#+end_subfigure
|
||||
#+attr_latex: :caption \subcaption{\label{fig:detail_kinematics_cubic_above_large_side}Side view}
|
||||
#+attr_latex: :options {0.30\textwidth}
|
||||
#+attr_latex: :options {\linewidth}
|
||||
#+begin_subfigure
|
||||
#+attr_latex: :width 0.9\linewidth
|
||||
#+attr_latex: :scale 0.7
|
||||
[[file:figs/detail_kinematics_cubic_above_large_side.png]]
|
||||
#+end_subfigure
|
||||
#+attr_latex: :caption \subcaption{\label{fig:detail_kinematics_cubic_above_large_top}Top view}
|
||||
#+attr_latex: :options {0.30\textwidth}
|
||||
#+attr_latex: :options {\linewidth}
|
||||
#+begin_subfigure
|
||||
#+attr_latex: :width 0.9\linewidth
|
||||
#+attr_latex: :scale 0.7
|
||||
[[file:figs/detail_kinematics_cubic_above_large_top.png]]
|
||||
#+end_subfigure
|
||||
#+end_figure
|
||||
@@ -563,5 +669,23 @@ To address this limitation, modified cubic architectures have been proposed with
|
||||
Three distinct configurations have been identified, each with different geometric arrangements but sharing the common characteristic that the cube's center is positioned above the top platform.
|
||||
This structural modification enables the alignment of the moving body's center of mass with the center of stiffness, resulting in beneficial decoupling properties in the Cartesian frame.
|
||||
|
||||
* Acknowledgment :ignore:
|
||||
#+begin_export latex
|
||||
\begin{acknowledgment}
|
||||
ASME Technical Publications provided the format specifications for the Journal of Mechanical Design, though they are not easy to reproduce. It is their commitment to ensuring quality figures in every issue of JMD that motivates this effort to have authors review the presentation of their figures.
|
||||
|
||||
Thanks go to D. E. Knuth and L. Lamport for developing the wonderful word processing software packages \TeX\ and \LaTeX. We would like to thank Ken Sprott, Kirk van Katwyk, and Matt Campbell for fixing bugs in the ASME style file \verb+asme2ej.cls+, and Geoff Shiflett for creating
|
||||
ASME bibliography stype file \verb+asmems4.bst+.
|
||||
\end{acknowledgment}
|
||||
#+end_export
|
||||
|
||||
* Bibliography :ignore:
|
||||
#+latex: \printbibliography[heading=bibintoc,title={Bibliography}]
|
||||
#+begin_export latex
|
||||
\bibliographystyle{asmems4}
|
||||
|
||||
% Here's where you specify the bibliography database file.
|
||||
% The full file name of the bibliography database for this
|
||||
% article is asme2e.bib. The name for your database is up
|
||||
% to you.
|
||||
\bibliography{dehaeze26_cubic_architecture}
|
||||
#+end_export
|
||||
|
||||
Reference in New Issue
Block a user