2020-01-27 17:42:09 +01:00
|
|
|
#+TITLE: Stewart Platform - Static Analysis
|
|
|
|
|
:DRAWER:
|
2020-02-11 15:50:52 +01:00
|
|
|
#+STARTUP: overview
|
|
|
|
|
|
|
|
|
|
#+LANGUAGE: en
|
|
|
|
|
#+EMAIL: dehaeze.thomas@gmail.com
|
|
|
|
|
#+AUTHOR: Dehaeze Thomas
|
|
|
|
|
|
2020-01-27 17:42:09 +01:00
|
|
|
#+HTML_LINK_HOME: ./index.html
|
|
|
|
|
#+HTML_LINK_UP: ./index.html
|
|
|
|
|
|
|
|
|
|
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="./css/htmlize.css"/>
|
|
|
|
|
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="./css/readtheorg.css"/>
|
|
|
|
|
#+HTML_HEAD: <script src="./js/jquery.min.js"></script>
|
|
|
|
|
#+HTML_HEAD: <script src="./js/bootstrap.min.js"></script>
|
|
|
|
|
#+HTML_HEAD: <script src="./js/jquery.stickytableheaders.min.js"></script>
|
|
|
|
|
#+HTML_HEAD: <script src="./js/readtheorg.js"></script>
|
|
|
|
|
|
|
|
|
|
#+PROPERTY: header-args:matlab :session *MATLAB*
|
|
|
|
|
#+PROPERTY: header-args:matlab+ :comments org
|
|
|
|
|
#+PROPERTY: header-args:matlab+ :exports both
|
|
|
|
|
#+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
|
2020-02-11 15:50:52 +01:00
|
|
|
|
|
|
|
|
#+PROPERTY: header-args:latex :headers '("\\usepackage{tikz}" "\\usepackage{import}" "\\import{$HOME/Cloud/thesis/latex/}{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+ :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")
|
2020-01-27 17:42:09 +01:00
|
|
|
:END:
|
|
|
|
|
|
|
|
|
|
* Coupling
|
|
|
|
|
What causes the coupling from $F_i$ to $X_i$ ?
|
|
|
|
|
|
|
|
|
|
#+begin_src latex :file coupling.pdf :post pdf2svg(file=*this*, ext="png") :exports both
|
|
|
|
|
\begin{tikzpicture}
|
|
|
|
|
\node[block] (Jt) at (0, 0) {$J^{-T}$};
|
|
|
|
|
\node[block, right= of Jt] (G) {$G$};
|
|
|
|
|
\node[block, right= of G] (J) {$J^{-1}$};
|
|
|
|
|
|
|
|
|
|
\draw[->] ($(Jt.west)+(-0.8, 0)$) -- (Jt.west) node[above left]{$F_i$};
|
|
|
|
|
\draw[->] (Jt.east) -- (G.west) node[above left]{$\tau_i$};
|
|
|
|
|
\draw[->] (G.east) -- (J.west) node[above left]{$q_i$};
|
|
|
|
|
\draw[->] (J.east) -- ++(0.8, 0) node[above left]{$X_i$};
|
|
|
|
|
\end{tikzpicture}
|
|
|
|
|
#+end_src
|
|
|
|
|
|
|
|
|
|
#+name: fig:block_diag_coupling
|
|
|
|
|
#+caption: Block diagram to control an hexapod
|
|
|
|
|
#+RESULTS:
|
|
|
|
|
[[file:figs/coupling.png]]
|
|
|
|
|
|
|
|
|
|
There is no coupling from $F_i$ to $X_j$ if $J^{-1} G J^{-T}$ is diagonal.
|
|
|
|
|
|
|
|
|
|
If $G$ is diagonal (cubic configuration), then $J^{-1} G J^{-T} = G J^{-1} J^{-T} = G (J^{T} J)^{-1} = G K^{-1}$
|
|
|
|
|
|
|
|
|
|
Thus, the system is uncoupled if $G$ and $K$ are diagonal.
|
