2020-01-22 15:47:00 +01:00
|
|
|
<?xml version="1.0" encoding="utf-8"?>
|
|
|
|
|
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
|
|
|
|
|
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
|
|
|
|
|
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
|
|
|
|
|
<head>
|
2020-08-05 13:28:14 +02:00
|
|
|
<!-- 2020-08-05 mer. 13:27 -->
|
2020-01-22 15:47:00 +01:00
|
|
|
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
|
2020-02-11 15:27:39 +01:00
|
|
|
<title>Stewart Platform - Static Analysis</title>
|
2020-01-22 15:47:00 +01:00
|
|
|
<meta name="generator" content="Org mode" />
|
|
|
|
|
<meta name="author" content="Dehaeze Thomas" />
|
|
|
|
|
<link rel="stylesheet" type="text/css" href="./css/htmlize.css"/>
|
|
|
|
|
<link rel="stylesheet" type="text/css" href="./css/readtheorg.css"/>
|
2020-02-11 15:27:39 +01:00
|
|
|
<script src="./js/jquery.min.js"></script>
|
|
|
|
|
<script src="./js/bootstrap.min.js"></script>
|
|
|
|
|
<script src="./js/jquery.stickytableheaders.min.js"></script>
|
|
|
|
|
<script src="./js/readtheorg.js"></script>
|
2020-08-05 13:28:14 +02:00
|
|
|
<script>MathJax = {
|
|
|
|
|
tex: {
|
|
|
|
|
tags: 'ams',
|
|
|
|
|
macros: {bm: ["\\boldsymbol{#1}",1],}
|
|
|
|
|
}
|
2020-02-11 15:27:39 +01:00
|
|
|
};
|
|
|
|
|
</script>
|
2020-08-05 13:28:14 +02:00
|
|
|
<script type="text/javascript" src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
|
2020-01-22 15:47:00 +01:00
|
|
|
</head>
|
|
|
|
|
<body>
|
|
|
|
|
<div id="org-div-home-and-up">
|
|
|
|
|
<a accesskey="h" href="./index.html"> UP </a>
|
|
|
|
|
|
|
|
|
|
|
<a accesskey="H" href="./index.html"> HOME </a>
|
|
|
|
|
</div><div id="content">
|
2020-02-11 15:27:39 +01:00
|
|
|
<h1 class="title">Stewart Platform - Static Analysis</h1>
|
|
|
|
|
<div id="table-of-contents">
|
|
|
|
|
<h2>Table of Contents</h2>
|
|
|
|
|
<div id="text-table-of-contents">
|
|
|
|
|
<ul>
|
2020-02-11 15:50:52 +01:00
|
|
|
<li><a href="#orgc502e97">1. Coupling</a></li>
|
2020-01-22 15:47:00 +01:00
|
|
|
</ul>
|
2020-02-11 15:27:39 +01:00
|
|
|
</div>
|
|
|
|
|
</div>
|
2020-01-22 15:47:00 +01:00
|
|
|
|
2020-02-11 15:27:39 +01:00
|
|
|
<div id="outline-container-orgc502e97" class="outline-2">
|
2020-02-11 15:50:52 +01:00
|
|
|
<h2 id="orgc502e97"><span class="section-number-2">1</span> Coupling</h2>
|
|
|
|
|
<div class="outline-text-2" id="text-1">
|
2020-01-22 15:47:00 +01:00
|
|
|
<p>
|
2020-02-11 15:27:39 +01:00
|
|
|
What causes the coupling from \(F_i\) to \(X_i\) ?
|
2020-01-22 15:47:00 +01:00
|
|
|
</p>
|
|
|
|
|
|
|
|
|
|
|
2020-02-11 15:27:39 +01:00
|
|
|
<div id="org41430df" class="figure">
|
|
|
|
|
<p><img src="figs/coupling.png" alt="coupling.png" />
|
|
|
|
|
</p>
|
|
|
|
|
<p><span class="figure-number">Figure 1: </span>Block diagram to control an hexapod</p>
|
2020-01-22 15:47:00 +01:00
|
|
|
</div>
|
|
|
|
|
|
|
|
|
|
<p>
|
2020-02-11 15:27:39 +01:00
|
|
|
There is no coupling from \(F_i\) to \(X_j\) if \(J^{-1} G J^{-T}\) is diagonal.
|
|
|
|
|
</p>
|
|
|
|
|
|
|
|
|
|
<p>
|
|
|
|
|
If \(G\) is diagonal (cubic configuration), then \(J^{-1} G J^{-T} = G J^{-1} J^{-T} = G (J^{T} J)^{-1} = G K^{-1}\)
|
2020-01-22 15:47:00 +01:00
|
|
|
</p>
|
|
|
|
|
|
|
|
|
|
<p>
|
2020-02-11 15:27:39 +01:00
|
|
|
Thus, the system is uncoupled if \(G\) and \(K\) are diagonal.
|
2020-01-22 15:47:00 +01:00
|
|
|
</p>
|
|
|
|
|
</div>
|
2020-02-11 15:27:39 +01:00
|
|
|
</div>
|
|
|
|
|
</div>
|
|
|
|
|
<div id="postamble" class="status">
|
|
|
|
|
<p class="author">Author: Dehaeze Thomas</p>
|
2020-08-05 13:28:14 +02:00
|
|
|
<p class="date">Created: 2020-08-05 mer. 13:27</p>
|
2020-02-11 15:27:39 +01:00
|
|
|
</div>
|
2020-01-22 15:47:00 +01:00
|
|
|
</body>
|
|
|
|
|
</html>
|
