tdehaeze/stewart-simscape
1
0
Fork 0
Code Issues Pull Requests Releases Wiki Activity
dda9ce734a
stewart-simscape/kinematic-study.html

466 lines
32 KiB
HTML
Raw Blame History

<?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>
<!-- 2019-03-26 mar. 09:24 -->
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
<meta name="viewport" content="width=device-width, initial-scale=1" />
<title>Kinematic Study of the Stewart Platform</title>
<meta name="generator" content="Org mode" />
<meta name="author" content="Thomas Dehaeze" />
<style type="text/css">
<!--/*--><![CDATA[/*><!--*/
.title { text-align: center;
margin-bottom: .2em; }
.subtitle { text-align: center;
font-size: medium;
font-weight: bold;
margin-top:0; }
.todo { font-family: monospace; color: red; }
.done { font-family: monospace; color: green; }
.priority { font-family: monospace; color: orange; }
.tag { background-color: #eee; font-family: monospace;
padding: 2px; font-size: 80%; font-weight: normal; }
.timestamp { color: #bebebe; }
.timestamp-kwd { color: #5f9ea0; }
.org-right { margin-left: auto; margin-right: 0px; text-align: right; }
.org-left { margin-left: 0px; margin-right: auto; text-align: left; }
.org-center { margin-left: auto; margin-right: auto; text-align: center; }
.underline { text-decoration: underline; }
#postamble p, #preamble p { font-size: 90%; margin: .2em; }
p.verse { margin-left: 3%; }
pre {
border: 1px solid #ccc;
box-shadow: 3px 3px 3px #eee;
padding: 8pt;
font-family: monospace;
overflow: auto;
margin: 1.2em;
}
pre.src {
position: relative;
overflow: visible;
padding-top: 1.2em;
}
pre.src:before {
display: none;
position: absolute;
background-color: white;
top: -10px;
right: 10px;
padding: 3px;
border: 1px solid black;
}
pre.src:hover:before { display: inline;}
/* Languages per Org manual */
pre.src-asymptote:before { content: 'Asymptote'; }
pre.src-awk:before { content: 'Awk'; }
pre.src-C:before { content: 'C'; }
/* pre.src-C++ doesn't work in CSS */
pre.src-clojure:before { content: 'Clojure'; }
pre.src-css:before { content: 'CSS'; }
pre.src-D:before { content: 'D'; }
pre.src-ditaa:before { content: 'ditaa'; }
pre.src-dot:before { content: 'Graphviz'; }
pre.src-calc:before { content: 'Emacs Calc'; }
pre.src-emacs-lisp:before { content: 'Emacs Lisp'; }
pre.src-fortran:before { content: 'Fortran'; }
pre.src-gnuplot:before { content: 'gnuplot'; }
pre.src-haskell:before { content: 'Haskell'; }
pre.src-hledger:before { content: 'hledger'; }
pre.src-java:before { content: 'Java'; }
pre.src-js:before { content: 'Javascript'; }
pre.src-latex:before { content: 'LaTeX'; }
pre.src-ledger:before { content: 'Ledger'; }
pre.src-lisp:before { content: 'Lisp'; }
pre.src-lilypond:before { content: 'Lilypond'; }
pre.src-lua:before { content: 'Lua'; }
pre.src-matlab:before { content: 'MATLAB'; }
pre.src-mscgen:before { content: 'Mscgen'; }
pre.src-ocaml:before { content: 'Objective Caml'; }
pre.src-octave:before { content: 'Octave'; }
pre.src-org:before { content: 'Org mode'; }
pre.src-oz:before { content: 'OZ'; }
pre.src-plantuml:before { content: 'Plantuml'; }
pre.src-processing:before { content: 'Processing.js'; }
pre.src-python:before { content: 'Python'; }
pre.src-R:before { content: 'R'; }
pre.src-ruby:before { content: 'Ruby'; }
pre.src-sass:before { content: 'Sass'; }
pre.src-scheme:before { content: 'Scheme'; }
pre.src-screen:before { content: 'Gnu Screen'; }
pre.src-sed:before { content: 'Sed'; }
pre.src-sh:before { content: 'shell'; }
pre.src-sql:before { content: 'SQL'; }
pre.src-sqlite:before { content: 'SQLite'; }
/* additional languages in org.el's org-babel-load-languages alist */
pre.src-forth:before { content: 'Forth'; }
pre.src-io:before { content: 'IO'; }
pre.src-J:before { content: 'J'; }
pre.src-makefile:before { content: 'Makefile'; }
pre.src-maxima:before { content: 'Maxima'; }
pre.src-perl:before { content: 'Perl'; }
pre.src-picolisp:before { content: 'Pico Lisp'; }
pre.src-scala:before { content: 'Scala'; }
pre.src-shell:before { content: 'Shell Script'; }
pre.src-ebnf2ps:before { content: 'ebfn2ps'; }
/* additional language identifiers per "defun org-babel-execute"
in ob-*.el */
pre.src-cpp:before { content: 'C++'; }
pre.src-abc:before { content: 'ABC'; }
pre.src-coq:before { content: 'Coq'; }
pre.src-groovy:before { content: 'Groovy'; }
/* additional language identifiers from org-babel-shell-names in
ob-shell.el: ob-shell is the only babel language using a lambda to put
the execution function name together. */
pre.src-bash:before { content: 'bash'; }
pre.src-csh:before { content: 'csh'; }
pre.src-ash:before { content: 'ash'; }
pre.src-dash:before { content: 'dash'; }
pre.src-ksh:before { content: 'ksh'; }
pre.src-mksh:before { content: 'mksh'; }
pre.src-posh:before { content: 'posh'; }
/* Additional Emacs modes also supported by the LaTeX listings package */
pre.src-ada:before { content: 'Ada'; }
pre.src-asm:before { content: 'Assembler'; }
pre.src-caml:before { content: 'Caml'; }
pre.src-delphi:before { content: 'Delphi'; }
pre.src-html:before { content: 'HTML'; }
pre.src-idl:before { content: 'IDL'; }
pre.src-mercury:before { content: 'Mercury'; }
pre.src-metapost:before { content: 'MetaPost'; }
pre.src-modula-2:before { content: 'Modula-2'; }
pre.src-pascal:before { content: 'Pascal'; }
pre.src-ps:before { content: 'PostScript'; }
pre.src-prolog:before { content: 'Prolog'; }
pre.src-simula:before { content: 'Simula'; }
pre.src-tcl:before { content: 'tcl'; }
pre.src-tex:before { content: 'TeX'; }
pre.src-plain-tex:before { content: 'Plain TeX'; }
pre.src-verilog:before { content: 'Verilog'; }
pre.src-vhdl:before { content: 'VHDL'; }
pre.src-xml:before { content: 'XML'; }
pre.src-nxml:before { content: 'XML'; }
/* add a generic configuration mode; LaTeX export needs an additional
(add-to-list 'org-latex-listings-langs '(conf " ")) in .emacs */
pre.src-conf:before { content: 'Configuration File'; }
table { border-collapse:collapse; }
caption.t-above { caption-side: top; }
caption.t-bottom { caption-side: bottom; }
td, th { vertical-align:top; }
th.org-right { text-align: center; }
th.org-left { text-align: center; }
th.org-center { text-align: center; }
td.org-right { text-align: right; }
td.org-left { text-align: left; }
td.org-center { text-align: center; }
dt { font-weight: bold; }
.footpara { display: inline; }
.footdef { margin-bottom: 1em; }
.figure { padding: 1em; }
.figure p { text-align: center; }
.equation-container {
display: table;
text-align: center;
width: 100%;
}
.equation {
vertical-align: middle;
}
.equation-label {
display: table-cell;
text-align: right;
vertical-align: middle;
}
.inlinetask {
padding: 10px;
border: 2px solid gray;
margin: 10px;
background: #ffffcc;
}
#org-div-home-and-up
{ text-align: right; font-size: 70%; white-space: nowrap; }
textarea { overflow-x: auto; }
.linenr { font-size: smaller }
.code-highlighted { background-color: #ffff00; }
.org-info-js_info-navigation { border-style: none; }
#org-info-js_console-label
{ font-size: 10px; font-weight: bold; white-space: nowrap; }
.org-info-js_search-highlight
{ background-color: #ffff00; color: #000000; font-weight: bold; }
.org-svg { width: 90%; }
/*]]>*/-->
</style>
<link rel="stylesheet" type="text/css" href="css/htmlize.css"/>
<link rel="stylesheet" type="text/css" href="css/readtheorg.css"/>
<script src="js/jquery.min.js"></script>
<script src="js/bootstrap.min.js"></script>
<script type="text/javascript" src="js/jquery.stickytableheaders.min.js"></script>
<script type="text/javascript" src="js/readtheorg.js"></script>
<script type="text/javascript">
/*
@licstart The following is the entire license notice for the
JavaScript code in this tag.
Copyright (C) 2012-2019 Free Software Foundation, Inc.
The JavaScript code in this tag is free software: you can
redistribute it and/or modify it under the terms of the GNU
General Public License (GNU GPL) as published by the Free Software
Foundation, either version 3 of the License, or (at your option)
any later version. The code is distributed WITHOUT ANY WARRANTY;
without even the implied warranty of MERCHANTABILITY or FITNESS
FOR A PARTICULAR PURPOSE. See the GNU GPL for more details.
As additional permission under GNU GPL version 3 section 7, you
may distribute non-source (e.g., minimized or compacted) forms of
that code without the copy of the GNU GPL normally required by
section 4, provided you include this license notice and a URL
through which recipients can access the Corresponding Source.
@licend The above is the entire license notice
for the JavaScript code in this tag.
*/
<!--/*--><![CDATA[/*><!--*/
function CodeHighlightOn(elem, id)
{
var target = document.getElementById(id);
if(null != target) {
elem.cacheClassElem = elem.className;
elem.cacheClassTarget = target.className;
target.className = "code-highlighted";
elem.className = "code-highlighted";
}
}
function CodeHighlightOff(elem, id)
{
var target = document.getElementById(id);
if(elem.cacheClassElem)
elem.className = elem.cacheClassElem;
if(elem.cacheClassTarget)
target.className = elem.cacheClassTarget;
}
/*]]>*///-->
</script>
</head>
<body>
<div id="content">
<h1 class="title">Kinematic Study of the Stewart Platform</h1>
<div id="table-of-contents">
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#org2e1bd58">1. Needed Actuator Stroke</a>
<ul>
<li><a href="#org16d1370">1.1. Stewart architecture definition</a></li>
<li><a href="#orgaf07b82">1.2. Wanted translations and rotations</a></li>
<li><a href="#org920b62b">1.3. Needed stroke for "pure" rotations or translations</a></li>
<li><a href="#org27bf97e">1.4. Needed stroke for combined translations and rotations</a></li>
</ul>
</li>
<li><a href="#orgaebf111">2. Maximum Stroke</a></li>
<li><a href="#orgfb8a1e7">3. Functions</a>
<ul>
<li><a href="#org465746a">3.1. getMaxPositions</a></li>
<li><a href="#org527f7ca">3.2. getMaxPureDisplacement</a></li>
</ul>
</li>
</ul>
</div>
</div>
<div id="outline-container-org2e1bd58" class="outline-2">
<h2 id="org2e1bd58"><span class="section-number-2">1</span> Needed Actuator Stroke</h2>
<div class="outline-text-2" id="text-1">
<p>
The goal is to determine the needed stroke of the actuators to obtain wanted translations and rotations.
</p>
</div>
<div id="outline-container-org16d1370" class="outline-3">
<h3 id="org16d1370"><span class="section-number-3">1.1</span> Stewart architecture definition</h3>
<div class="outline-text-3" id="text-1-1">
<p>
We use a cubic architecture.
</p>
<div class="org-src-container">
<pre class="src src-matlab">opts = struct<span style="color: #DCDCCC;">(</span><span style="text-decoration: underline;">...</span>
<span style="color: #CC9393;">'H_tot'</span>, <span style="color: #BFEBBF;">90</span>, <span style="text-decoration: underline;">...</span> <span style="color: #7F9F7F;">% Total height of the Hexapod [mm]</span>
<span style="color: #CC9393;">'L'</span>, <span style="color: #BFEBBF;">180</span><span style="color: #7CB8BB;">/</span>sqrt<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">3</span><span style="color: #BFEBBF;">)</span>, <span style="text-decoration: underline;">...</span> <span style="color: #7F9F7F;">% Size of the Cube [mm]</span>
<span style="color: #CC9393;">'H'</span>, <span style="color: #BFEBBF;">60</span>, <span style="text-decoration: underline;">...</span> <span style="color: #7F9F7F;">% Height between base joints and platform joints [mm]</span>
<span style="color: #CC9393;">'H0'</span>, <span style="color: #BFEBBF;">180</span><span style="color: #7CB8BB;">/</span><span style="color: #BFEBBF;">2</span><span style="color: #7CB8BB;">-</span><span style="color: #BFEBBF;">60</span><span style="color: #7CB8BB;">/</span><span style="color: #BFEBBF;">2</span> <span style="text-decoration: underline;">...</span> <span style="color: #7F9F7F;">% Height between the corner of the cube and the plane containing the base joints [mm]</span>
<span style="color: #DCDCCC;">)</span>;
stewart = initializeCubicConfiguration<span style="color: #DCDCCC;">(</span>opts<span style="color: #DCDCCC;">)</span>;
opts = struct<span style="color: #DCDCCC;">(</span><span style="text-decoration: underline;">...</span>
<span style="color: #CC9393;">'Jd_pos'</span>, <span style="color: #BFEBBF;">[</span><span style="color: #BFEBBF;">0</span>, <span style="color: #BFEBBF;">0</span>, <span style="color: #BFEBBF;">100</span><span style="color: #BFEBBF;">]</span>, <span style="text-decoration: underline;">...</span> <span style="color: #7F9F7F;">% Position of the Jacobian for displacement estimation from the top of the mobile platform [mm]</span>
<span style="color: #CC9393;">'Jf_pos'</span>, <span style="color: #BFEBBF;">[</span><span style="color: #BFEBBF;">0</span>, <span style="color: #BFEBBF;">0</span>, <span style="color: #7CB8BB;">-</span><span style="color: #BFEBBF;">50</span><span style="color: #BFEBBF;">]</span> <span style="text-decoration: underline;">...</span> <span style="color: #7F9F7F;">% Position of the Jacobian for force location from the top of the mobile platform [mm]</span>
<span style="color: #DCDCCC;">)</span>;
stewart = computeGeometricalProperties<span style="color: #DCDCCC;">(</span>stewart, opts<span style="color: #DCDCCC;">)</span>;
opts = struct<span style="color: #DCDCCC;">(</span><span style="text-decoration: underline;">...</span>
<span style="color: #CC9393;">'stroke'</span>, <span style="color: #BFEBBF;">50e</span><span style="color: #7CB8BB;">-</span><span style="color: #BFEBBF;">6</span> <span style="text-decoration: underline;">...</span> <span style="color: #7F9F7F;">% Maximum stroke of each actuator [m]</span>
<span style="color: #DCDCCC;">)</span>;
stewart = initializeMechanicalElements<span style="color: #DCDCCC;">(</span>stewart, opts<span style="color: #DCDCCC;">)</span>;
save<span style="color: #DCDCCC;">(</span><span style="color: #CC9393;">'./mat/stewart.mat', 'stewart'</span><span style="color: #DCDCCC;">)</span>;
</pre>
</div>
</div>
</div>
<div id="outline-container-orgaf07b82" class="outline-3">
<h3 id="orgaf07b82"><span class="section-number-3">1.2</span> Wanted translations and rotations</h3>
<div class="outline-text-3" id="text-1-2">
<p>
We define wanted translations and rotations
</p>
<div class="org-src-container">
<pre class="src src-matlab">Tx_max = <span style="color: #BFEBBF;">15e</span><span style="color: #7CB8BB;">-</span><span style="color: #BFEBBF;">6</span>; <span style="color: #7F9F7F;">% Translation [m]</span>
Ty_max = <span style="color: #BFEBBF;">15e</span><span style="color: #7CB8BB;">-</span><span style="color: #BFEBBF;">6</span>; <span style="color: #7F9F7F;">% Translation [m]</span>
Tz_max = <span style="color: #BFEBBF;">15e</span><span style="color: #7CB8BB;">-</span><span style="color: #BFEBBF;">6</span>; <span style="color: #7F9F7F;">% Translation [m]</span>
Rx_max = <span style="color: #BFEBBF;">30e</span><span style="color: #7CB8BB;">-</span><span style="color: #BFEBBF;">6</span>; <span style="color: #7F9F7F;">% Rotation [rad]</span>
Ry_max = <span style="color: #BFEBBF;">30e</span><span style="color: #7CB8BB;">-</span><span style="color: #BFEBBF;">6</span>; <span style="color: #7F9F7F;">% Rotation [rad]</span>
</pre>
</div>
</div>
</div>
<div id="outline-container-org920b62b" class="outline-3">
<h3 id="org920b62b"><span class="section-number-3">1.3</span> Needed stroke for "pure" rotations or translations</h3>
<div class="outline-text-3" id="text-1-3">
<p>
First, we estimate the needed actuator stroke for "pure" rotations and translation.
</p>
<div class="org-src-container">
<pre class="src src-matlab">LTx = stewart.Jd<span style="color: #7CB8BB;">*</span><span style="color: #DCDCCC;">[</span>Tx_max <span style="color: #BFEBBF;">0</span> <span style="color: #BFEBBF;">0</span> <span style="color: #BFEBBF;">0</span> <span style="color: #BFEBBF;">0</span> <span style="color: #BFEBBF;">0</span><span style="color: #DCDCCC;">]</span>';
LTy = stewart.Jd<span style="color: #7CB8BB;">*</span><span style="color: #DCDCCC;">[</span><span style="color: #BFEBBF;">0</span> Ty_max <span style="color: #BFEBBF;">0</span> <span style="color: #BFEBBF;">0</span> <span style="color: #BFEBBF;">0</span> <span style="color: #BFEBBF;">0</span><span style="color: #DCDCCC;">]</span>';
LTz = stewart.Jd<span style="color: #7CB8BB;">*</span><span style="color: #DCDCCC;">[</span><span style="color: #BFEBBF;">0</span> <span style="color: #BFEBBF;">0</span> Tz_max <span style="color: #BFEBBF;">0</span> <span style="color: #BFEBBF;">0</span> <span style="color: #BFEBBF;">0</span><span style="color: #DCDCCC;">]</span>';
LRx = stewart.Jd<span style="color: #7CB8BB;">*</span><span style="color: #DCDCCC;">[</span><span style="color: #BFEBBF;">0</span> <span style="color: #BFEBBF;">0</span> <span style="color: #BFEBBF;">0</span> Rx_max <span style="color: #BFEBBF;">0</span> <span style="color: #BFEBBF;">0</span><span style="color: #DCDCCC;">]</span>';
LRy = stewart.Jd<span style="color: #7CB8BB;">*</span><span style="color: #DCDCCC;">[</span><span style="color: #BFEBBF;">0</span> <span style="color: #BFEBBF;">0</span> <span style="color: #BFEBBF;">0</span> <span style="color: #BFEBBF;">0</span> Ry_max <span style="color: #BFEBBF;">0</span><span style="color: #DCDCCC;">]</span>';
</pre>
</div>
<pre class="example">
1.0607e-05
</pre>
</div>
</div>
<div id="outline-container-org27bf97e" class="outline-3">
<h3 id="org27bf97e"><span class="section-number-3">1.4</span> Needed stroke for combined translations and rotations</h3>
<div class="outline-text-3" id="text-1-4">
<p>
Now, we combine translations and rotations, and we try to find the worst case (that we suppose to happen at the border).
</p>
<div class="org-src-container">
<pre class="src src-matlab">Lmax = <span style="color: #BFEBBF;">0</span>;
pos = <span style="color: #DCDCCC;">[</span><span style="color: #BFEBBF;">0</span>, <span style="color: #BFEBBF;">0</span>, <span style="color: #BFEBBF;">0</span>, <span style="color: #BFEBBF;">0</span>, <span style="color: #BFEBBF;">0</span><span style="color: #DCDCCC;">]</span>;
<span style="color: #F0DFAF; font-weight: bold;">for</span> <span style="color: #DFAF8F;">Tx</span> = <span style="color: #DCDCCC;">[</span><span style="color: #BFEBBF;">-Tx_max</span>,Tx_max<span style="color: #DCDCCC;">]</span>
<span style="color: #F0DFAF; font-weight: bold;">for</span> <span style="color: #DFAF8F;">Ty</span> = <span style="color: #DCDCCC;">[</span><span style="color: #BFEBBF;">-Ty_max</span>,Ty_max<span style="color: #DCDCCC;">]</span>
<span style="color: #F0DFAF; font-weight: bold;">for</span> <span style="color: #DFAF8F;">Tz</span> = <span style="color: #DCDCCC;">[</span><span style="color: #BFEBBF;">-Tz_max</span>,Tz_max<span style="color: #DCDCCC;">]</span>
<span style="color: #F0DFAF; font-weight: bold;">for</span> <span style="color: #DFAF8F;">Rx</span> = <span style="color: #DCDCCC;">[</span><span style="color: #BFEBBF;">-Rx_max</span>,Rx_max<span style="color: #DCDCCC;">]</span>
<span style="color: #F0DFAF; font-weight: bold;">for</span> <span style="color: #DFAF8F;">Ry</span> = <span style="color: #DCDCCC;">[</span><span style="color: #BFEBBF;">-Ry_max</span>,Ry_max<span style="color: #DCDCCC;">]</span>
L = max<span style="color: #DCDCCC;">(</span>stewart.Jd<span style="color: #7CB8BB;">*</span><span style="color: #BFEBBF;">[</span>Tx Ty Tz Rx Ry <span style="color: #BFEBBF;">0</span><span style="color: #BFEBBF;">]</span>'<span style="color: #DCDCCC;">)</span>;
<span style="color: #F0DFAF; font-weight: bold;">if</span> L <span style="color: #7CB8BB;">&gt;</span> Lmax
Lmax = L;
pos = <span style="color: #DCDCCC;">[</span>Tx Ty Tz Rx Ry<span style="color: #DCDCCC;">]</span>;
<span style="color: #F0DFAF; font-weight: bold;">end</span>
<span style="color: #F0DFAF; font-weight: bold;">end</span>
<span style="color: #F0DFAF; font-weight: bold;">end</span>
<span style="color: #F0DFAF; font-weight: bold;">end</span>
<span style="color: #F0DFAF; font-weight: bold;">end</span>
<span style="color: #F0DFAF; font-weight: bold;">end</span>
</pre>
</div>
<p>
We obtain a needed stroke shown below (almost two times the needed stroke for "pure" rotations and translations).
</p>
<pre class="example">
3.0927e-05
</pre>
</div>
</div>
</div>
<div id="outline-container-orgaebf111" class="outline-2">
<h2 id="orgaebf111"><span class="section-number-2">2</span> Maximum Stroke</h2>
<div class="outline-text-2" id="text-2">
<p>
From a specified actuator stroke, we try to estimate the available maneuverability of the Stewart platform.
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span style="color: #DCDCCC;">[</span>X, Y, Z<span style="color: #DCDCCC;">]</span> = getMaxPositions<span style="color: #DCDCCC;">(</span><span style="color: #DFAF8F;">stewart</span><span style="color: #DCDCCC;">)</span>;
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab"><span style="color: #7CB8BB;">figure</span>;
plot3<span style="color: #DCDCCC;">(</span>X, Y, Z, <span style="color: #CC9393;">'k-'</span><span style="color: #DCDCCC;">)</span>
</pre>
</div>
</div>
</div>
<div id="outline-container-orgfb8a1e7" class="outline-2">
<h2 id="orgfb8a1e7"><span class="section-number-2">3</span> Functions</h2>
<div class="outline-text-2" id="text-3">
</div>
<div id="outline-container-org465746a" class="outline-3">
<h3 id="org465746a"><span class="section-number-3">3.1</span> getMaxPositions</h3>
<div class="outline-text-3" id="text-3-1">
<div class="org-src-container">
<pre class="src src-matlab"><span style="color: #F0DFAF; font-weight: bold;">function</span> <span style="color: #DCDCCC;">[</span><span style="color: #DFAF8F;">X, Y, Z</span><span style="color: #DCDCCC;">]</span> = <span style="color: #93E0E3;">getMaxPositions</span><span style="color: #DCDCCC;">(</span><span style="color: #DFAF8F;">stewart</span><span style="color: #DCDCCC;">)</span>
Leg = stewart.Leg;
J = stewart.Jd;
theta = linspace<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">0</span>, <span style="color: #BFEBBF;">2</span><span style="color: #7CB8BB;">*</span><span style="color: #BFEBBF;">pi</span>, <span style="color: #BFEBBF;">100</span><span style="color: #DCDCCC;">)</span>;
phi = linspace<span style="color: #DCDCCC;">(</span><span style="color: #7CB8BB;">-</span><span style="color: #BFEBBF;">pi</span><span style="color: #7CB8BB;">/</span><span style="color: #BFEBBF;">2</span> , <span style="color: #BFEBBF;">pi</span><span style="color: #7CB8BB;">/</span><span style="color: #BFEBBF;">2</span>, <span style="color: #BFEBBF;">100</span><span style="color: #DCDCCC;">)</span>;
dmax = zeros<span style="color: #DCDCCC;">(</span>length<span style="color: #BFEBBF;">(</span>theta<span style="color: #BFEBBF;">)</span>, length<span style="color: #BFEBBF;">(</span>phi<span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
<span style="color: #F0DFAF; font-weight: bold;">for</span> <span style="color: #DFAF8F;">i</span> = <span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">:length</span><span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">theta</span><span style="color: #DCDCCC;">)</span>
<span style="color: #F0DFAF; font-weight: bold;">for</span> <span style="color: #DFAF8F;">j</span> = <span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">:length</span><span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">phi</span><span style="color: #DCDCCC;">)</span>
L = J<span style="color: #7CB8BB;">*</span><span style="color: #DCDCCC;">[</span>cos<span style="color: #BFEBBF;">(</span>phi<span style="color: #D0BF8F;">(</span><span style="color: #BFEBBF;">j</span><span style="color: #D0BF8F;">)</span><span style="color: #BFEBBF;">)</span><span style="color: #7CB8BB;">*</span>cos<span style="color: #BFEBBF;">(</span>theta<span style="color: #D0BF8F;">(</span><span style="color: #BFEBBF;">i</span><span style="color: #D0BF8F;">)</span><span style="color: #BFEBBF;">)</span> cos<span style="color: #BFEBBF;">(</span>phi<span style="color: #D0BF8F;">(</span><span style="color: #BFEBBF;">j</span><span style="color: #D0BF8F;">)</span><span style="color: #BFEBBF;">)</span><span style="color: #7CB8BB;">*</span>sin<span style="color: #BFEBBF;">(</span>theta<span style="color: #D0BF8F;">(</span><span style="color: #BFEBBF;">i</span><span style="color: #D0BF8F;">)</span><span style="color: #BFEBBF;">)</span> sin<span style="color: #BFEBBF;">(</span>phi<span style="color: #D0BF8F;">(</span><span style="color: #BFEBBF;">j</span><span style="color: #D0BF8F;">)</span><span style="color: #BFEBBF;">)</span> <span style="color: #BFEBBF;">0</span> <span style="color: #BFEBBF;">0</span> <span style="color: #BFEBBF;">0</span><span style="color: #DCDCCC;">]</span>';
dmax<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">i</span>, <span style="color: #BFEBBF;">j</span><span style="color: #DCDCCC;">)</span> = Leg.stroke<span style="color: #7CB8BB;">/</span>max<span style="color: #DCDCCC;">(</span>abs<span style="color: #BFEBBF;">(</span>L<span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
<span style="color: #F0DFAF; font-weight: bold;">end</span>
<span style="color: #F0DFAF; font-weight: bold;">end</span>
X = dmax<span style="color: #7CB8BB;">.*</span>cos<span style="color: #DCDCCC;">(</span>repmat<span style="color: #BFEBBF;">(</span>phi,length<span style="color: #D0BF8F;">(</span>theta<span style="color: #D0BF8F;">)</span>,<span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span><span style="color: #7CB8BB;">.*</span>cos<span style="color: #DCDCCC;">(</span>repmat<span style="color: #BFEBBF;">(</span>theta,length<span style="color: #D0BF8F;">(</span>phi<span style="color: #D0BF8F;">)</span>,<span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>';
Y = dmax<span style="color: #7CB8BB;">.*</span>cos<span style="color: #DCDCCC;">(</span>repmat<span style="color: #BFEBBF;">(</span>phi,length<span style="color: #D0BF8F;">(</span>theta<span style="color: #D0BF8F;">)</span>,<span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span><span style="color: #7CB8BB;">.*</span>sin<span style="color: #DCDCCC;">(</span>repmat<span style="color: #BFEBBF;">(</span>theta,length<span style="color: #D0BF8F;">(</span>phi<span style="color: #D0BF8F;">)</span>,<span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>';
Z = dmax<span style="color: #7CB8BB;">.*</span>sin<span style="color: #DCDCCC;">(</span>repmat<span style="color: #BFEBBF;">(</span>phi,length<span style="color: #D0BF8F;">(</span>theta<span style="color: #D0BF8F;">)</span>,<span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
<span style="color: #F0DFAF; font-weight: bold;">end</span>
</pre>
</div>
</div>
</div>
<div id="outline-container-org527f7ca" class="outline-3">
<h3 id="org527f7ca"><span class="section-number-3">3.2</span> getMaxPureDisplacement</h3>
<div class="outline-text-3" id="text-3-2">
<div class="org-src-container">
<pre class="src src-matlab"><span style="color: #F0DFAF; font-weight: bold;">function</span> <span style="color: #DCDCCC;">[</span><span style="color: #DFAF8F;">max_disp</span><span style="color: #DCDCCC;">]</span> = <span style="color: #93E0E3;">getMaxPureDisplacement</span><span style="color: #DCDCCC;">(</span><span style="color: #DFAF8F;">Leg</span>, <span style="color: #DFAF8F;">J</span><span style="color: #DCDCCC;">)</span>
max_disp = zeros<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">6</span>, <span style="color: #BFEBBF;">1</span><span style="color: #DCDCCC;">)</span>;
max_disp<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">1</span><span style="color: #DCDCCC;">)</span> = Leg.stroke<span style="color: #7CB8BB;">/</span>max<span style="color: #DCDCCC;">(</span>abs<span style="color: #BFEBBF;">(</span>J<span style="color: #7CB8BB;">*</span><span style="color: #D0BF8F;">[</span><span style="color: #BFEBBF;">1</span> <span style="color: #BFEBBF;">0</span> <span style="color: #BFEBBF;">0</span> <span style="color: #BFEBBF;">0</span> <span style="color: #BFEBBF;">0</span> <span style="color: #BFEBBF;">0</span><span style="color: #D0BF8F;">]</span>'<span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
max_disp<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">2</span><span style="color: #DCDCCC;">)</span> = Leg.stroke<span style="color: #7CB8BB;">/</span>max<span style="color: #DCDCCC;">(</span>abs<span style="color: #BFEBBF;">(</span>J<span style="color: #7CB8BB;">*</span><span style="color: #D0BF8F;">[</span><span style="color: #BFEBBF;">0</span> <span style="color: #BFEBBF;">1</span> <span style="color: #BFEBBF;">0</span> <span style="color: #BFEBBF;">0</span> <span style="color: #BFEBBF;">0</span> <span style="color: #BFEBBF;">0</span><span style="color: #D0BF8F;">]</span>'<span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
max_disp<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">3</span><span style="color: #DCDCCC;">)</span> = Leg.stroke<span style="color: #7CB8BB;">/</span>max<span style="color: #DCDCCC;">(</span>abs<span style="color: #BFEBBF;">(</span>J<span style="color: #7CB8BB;">*</span><span style="color: #D0BF8F;">[</span><span style="color: #BFEBBF;">0</span> <span style="color: #BFEBBF;">0</span> <span style="color: #BFEBBF;">1</span> <span style="color: #BFEBBF;">0</span> <span style="color: #BFEBBF;">0</span> <span style="color: #BFEBBF;">0</span><span style="color: #D0BF8F;">]</span>'<span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
max_disp<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">4</span><span style="color: #DCDCCC;">)</span> = Leg.stroke<span style="color: #7CB8BB;">/</span>max<span style="color: #DCDCCC;">(</span>abs<span style="color: #BFEBBF;">(</span>J<span style="color: #7CB8BB;">*</span><span style="color: #D0BF8F;">[</span><span style="color: #BFEBBF;">0</span> <span style="color: #BFEBBF;">0</span> <span style="color: #BFEBBF;">0</span> <span style="color: #BFEBBF;">1</span> <span style="color: #BFEBBF;">0</span> <span style="color: #BFEBBF;">0</span><span style="color: #D0BF8F;">]</span>'<span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
max_disp<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">5</span><span style="color: #DCDCCC;">)</span> = Leg.stroke<span style="color: #7CB8BB;">/</span>max<span style="color: #DCDCCC;">(</span>abs<span style="color: #BFEBBF;">(</span>J<span style="color: #7CB8BB;">*</span><span style="color: #D0BF8F;">[</span><span style="color: #BFEBBF;">0</span> <span style="color: #BFEBBF;">0</span> <span style="color: #BFEBBF;">0</span> <span style="color: #BFEBBF;">0</span> <span style="color: #BFEBBF;">1</span> <span style="color: #BFEBBF;">0</span><span style="color: #D0BF8F;">]</span>'<span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
max_disp<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">6</span><span style="color: #DCDCCC;">)</span> = Leg.stroke<span style="color: #7CB8BB;">/</span>max<span style="color: #DCDCCC;">(</span>abs<span style="color: #BFEBBF;">(</span>J<span style="color: #7CB8BB;">*</span><span style="color: #D0BF8F;">[</span><span style="color: #BFEBBF;">0</span> <span style="color: #BFEBBF;">0</span> <span style="color: #BFEBBF;">0</span> <span style="color: #BFEBBF;">0</span> <span style="color: #BFEBBF;">0</span> <span style="color: #BFEBBF;">1</span><span style="color: #D0BF8F;">]</span>'<span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
<span style="color: #F0DFAF; font-weight: bold;">end</span>
</pre>
</div>
</div>
</div>
</div>
</div>
<div id="postamble" class="status">
<p class="author">Author: Thomas Dehaeze</p>
<p class="date">Created: 2019-03-26 mar. 09:24</p>
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
</div>
</body>
</html>
Reference in New Issue View Git Blame Copy Permalink