550 lines
15 KiB
HTML
550 lines
15 KiB
HTML
<?xml version="1.0" encoding="utf-8"?>
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<?xml version="1.0" encoding="utf-8"?>
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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
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"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
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<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
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<head>
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<!-- 2020-04-17 ven. 09:35 -->
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<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
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<title>Simscape Model</title>
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<meta name="generator" content="Org mode" />
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<meta name="author" content="Dehaeze Thomas" />
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<link rel="stylesheet" type="text/css" href="./css/htmlize.css"/>
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<link rel="stylesheet" type="text/css" href="./css/readtheorg.css"/>
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<script src="./js/jquery.min.js"></script>
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<script src="./js/bootstrap.min.js"></script>
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<script src="./js/jquery.stickytableheaders.min.js"></script>
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<script src="./js/readtheorg.js"></script>
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</head>
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<body>
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<div id="org-div-home-and-up">
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<a accesskey="h" href="./index.html"> UP </a>
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<a accesskey="H" href="./index.html"> HOME </a>
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</div><div id="content">
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<h1 class="title">Simscape Model</h1>
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<div id="table-of-contents">
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<h2>Table of Contents</h2>
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<div id="text-table-of-contents">
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<ul>
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<li><a href="#orge12e7ea">1. Solid bodies</a></li>
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<li><a href="#org6e14a53">2. Frames</a></li>
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<li><a href="#orgbcbe86d">3. Joints</a></li>
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<li><a href="#orgafe97a3">4. Measurements</a></li>
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<li><a href="#orgdee3066">5. Excitation</a></li>
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</ul>
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</div>
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</div>
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<p>
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A <a href="https://.mathworks.com/products/simscape.html">simscape</a> model permits to model multi-physics systems.
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</p>
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<p>
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<a href="https://mathworks.com/products/simmechanics.html">Simscape Multibody</a> permits to model multibody systems using blocks representing bodies, joints, constraints, force elements, and sensors.
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</p>
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<div id="outline-container-orge12e7ea" class="outline-2">
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<h2 id="orge12e7ea"><span class="section-number-2">1</span> Solid bodies</h2>
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<div class="outline-text-2" id="text-1">
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<p>
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Each solid body is represented by a <a href="https://mathworks.com/help/physmod/sm/ref/solid.html">solid block</a>.
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The geometry of the solid body can be imported using a <code>step</code> file. The properties of the solid body such as its mass, center of mass and moment of inertia can be derived from its density and its geometry as defined by the <code>step</code> file. They also can be set by hand.
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</p>
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</div>
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</div>
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<div id="outline-container-org6e14a53" class="outline-2">
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<h2 id="org6e14a53"><span class="section-number-2">2</span> Frames</h2>
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<div class="outline-text-2" id="text-2">
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<p>
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Frames are very important in simscape multibody, they defined where the forces are applied, where the joints are located and where the measurements are made.
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</p>
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<p>
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They can be defined from the solid body geometry, or using the <a href="https://mathworks.com/help/physmod/sm/ref/rigidtransform.html">rigid transform block</a>.
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</p>
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</div>
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</div>
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<div id="outline-container-orgbcbe86d" class="outline-2">
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<h2 id="orgbcbe86d"><span class="section-number-2">3</span> Joints</h2>
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<div class="outline-text-2" id="text-3">
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<p>
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Solid Bodies are connected with joints (between frames of the two solid bodies).
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</p>
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<p>
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There are various types of joints that are all described <a href="https://mathworks.com/help/physmod/sm/ug/joints.html">here</a>.
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</p>
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<table id="orgbc35961" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
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<caption class="t-above"><span class="table-number">Table 1:</span> Degrees of freedom associated with each joint</caption>
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<colgroup>
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<col class="org-left" />
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<col class="org-right" />
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<col class="org-right" />
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</colgroup>
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<thead>
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<tr>
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<th scope="col" class="org-left">Joint Block</th>
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<th scope="col" class="org-right">Translational DOFs</th>
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<th scope="col" class="org-right">Rotational DOFs</th>
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</tr>
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</thead>
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<tbody>
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<tr>
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<td class="org-left">6-DOF</td>
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<td class="org-right">3</td>
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<td class="org-right">3</td>
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</tr>
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<tr>
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<td class="org-left">Bearing</td>
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<td class="org-right">1</td>
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<td class="org-right">3</td>
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</tr>
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<tr>
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<td class="org-left">Bushing</td>
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<td class="org-right">3</td>
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<td class="org-right">3</td>
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</tr>
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<tr>
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<td class="org-left">Cartesian</td>
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<td class="org-right">3</td>
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<td class="org-right">0</td>
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</tr>
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<tr>
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<td class="org-left">Constant Velocity</td>
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<td class="org-right">0</td>
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<td class="org-right">2</td>
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</tr>
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<tr>
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<td class="org-left">Cylindrical</td>
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<td class="org-right">1</td>
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<td class="org-right">1</td>
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</tr>
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<tr>
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<td class="org-left">Gimbal</td>
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<td class="org-right">0</td>
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<td class="org-right">3</td>
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</tr>
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<tr>
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<td class="org-left">Leadscrew</td>
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<td class="org-right">1 (coupled)</td>
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<td class="org-right">1 (coupled)</td>
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</tr>
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<tr>
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<td class="org-left">Pin Slot</td>
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<td class="org-right">1</td>
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<td class="org-right">1</td>
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</tr>
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<tr>
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<td class="org-left">Planar</td>
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<td class="org-right">2</td>
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<td class="org-right">1</td>
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</tr>
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<tr>
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<td class="org-left">Prismatic</td>
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<td class="org-right">1</td>
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<td class="org-right">0</td>
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</tr>
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<tr>
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<td class="org-left">Rectangular</td>
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<td class="org-right">2</td>
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<td class="org-right">0</td>
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</tr>
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<tr>
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<td class="org-left">Revolute</td>
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<td class="org-right">0</td>
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<td class="org-right">1</td>
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</tr>
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<tr>
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<td class="org-left">Spherical</td>
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<td class="org-right">1</td>
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<td class="org-right">3</td>
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</tr>
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<tr>
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<td class="org-left">Telescoping</td>
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<td class="org-right">1</td>
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<td class="org-right">3</td>
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</tr>
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<tr>
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<td class="org-left">Universal</td>
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<td class="org-right">0</td>
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<td class="org-right">2</td>
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</tr>
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<tr>
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<td class="org-left">Weld</td>
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<td class="org-right">0</td>
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<td class="org-right">0</td>
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</tr>
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</tbody>
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</table>
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<p>
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Joint blocks are assortments of joint primitives:
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</p>
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<ul class="org-ul">
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<li><b>Prismatic</b>: allows translation along a single standard axis: <code>Px</code>, <code>Py</code>, <code>Pz</code></li>
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<li><b>Revolute</b>: allows rotation about a single standard axis: <code>Rx</code>, <code>Ry</code>, <code>Rz</code></li>
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<li><b>Spherical</b>: allow rotation about any 3D axis: <code>S</code></li>
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<li><b>Lead Screw</b>: allows coupled rotation and translation on a standard axis: <code>LSz</code></li>
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<li><b>Constant Velocity</b>: Allows rotation at constant velocity between intersection through arbitrarily aligned shafts: <code>CV</code></li>
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</ul>
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<table id="org3352129" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
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<caption class="t-above"><span class="table-number">Table 2:</span> Joint primitives for each joint type</caption>
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<colgroup>
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<col class="org-left" />
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<col class="org-left" />
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<col class="org-left" />
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<col class="org-left" />
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<col class="org-left" />
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<col class="org-left" />
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<col class="org-left" />
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<col class="org-left" />
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<col class="org-left" />
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<col class="org-left" />
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</colgroup>
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<thead>
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<tr>
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<th scope="col" class="org-left">Joint Block</th>
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<th scope="col" class="org-left">Px</th>
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<th scope="col" class="org-left">Py</th>
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<th scope="col" class="org-left">Pz</th>
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<th scope="col" class="org-left">Rx</th>
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<th scope="col" class="org-left">Ry</th>
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<th scope="col" class="org-left">Rz</th>
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<th scope="col" class="org-left">S</th>
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<th scope="col" class="org-left">CV</th>
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<th scope="col" class="org-left">LSz</th>
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</tr>
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</thead>
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<tbody>
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<tr>
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<td class="org-left">6-DOF</td>
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<td class="org-left">x</td>
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<td class="org-left">x</td>
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<td class="org-left">x</td>
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<td class="org-left"> </td>
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<td class="org-left"> </td>
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<td class="org-left"> </td>
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<td class="org-left">x</td>
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<td class="org-left"> </td>
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<td class="org-left"> </td>
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</tr>
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<tr>
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<td class="org-left">Bearing</td>
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<td class="org-left"> </td>
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<td class="org-left"> </td>
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<td class="org-left">x</td>
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<td class="org-left">x</td>
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<td class="org-left">x</td>
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<td class="org-left">x</td>
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<td class="org-left"> </td>
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<td class="org-left"> </td>
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<td class="org-left"> </td>
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</tr>
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<tr>
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<td class="org-left">Bushing</td>
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<td class="org-left">x</td>
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<td class="org-left">x</td>
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<td class="org-left">x</td>
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<td class="org-left">x</td>
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<td class="org-left">x</td>
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<td class="org-left">x</td>
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<td class="org-left"> </td>
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<td class="org-left"> </td>
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<td class="org-left"> </td>
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</tr>
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<tr>
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<td class="org-left">Cartesian</td>
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<td class="org-left">x</td>
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<td class="org-left">x</td>
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<td class="org-left">x</td>
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<td class="org-left"> </td>
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<td class="org-left"> </td>
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<td class="org-left"> </td>
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<td class="org-left"> </td>
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<td class="org-left"> </td>
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<td class="org-left"> </td>
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</tr>
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<tr>
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<td class="org-left">Constant Velocity</td>
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<td class="org-left"> </td>
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<td class="org-left"> </td>
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<td class="org-left"> </td>
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<td class="org-left"> </td>
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<td class="org-left"> </td>
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<td class="org-left"> </td>
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<td class="org-left"> </td>
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<td class="org-left">x</td>
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<td class="org-left"> </td>
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</tr>
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<tr>
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<td class="org-left">Cylindrical</td>
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<td class="org-left"> </td>
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<td class="org-left"> </td>
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<td class="org-left">x</td>
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<td class="org-left"> </td>
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<td class="org-left"> </td>
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<td class="org-left">x</td>
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<td class="org-left"> </td>
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<td class="org-left"> </td>
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<td class="org-left"> </td>
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</tr>
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<tr>
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<td class="org-left">Gimbal</td>
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<td class="org-left"> </td>
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<td class="org-left"> </td>
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<td class="org-left"> </td>
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<td class="org-left">x</td>
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<td class="org-left">x</td>
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<td class="org-left">x</td>
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<td class="org-left"> </td>
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<td class="org-left"> </td>
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<td class="org-left"> </td>
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</tr>
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<tr>
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<td class="org-left">Leadscrew</td>
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<td class="org-left"> </td>
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<td class="org-left"> </td>
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<td class="org-left"> </td>
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<td class="org-left"> </td>
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<td class="org-left"> </td>
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<td class="org-left"> </td>
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<td class="org-left"> </td>
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<td class="org-left"> </td>
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<td class="org-left">x</td>
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</tr>
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<tr>
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<td class="org-left">Pin Slot</td>
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<td class="org-left">x</td>
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<td class="org-left"> </td>
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<td class="org-left"> </td>
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<td class="org-left"> </td>
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<td class="org-left"> </td>
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<td class="org-left">x</td>
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<td class="org-left"> </td>
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<td class="org-left"> </td>
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<td class="org-left"> </td>
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</tr>
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<tr>
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<td class="org-left">Planar</td>
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<td class="org-left">x</td>
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<td class="org-left">x</td>
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<td class="org-left"> </td>
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<td class="org-left"> </td>
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<td class="org-left"> </td>
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<td class="org-left">x</td>
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<td class="org-left"> </td>
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<td class="org-left"> </td>
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<td class="org-left"> </td>
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</tr>
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<tr>
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<td class="org-left">Prismatic</td>
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<td class="org-left"> </td>
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<td class="org-left"> </td>
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<td class="org-left">x</td>
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<td class="org-left"> </td>
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<td class="org-left"> </td>
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<td class="org-left"> </td>
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<td class="org-left"> </td>
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<td class="org-left"> </td>
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<td class="org-left"> </td>
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</tr>
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<tr>
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<td class="org-left">Rectangular</td>
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<td class="org-left">x</td>
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<td class="org-left">x</td>
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<td class="org-left"> </td>
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<td class="org-left"> </td>
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<td class="org-left"> </td>
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<td class="org-left"> </td>
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<td class="org-left"> </td>
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<td class="org-left"> </td>
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<td class="org-left"> </td>
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</tr>
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<tr>
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<td class="org-left">Revolute</td>
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<td class="org-left"> </td>
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<td class="org-left"> </td>
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<td class="org-left"> </td>
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<td class="org-left"> </td>
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<td class="org-left"> </td>
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<td class="org-left">x</td>
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<td class="org-left"> </td>
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<td class="org-left"> </td>
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<td class="org-left"> </td>
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</tr>
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<tr>
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<td class="org-left">Spherical</td>
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<td class="org-left"> </td>
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<td class="org-left"> </td>
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<td class="org-left"> </td>
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<td class="org-left"> </td>
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<td class="org-left"> </td>
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<td class="org-left"> </td>
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<td class="org-left">x</td>
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<td class="org-left"> </td>
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<td class="org-left"> </td>
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</tr>
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<tr>
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<td class="org-left">Telescoping</td>
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<td class="org-left"> </td>
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<td class="org-left"> </td>
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<td class="org-left">x</td>
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<td class="org-left"> </td>
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<td class="org-left"> </td>
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<td class="org-left"> </td>
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<td class="org-left">x</td>
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<td class="org-left"> </td>
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<td class="org-left"> </td>
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</tr>
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<tr>
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<td class="org-left">Universal</td>
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<td class="org-left"> </td>
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<td class="org-left"> </td>
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<td class="org-left"> </td>
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<td class="org-left">x</td>
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<td class="org-left">x</td>
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<td class="org-left"> </td>
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<td class="org-left"> </td>
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<td class="org-left"> </td>
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<td class="org-left"> </td>
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</tr>
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<tr>
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<td class="org-left">Weld</td>
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|
<td class="org-left"> </td>
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|
<td class="org-left"> </td>
|
|
<td class="org-left"> </td>
|
|
<td class="org-left"> </td>
|
|
<td class="org-left"> </td>
|
|
<td class="org-left"> </td>
|
|
<td class="org-left"> </td>
|
|
<td class="org-left"> </td>
|
|
<td class="org-left"> </td>
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|
</tr>
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|
</tbody>
|
|
</table>
|
|
|
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<p>
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For each of the joint primitive, we can specify the dynamical properties:
|
|
</p>
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|
<ul class="org-ul">
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|
<li>The <b>spring stiffness</b>: either linear or rotational one</li>
|
|
<li>The <b>damping coefficient</b></li>
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|
</ul>
|
|
|
|
<p>
|
|
For the actuation, we can either specify the motion or the force:
|
|
</p>
|
|
<ul class="org-ul">
|
|
<li>the force applied in the corresponding DOF is provided by the input</li>
|
|
<li>the motion is provided by the input</li>
|
|
</ul>
|
|
|
|
<p>
|
|
A sensor can be added to measure either the position, velocity or acceleration of the joint DOF.
|
|
</p>
|
|
|
|
<p>
|
|
Composite Force/Torque sensing:
|
|
</p>
|
|
<ul class="org-ul">
|
|
<li>Constraint force</li>
|
|
<li>Total force: gives the sum across all joint primitives over all sources: actuation inputs, internal springs and dampers.</li>
|
|
</ul>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgafe97a3" class="outline-2">
|
|
<h2 id="orgafe97a3"><span class="section-number-2">4</span> Measurements</h2>
|
|
<div class="outline-text-2" id="text-4">
|
|
<p>
|
|
A transform sensor block measures the spatial relationship between two frames: the base <code>B</code> and the follower <code>F</code>.
|
|
</p>
|
|
|
|
<p>
|
|
It can give the rotational and translational position, velocity and acceleration.
|
|
</p>
|
|
|
|
<p>
|
|
The measurement frame should be specified: it corresponds to the frame in which to resolve the selected spatial measurements. The default is <code>world</code>.
|
|
</p>
|
|
|
|
<p>
|
|
If we want to simulate an <b>inertial sensor</b>, we just have to choose <code>B</code> to be the <code>world</code> frame.
|
|
</p>
|
|
|
|
<p>
|
|
<b>Force sensors</b> are included in the joints blocks.
|
|
</p>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgdee3066" class="outline-2">
|
|
<h2 id="orgdee3066"><span class="section-number-2">5</span> Excitation</h2>
|
|
<div class="outline-text-2" id="text-5">
|
|
<p>
|
|
We can apply <b>external forces</b> to the model by using an <a href="https://mathworks.com/help/physmod/sm/ref/externalforceandtorque.html">external force and torque block</a>.
|
|
</p>
|
|
|
|
<p>
|
|
Internal force, acting reciprocally between base and following origins is implemented using the <a href="https://mathworks.com/help/physmod/sm/ref/internalforce.html">internal force block</a> even though it is usually included in one joint block.
|
|
</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
<div id="postamble" class="status">
|
|
<p class="author">Author: Dehaeze Thomas</p>
|
|
<p class="date">Created: 2020-04-17 ven. 09:35</p>
|
|
</div>
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</body>
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</html>
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