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</div><div id="content">
<h1 class="title">Simscape Model</h1>
<div id="table-of-contents">
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#orge12e7ea">1. Solid bodies</a></li>
<li><a href="#org6e14a53">2. Frames</a></li>
<li><a href="#orgbcbe86d">3. Joints</a></li>
<li><a href="#orgafe97a3">4. Measurements</a></li>
<li><a href="#orgdee3066">5. Excitation</a></li>
</ul>
</div>
</div>
<p>
A <a href="https://.mathworks.com/products/simscape.html">simscape</a> model permits to model multi-physics systems.
</p>
<p>
<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.
</p>
<div id="outline-container-orge12e7ea" class="outline-2">
<h2 id="orge12e7ea"><span class="section-number-2">1</span> Solid bodies</h2>
<div class="outline-text-2" id="text-1">
<p>
Each solid body is represented by a <a href="https://mathworks.com/help/physmod/sm/ref/solid.html">solid block</a>.
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.
</p>
</div>
</div>
<div id="outline-container-org6e14a53" class="outline-2">
<h2 id="org6e14a53"><span class="section-number-2">2</span> Frames</h2>
<div class="outline-text-2" id="text-2">
<p>
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.
</p>
<p>
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>.
</p>
</div>
</div>
<div id="outline-container-orgbcbe86d" class="outline-2">
<h2 id="orgbcbe86d"><span class="section-number-2">3</span> Joints</h2>
<div class="outline-text-2" id="text-3">
<p>
Solid Bodies are connected with joints (between frames of the two solid bodies).
</p>
<p>
There are various types of joints that are all described <a href="https://mathworks.com/help/physmod/sm/ug/joints.html">here</a>.
</p>
<table id="orgbc35961" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<caption class="t-above"><span class="table-number">Table 1:</span> Degrees of freedom associated with each joint</caption>
<colgroup>
<col class="org-left" />
<col class="org-right" />
<col class="org-right" />
</colgroup>
<thead>
<tr>
<th scope="col" class="org-left">Joint Block</th>
<th scope="col" class="org-right">Translational DOFs</th>
<th scope="col" class="org-right">Rotational DOFs</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-left">6-DOF</td>
<td class="org-right">3</td>
<td class="org-right">3</td>
</tr>
<tr>
<td class="org-left">Bearing</td>
<td class="org-right">1</td>
<td class="org-right">3</td>
</tr>
<tr>
<td class="org-left">Bushing</td>
<td class="org-right">3</td>
<td class="org-right">3</td>
</tr>
<tr>
<td class="org-left">Cartesian</td>
<td class="org-right">3</td>
<td class="org-right">0</td>
</tr>
<tr>
<td class="org-left">Constant Velocity</td>
<td class="org-right">0</td>
<td class="org-right">2</td>
</tr>
<tr>
<td class="org-left">Cylindrical</td>
<td class="org-right">1</td>
<td class="org-right">1</td>
</tr>
<tr>
<td class="org-left">Gimbal</td>
<td class="org-right">0</td>
<td class="org-right">3</td>
</tr>
<tr>
<td class="org-left">Leadscrew</td>
<td class="org-right">1 (coupled)</td>
<td class="org-right">1 (coupled)</td>
</tr>
<tr>
<td class="org-left">Pin Slot</td>
<td class="org-right">1</td>
<td class="org-right">1</td>
</tr>
<tr>
<td class="org-left">Planar</td>
<td class="org-right">2</td>
<td class="org-right">1</td>
</tr>
<tr>
<td class="org-left">Prismatic</td>
<td class="org-right">1</td>
<td class="org-right">0</td>
</tr>
<tr>
<td class="org-left">Rectangular</td>
<td class="org-right">2</td>
<td class="org-right">0</td>
</tr>
<tr>
<td class="org-left">Revolute</td>
<td class="org-right">0</td>
<td class="org-right">1</td>
</tr>
<tr>
<td class="org-left">Spherical</td>
<td class="org-right">1</td>
<td class="org-right">3</td>
</tr>
<tr>
<td class="org-left">Telescoping</td>
<td class="org-right">1</td>
<td class="org-right">3</td>
</tr>
<tr>
<td class="org-left">Universal</td>
<td class="org-right">0</td>
<td class="org-right">2</td>
</tr>
<tr>
<td class="org-left">Weld</td>
<td class="org-right">0</td>
<td class="org-right">0</td>
</tr>
</tbody>
</table>
<p>
Joint blocks are assortments of joint primitives:
</p>
<ul class="org-ul">
<li><b>Prismatic</b>: allows translation along a single standard axis: <code>Px</code>, <code>Py</code>, <code>Pz</code></li>
<li><b>Revolute</b>: allows rotation about a single standard axis: <code>Rx</code>, <code>Ry</code>, <code>Rz</code></li>
<li><b>Spherical</b>: allow rotation about any 3D axis: <code>S</code></li>
<li><b>Lead Screw</b>: allows coupled rotation and translation on a standard axis: <code>LSz</code></li>
<li><b>Constant Velocity</b>: Allows rotation at constant velocity between intersection through arbitrarily aligned shafts: <code>CV</code></li>
</ul>
<table id="org3352129" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<caption class="t-above"><span class="table-number">Table 2:</span> Joint primitives for each joint type</caption>
<colgroup>
<col class="org-left" />
<col class="org-left" />
<col class="org-left" />
<col class="org-left" />
<col class="org-left" />
<col class="org-left" />
<col class="org-left" />
<col class="org-left" />
<col class="org-left" />
<col class="org-left" />
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<thead>
<tr>
<th scope="col" class="org-left">Joint Block</th>
<th scope="col" class="org-left">Px</th>
<th scope="col" class="org-left">Py</th>
<th scope="col" class="org-left">Pz</th>
<th scope="col" class="org-left">Rx</th>
<th scope="col" class="org-left">Ry</th>
<th scope="col" class="org-left">Rz</th>
<th scope="col" class="org-left">S</th>
<th scope="col" class="org-left">CV</th>
<th scope="col" class="org-left">LSz</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-left">6-DOF</td>
<td class="org-left">x</td>
<td class="org-left">x</td>
<td class="org-left">x</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">x</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
</tr>
<tr>
<td class="org-left">Bearing</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">x</td>
<td class="org-left">x</td>
<td class="org-left">x</td>
<td class="org-left">x</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
</tr>
<tr>
<td class="org-left">Bushing</td>
<td class="org-left">x</td>
<td class="org-left">x</td>
<td class="org-left">x</td>
<td class="org-left">x</td>
<td class="org-left">x</td>
<td class="org-left">x</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
</tr>
<tr>
<td class="org-left">Cartesian</td>
<td class="org-left">x</td>
<td class="org-left">x</td>
<td class="org-left">x</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
</tr>
<tr>
<td class="org-left">Constant Velocity</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">x</td>
<td class="org-left">&#xa0;</td>
</tr>
<tr>
<td class="org-left">Cylindrical</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">x</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">x</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
</tr>
<tr>
<td class="org-left">Gimbal</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">x</td>
<td class="org-left">x</td>
<td class="org-left">x</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
</tr>
<tr>
<td class="org-left">Leadscrew</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">x</td>
</tr>
<tr>
<td class="org-left">Pin Slot</td>
<td class="org-left">x</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">x</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
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<tr>
<td class="org-left">Planar</td>
<td class="org-left">x</td>
<td class="org-left">x</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">x</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
</tr>
<tr>
<td class="org-left">Prismatic</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">x</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
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<tr>
<td class="org-left">Rectangular</td>
<td class="org-left">x</td>
<td class="org-left">x</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
</tr>
<tr>
<td class="org-left">Revolute</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">x</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
</tr>
<tr>
<td class="org-left">Spherical</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">x</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
</tr>
<tr>
<td class="org-left">Telescoping</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">x</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">x</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
</tr>
<tr>
<td class="org-left">Universal</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">x</td>
<td class="org-left">x</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
</tr>
<tr>
<td class="org-left">Weld</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
<td class="org-left">&#xa0;</td>
</tr>
</tbody>
</table>
<p>
For each of the joint primitive, we can specify the dynamical properties:
</p>
<ul class="org-ul">
<li>The <b>spring stiffness</b>: either linear or rotational one</li>
<li>The <b>damping coefficient</b></li>
</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: 2020-02-25 mar. 18:08</p>
</div>
</body>
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