tdehaeze/stewart-simscape
1
0
Fork 0
Code Issues Pull Requests Releases Wiki Activity

Update html pages

Browse Source
This commit is contained in:
Thomas Dehaeze
2020-03-03 15:53:02 +01:00
parent 467a04e239
commit 304ecf031b
14 changed files with 578 additions and 608 deletions
Download Patch File Download Diff File Expand all files Collapse all files

113
docs/cubic-configuration.html
View File

@@ -4,7 +4,7 @@
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
<head>
<!-- 2020-02-28 ven. 17:34 -->
<!-- 2020-03-03 mar. 15:51 -->
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
<meta name="viewport" content="width=device-width, initial-scale=1" />
<title>Cubic configuration for the Stewart Platform</title>
@@ -252,33 +252,33 @@
<li><a href="#orga88e79a">1.2. Cubic Stewart platform centered with the cube center - Jacobian not estimated at the cube center</a></li>
<li><a href="#orge02ec88">1.3. Cubic Stewart platform not centered with the cube center - Jacobian estimated at the cube center</a></li>
<li><a href="#org43fd7e4">1.4. Cubic Stewart platform not centered with the cube center - Jacobian estimated at the Stewart platform center</a></li>
<li><a href="#org3e2b41c">1.5. Conclusion</a></li>
<li><a href="#org64395b6">1.5. Conclusion</a></li>
</ul>
</li>
<li><a href="#orgd70418b">2. Configuration with the Cube&rsquo;s center above the mobile platform</a>
<ul>
<li><a href="#org8afa645">2.1. Having Cube&rsquo;s center above the top platform</a></li>
<li><a href="#orgeeac940">2.2. Conclusion</a></li>
<li><a href="#org8e09793">2.2. Conclusion</a></li>
</ul>
</li>
<li><a href="#orgcc4ecce">3. Cubic size analysis</a>
<ul>
<li><a href="#org0029d8c">3.1. Analysis</a></li>
<li><a href="#org991d232">3.2. Conclusion</a></li>
<li><a href="#orgc5a2e1f">3.2. Conclusion</a></li>
</ul>
</li>
<li><a href="#orgf09da67">4. Dynamic Coupling in the Cartesian Frame</a>
<ul>
<li><a href="#org5fe01ec">4.1. Cube&rsquo;s center at the Center of Mass of the mobile platform</a></li>
<li><a href="#org4cb2a36">4.2. Cube&rsquo;s center not coincident with the Mass of the Mobile platform</a></li>
<li><a href="#orgf0acd1f">4.3. Conclusion</a></li>
<li><a href="#org24cd25e">4.3. Conclusion</a></li>
</ul>
</li>
<li><a href="#org8f26dc0">5. Dynamic Coupling between actuators and sensors of each strut</a>
<ul>
<li><a href="#org6e391c9">5.1. Coupling between the actuators and sensors - Cubic Architecture</a></li>
<li><a href="#orgafd808d">5.2. Coupling between the actuators and sensors - Non-Cubic Architecture</a></li>
<li><a href="#org78c4967">5.3. Conclusion</a></li>
<li><a href="#org3356db5">5.3. Conclusion</a></li>
</ul>
</li>
<li><a href="#org3044455">6. Functions</a>
@@ -826,8 +826,8 @@ stewart = initializeCylindricalPlatforms(stewart, <span class="org-string">'Fpr'
</div>
</div>
<div id="outline-container-org3e2b41c" class="outline-3">
<h3 id="org3e2b41c"><span class="section-number-3">1.5</span> Conclusion</h3>
<div id="outline-container-org64395b6" class="outline-3">
<h3 id="org64395b6"><span class="section-number-3">1.5</span> Conclusion</h3>
<div class="outline-text-3" id="text-1-5">
<div class="important">
<p>
@@ -1164,8 +1164,8 @@ FOc = H <span class="org-type">+</span> MO_B; <span class="org-comment">% Cente
</div>
</div>
<div id="outline-container-orgeeac940" class="outline-3">
<h3 id="orgeeac940"><span class="section-number-3">2.2</span> Conclusion</h3>
<div id="outline-container-org8e09793" class="outline-3">
<h3 id="org8e09793"><span class="section-number-3">2.2</span> Conclusion</h3>
<div class="outline-text-3" id="text-2-2">
<div class="important">
<p>
@@ -1173,6 +1173,38 @@ We found that we can have a diagonal stiffness matrix using the cubic architectu
Depending on the cube&rsquo;s size, we obtain 3 different configurations.
</p>
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-left" />
<col class="org-left" />
</colgroup>
<thead>
<tr>
<th scope="col" class="org-left">Cube&rsquo;s Size</th>
<th scope="col" class="org-left">Paper with the corresponding cubic architecture</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-left">Small</td>
<td class="org-left"><a class='org-ref-reference' href="#furutani04_nanom_cuttin_machin_using_stewar">furutani04_nanom_cuttin_machin_using_stewar</a></td>
</tr>
<tr>
<td class="org-left">Medium</td>
<td class="org-left"><a class='org-ref-reference' href="#yang19_dynam_model_decoup_contr_flexib">yang19_dynam_model_decoup_contr_flexib</a></td>
</tr>
<tr>
<td class="org-left">Large</td>
<td class="org-left">&#xa0;</td>
</tr>
</tbody>
</table>
</div>
</div>
</div>
@@ -1251,8 +1283,8 @@ We also find that \(k_{\theta_x} = k_{\theta_y}\) and \(k_{\theta_z}\) are varyi
</div>
</div>
<div id="outline-container-org991d232" class="outline-3">
<h3 id="org991d232"><span class="section-number-3">3.2</span> Conclusion</h3>
<div id="outline-container-orgc5a2e1f" class="outline-3">
<h3 id="orgc5a2e1f"><span class="section-number-3">3.2</span> Conclusion</h3>
<div class="outline-text-3" id="text-3-2">
<p>
We observe that \(k_{\theta_x} = k_{\theta_y}\) and \(k_{\theta_z}\) increase linearly with the cube size.
@@ -1436,6 +1468,7 @@ Now, thanks to the Jacobian (Figure <a href="#org76f24a0">9</a>), we compute the
</p>
<div class="org-src-container">
<pre class="src src-matlab">Gc = inv(stewart.kinematics.J)<span class="org-type">*</span>G<span class="org-type">*</span>inv(stewart.kinematics.J<span class="org-type">'</span>);
Gc = inv(stewart.kinematics.J)<span class="org-type">*</span>G<span class="org-type">*</span>stewart.kinematics.J;
Gc.InputName = {<span class="org-string">'Fx'</span>, <span class="org-string">'Fy'</span>, <span class="org-string">'Fz'</span>, <span class="org-string">'Mx'</span>, <span class="org-string">'My'</span>, <span class="org-string">'Mz'</span>};
Gc.OutputName = {<span class="org-string">'Dx'</span>, <span class="org-string">'Dy'</span>, <span class="org-string">'Dz'</span>, <span class="org-string">'Rx'</span>, <span class="org-string">'Ry'</span>, <span class="org-string">'Rz'</span>};
</pre>
@@ -1452,6 +1485,17 @@ The obtain dynamics \(\bm{G}_{c}(s) = \bm{J}^{-T} \bm{G}(s) \bm{J}^{-1}\) is sho
<p><span class="figure-number">Figure 11: </span>Dynamics from \(\bm{\mathcal{F}}\) to \(\bm{\mathcal{X}}\) (<a href="./figs/stewart_cubic_decoupled_dynamics_cartesian.png">png</a>, <a href="./figs/stewart_cubic_decoupled_dynamics_cartesian.pdf">pdf</a>)</p>
</div>
<p>
It is interesting to note here that the system shown in Figure <a href="#org9e58bc5">12</a> also yield a decoupled system (explained in section 1.3.3 in <a class='org-ref-reference' href="#li01_simul_fault_vibrat_isolat_point">li01_simul_fault_vibrat_isolat_point</a>).
</p>
<div id="org9e58bc5" class="figure">
<p><img src="figs/local_to_cartesian_coordinates_bis.png" alt="local_to_cartesian_coordinates_bis.png" />
</p>
<p><span class="figure-number">Figure 12: </span>Alternative way to decouple the system</p>
</div>
<div class="important">
<p>
The dynamics is well decoupled at all frequencies.
@@ -1541,13 +1585,13 @@ controller = initializeController(<span class="org-string">'type'</span>, <span
</div>
<p>
The obtain geometry is shown in figure <a href="#orgfce7805">12</a>.
The obtain geometry is shown in figure <a href="#orgfce7805">13</a>.
</p>
<div id="orgfce7805" class="figure">
<p><img src="figs/stewart_cubic_conf_mass_above.png" alt="stewart_cubic_conf_mass_above.png" />
</p>
<p><span class="figure-number">Figure 12: </span>Geometry used for the simulations - The cube&rsquo;s center is coincident with the frames \(\{A\}\) and \(\{B\}\) but not with the Center of mass of the mobile platform (<a href="./figs/stewart_cubic_conf_mass_above.png">png</a>, <a href="./figs/stewart_cubic_conf_mass_above.pdf">pdf</a>)</p>
<p><span class="figure-number">Figure 13: </span>Geometry used for the simulations - The cube&rsquo;s center is coincident with the frames \(\{A\}\) and \(\{B\}\) but not with the Center of mass of the mobile platform (<a href="./figs/stewart_cubic_conf_mass_above.png">png</a>, <a href="./figs/stewart_cubic_conf_mass_above.pdf">pdf</a>)</p>
</div>
<p>
@@ -1586,14 +1630,14 @@ Gc.OutputName = {<span class="org-string">'Dx'</span>, <span class="org-string">
</div>
<p>
The obtain dynamics \(\bm{G}_{c}(s) = \bm{J}^{-T} \bm{G}(s) \bm{J}^{-1}\) is shown in Figure <a href="#org7a04d45">13</a>.
The obtain dynamics \(\bm{G}_{c}(s) = \bm{J}^{-T} \bm{G}(s) \bm{J}^{-1}\) is shown in Figure <a href="#org7a04d45">14</a>.
</p>
<div id="org7a04d45" class="figure">
<p><img src="figs/stewart_conf_coupling_mass_matrix.png" alt="stewart_conf_coupling_mass_matrix.png" />
</p>
<p><span class="figure-number">Figure 13: </span>Obtained Dynamics from \(\bm{\mathcal{F}}\) to \(\bm{\mathcal{X}}\) (<a href="./figs/stewart_conf_coupling_mass_matrix.png">png</a>, <a href="./figs/stewart_conf_coupling_mass_matrix.pdf">pdf</a>)</p>
<p><span class="figure-number">Figure 14: </span>Obtained Dynamics from \(\bm{\mathcal{F}}\) to \(\bm{\mathcal{X}}\) (<a href="./figs/stewart_conf_coupling_mass_matrix.png">png</a>, <a href="./figs/stewart_conf_coupling_mass_matrix.pdf">pdf</a>)</p>
</div>
<div class="important">
@@ -1609,8 +1653,8 @@ This was expected as the mass matrix is not diagonal (the Center of Mass of the
</div>
</div>
<div id="outline-container-orgf0acd1f" class="outline-3">
<h3 id="orgf0acd1f"><span class="section-number-3">4.3</span> Conclusion</h3>
<div id="outline-container-org24cd25e" class="outline-3">
<h3 id="org24cd25e"><span class="section-number-3">4.3</span> Conclusion</h3>
<div class="outline-text-3" id="text-4-3">
<div class="important">
<p>
@@ -1703,25 +1747,25 @@ controller = initializeController(<span class="org-string">'type'</span>, <span
<div id="org67d7284" class="figure">
<p><img src="figs/stewart_architecture_coupling_struts_cubic.png" alt="stewart_architecture_coupling_struts_cubic.png" />
</p>
<p><span class="figure-number">Figure 14: </span>Geometry of the generated Stewart platform (<a href="./figs/stewart_architecture_coupling_struts_cubic.png">png</a>, <a href="./figs/stewart_architecture_coupling_struts_cubic.pdf">pdf</a>)</p>
<p><span class="figure-number">Figure 15: </span>Geometry of the generated Stewart platform (<a href="./figs/stewart_architecture_coupling_struts_cubic.png">png</a>, <a href="./figs/stewart_architecture_coupling_struts_cubic.pdf">pdf</a>)</p>
</div>
<p>
And we identify the dynamics from the actuator forces \(\tau_{i}\) to the relative motion sensors \(\delta \mathcal{L}_{i}\) (Figure <a href="#orga20cd7d">15</a>) and to the force sensors \(\tau_{m,i}\) (Figure <a href="#org645e6c3">16</a>).
And we identify the dynamics from the actuator forces \(\tau_{i}\) to the relative motion sensors \(\delta \mathcal{L}_{i}\) (Figure <a href="#orga20cd7d">16</a>) and to the force sensors \(\tau_{m,i}\) (Figure <a href="#org645e6c3">17</a>).
</p>
<div id="orga20cd7d" class="figure">
<p><img src="figs/coupling_struts_relative_sensor_cubic.png" alt="coupling_struts_relative_sensor_cubic.png" />
</p>
<p><span class="figure-number">Figure 15: </span>Dynamics from the force actuators to the relative motion sensors (<a href="./figs/coupling_struts_relative_sensor_cubic.png">png</a>, <a href="./figs/coupling_struts_relative_sensor_cubic.pdf">pdf</a>)</p>
<p><span class="figure-number">Figure 16: </span>Dynamics from the force actuators to the relative motion sensors (<a href="./figs/coupling_struts_relative_sensor_cubic.png">png</a>, <a href="./figs/coupling_struts_relative_sensor_cubic.pdf">pdf</a>)</p>
</div>
<div id="org645e6c3" class="figure">
<p><img src="figs/coupling_struts_force_sensor_cubic.png" alt="coupling_struts_force_sensor_cubic.png" />
</p>
<p><span class="figure-number">Figure 16: </span>Dynamics from the force actuators to the force sensors (<a href="./figs/coupling_struts_force_sensor_cubic.png">png</a>, <a href="./figs/coupling_struts_force_sensor_cubic.pdf">pdf</a>)</p>
<p><span class="figure-number">Figure 17: </span>Dynamics from the force actuators to the force sensors (<a href="./figs/coupling_struts_force_sensor_cubic.png">png</a>, <a href="./figs/coupling_struts_force_sensor_cubic.pdf">pdf</a>)</p>
</div>
</div>
</div>
@@ -1771,31 +1815,31 @@ controller = initializeController(<span class="org-string">'type'</span>, <span
<div id="org14d3492" class="figure">
<p><img src="figs/stewart_architecture_coupling_struts_non_cubic.png" alt="stewart_architecture_coupling_struts_non_cubic.png" />
</p>
<p><span class="figure-number">Figure 17: </span>Geometry of the generated Stewart platform (<a href="./figs/stewart_architecture_coupling_struts_non_cubic.png">png</a>, <a href="./figs/stewart_architecture_coupling_struts_non_cubic.pdf">pdf</a>)</p>
<p><span class="figure-number">Figure 18: </span>Geometry of the generated Stewart platform (<a href="./figs/stewart_architecture_coupling_struts_non_cubic.png">png</a>, <a href="./figs/stewart_architecture_coupling_struts_non_cubic.pdf">pdf</a>)</p>
</div>
<p>
And we identify the dynamics from the actuator forces \(\tau_{i}\) to the relative motion sensors \(\delta \mathcal{L}_{i}\) (Figure <a href="#orgff23a38">18</a>) and to the force sensors \(\tau_{m,i}\) (Figure <a href="#orgd802951">19</a>).
And we identify the dynamics from the actuator forces \(\tau_{i}\) to the relative motion sensors \(\delta \mathcal{L}_{i}\) (Figure <a href="#orgff23a38">19</a>) and to the force sensors \(\tau_{m,i}\) (Figure <a href="#orgd802951">20</a>).
</p>
<div id="orgff23a38" class="figure">
<p><img src="figs/coupling_struts_relative_sensor_non_cubic.png" alt="coupling_struts_relative_sensor_non_cubic.png" />
</p>
<p><span class="figure-number">Figure 18: </span>Dynamics from the force actuators to the relative motion sensors (<a href="./figs/coupling_struts_relative_sensor_non_cubic.png">png</a>, <a href="./figs/coupling_struts_relative_sensor_non_cubic.pdf">pdf</a>)</p>
<p><span class="figure-number">Figure 19: </span>Dynamics from the force actuators to the relative motion sensors (<a href="./figs/coupling_struts_relative_sensor_non_cubic.png">png</a>, <a href="./figs/coupling_struts_relative_sensor_non_cubic.pdf">pdf</a>)</p>
</div>
<div id="orgd802951" class="figure">
<p><img src="figs/coupling_struts_force_sensor_non_cubic.png" alt="coupling_struts_force_sensor_non_cubic.png" />
</p>
<p><span class="figure-number">Figure 19: </span>Dynamics from the force actuators to the force sensors (<a href="./figs/coupling_struts_force_sensor_non_cubic.png">png</a>, <a href="./figs/coupling_struts_force_sensor_non_cubic.pdf">pdf</a>)</p>
<p><span class="figure-number">Figure 20: </span>Dynamics from the force actuators to the force sensors (<a href="./figs/coupling_struts_force_sensor_non_cubic.png">png</a>, <a href="./figs/coupling_struts_force_sensor_non_cubic.pdf">pdf</a>)</p>
</div>
</div>
</div>
<div id="outline-container-org78c4967" class="outline-3">
<h3 id="org78c4967"><span class="section-number-3">5.3</span> Conclusion</h3>
<div id="outline-container-org3356db5" class="outline-3">
<h3 id="org3356db5"><span class="section-number-3">5.3</span> Conclusion</h3>
<div class="outline-text-3" id="text-5-3">
<div class="important">
<p>
@@ -1861,7 +1905,7 @@ This Matlab function is accessible <a href="../src/generateCubicConfiguration.m"
<div id="org8a7f3d8" class="figure">
<p><img src="figs/cubic-configuration-definition.png" alt="cubic-configuration-definition.png" />
</p>
<p><span class="figure-number">Figure 20: </span>Cubic Configuration</p>
<p><span class="figure-number">Figure 21: </span>Cubic Configuration</p>
</div>
</div>
</div>
@@ -1961,12 +2005,21 @@ stewart.platform_M.Mb = Mb;
<ul class='org-ref-bib'><li><a id="geng94_six_degree_of_freed_activ">[geng94_six_degree_of_freed_activ]</a> <a name="geng94_six_degree_of_freed_activ"></a>Geng & Haynes, Six Degree-Of-Freedom Active Vibration Control Using the Stewart Platforms, <i>IEEE Transactions on Control Systems Technology</i>, <b>2(1)</b>, 45-53 (1994). <a href="https://doi.org/10.1109/87.273110">link</a>. <a href="http://dx.doi.org/10.1109/87.273110">doi</a>.</li>
<li><a id="preumont07_six_axis_singl_stage_activ">[preumont07_six_axis_singl_stage_activ]</a> <a name="preumont07_six_axis_singl_stage_activ"></a>Preumont, Horodinca, Romanescu, de Marneffe, Avraam, Deraemaeker, Bossens & Abu Hanieh, A Six-Axis Single-Stage Active Vibration Isolator Based on Stewart Platform, <i>Journal of Sound and Vibration</i>, <b>300(3-5)</b>, 644-661 (2007). <a href="https://doi.org/10.1016/j.jsv.2006.07.050">link</a>. <a href="http://dx.doi.org/10.1016/j.jsv.2006.07.050">doi</a>.</li>
<li><a id="jafari03_orthog_gough_stewar_platf_microm">[jafari03_orthog_gough_stewar_platf_microm]</a> <a name="jafari03_orthog_gough_stewar_platf_microm"></a>Jafari & McInroy, Orthogonal Gough-Stewart Platforms for Micromanipulation, <i>IEEE Transactions on Robotics and Automation</i>, <b>19(4)</b>, 595-603 (2003). <a href="https://doi.org/10.1109/tra.2003.814506">link</a>. <a href="http://dx.doi.org/10.1109/tra.2003.814506">doi</a>.</li>
<li><a id="furutani04_nanom_cuttin_machin_using_stewar">[furutani04_nanom_cuttin_machin_using_stewar]</a> <a name="furutani04_nanom_cuttin_machin_using_stewar"></a>Katsushi Furutani, Michio Suzuki & Ryusei Kudoh, Nanometre-Cutting Machine Using a Stewart-Platform Parallel Mechanism, <i>Measurement Science and Technology</i>, <b>15(2)</b>, 467-474 (2004). <a href="https://doi.org/10.1088/0957-0233/15/2/022">link</a>. <a href="http://dx.doi.org/10.1088/0957-0233/15/2/022">doi</a>.</li>
<li><a id="yang19_dynam_model_decoup_contr_flexib">[yang19_dynam_model_decoup_contr_flexib]</a> <a name="yang19_dynam_model_decoup_contr_flexib"></a>Yang, Wu, Chen, Kang & Cheng, Dynamic Modeling and Decoupled Control of a Flexible Stewart Platform for Vibration Isolation, <i>Journal of Sound and Vibration</i>, <b>439</b>, 398-412 (2019). <a href="https://doi.org/10.1016/j.jsv.2018.10.007">link</a>. <a href="http://dx.doi.org/10.1016/j.jsv.2018.10.007">doi</a>.</li>
<li><a id="li01_simul_fault_vibrat_isolat_point">[li01_simul_fault_vibrat_isolat_point]</a> <a name="li01_simul_fault_vibrat_isolat_point"></a>@phdthesisli01_simul_fault_vibrat_isolat_point,
author = Li, Xiaochun,
school = University of Wyoming,
title = Simultaneous, Fault-tolerant Vibration Isolation and Pointing Control of Flexure Jointed Hexapods,
year = 2001,
tags = parallel robot,
</li>
</ul>
</p>
</div>
<div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2020-02-28 ven. 17:34</p>
<p class="date">Created: 2020-03-03 mar. 15:51</p>
</div>
</body>
</html>