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

Remove figs, add table for stiffness matrices

Browse Source
This commit is contained in:
Thomas Dehaeze 2020-02-12 11:23:26 +01:00
parent e241d4e17e
commit 54f86884d5
2 changed files with 60 additions and 57 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

95
docs/cubic-configuration.html
View File

@ -4,7 +4,7 @@
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en"> <html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
<head> <head>
<!-- 2020-02-12 mer. 11:18 --> <!-- 2020-02-12 mer. 11:23 -->
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" /> <meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
<meta name="viewport" content="width=device-width, initial-scale=1" /> <meta name="viewport" content="width=device-width, initial-scale=1" />
<title>Cubic configuration for the Stewart Platform</title> <title>Cubic configuration for the Stewart Platform</title>
@ -274,26 +274,26 @@ for the JavaScript code in this tag.
<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="#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="#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="#org43fd7e4">1.4. Cubic Stewart platform not centered with the cube center - Jacobian estimated at the Stewart platform center</a></li>
<li><a href="#orgd35acc0">1.5. Conclusion</a></li> <li><a href="#org95af62e">1.5. Conclusion</a></li>
</ul> </ul>
</li> </li>
<li><a href="#orgd70418b">2. Configuration with the Cube&rsquo;s center above the mobile platform</a> <li><a href="#orgd70418b">2. Configuration with the Cube&rsquo;s center above the mobile platform</a>
<ul> <ul>
<li><a href="#org8afa645">2.1. Having Cube&rsquo;s center above the top platform</a></li> <li><a href="#org8afa645">2.1. Having Cube&rsquo;s center above the top platform</a></li>
<li><a href="#org4576402">2.2. Conclusion</a></li> <li><a href="#org7673551">2.2. Conclusion</a></li>
</ul> </ul>
</li> </li>
<li><a href="#orgcc4ecce">3. Cubic size analysis</a> <li><a href="#orgcc4ecce">3. Cubic size analysis</a>
<ul> <ul>
<li><a href="#org0029d8c">3.1. Analysis</a></li> <li><a href="#org0029d8c">3.1. Analysis</a></li>
<li><a href="#org04f1ef6">3.2. Conclusion</a></li> <li><a href="#orgcad29fd">3.2. Conclusion</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org5abef15">4. Dynamic Coupling</a> <li><a href="#org5abef15">4. Dynamic Coupling</a>
<ul> <ul>
<li><a href="#org0d67b92">4.1. Cube&rsquo;s center at the Center of Mass of the Payload</a></li> <li><a href="#org0d67b92">4.1. Cube&rsquo;s center at the Center of Mass of the Payload</a></li>
<li><a href="#org876e05f">4.2. Dynamic decoupling between the actuators and sensors</a></li> <li><a href="#org876e05f">4.2. Dynamic decoupling between the actuators and sensors</a></li>
<li><a href="#org95af62e">4.3. Conclusion</a></li> <li><a href="#org213d9b9">4.3. Conclusion</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org3044455">5. Functions</a> <li><a href="#org3044455">5. Functions</a>
@ -388,7 +388,7 @@ We here study what makes the Stiffness matrix diagonal when using a cubic config
<h3 id="orgf6f7ad2"><span class="section-number-3">1.1</span> Cubic Stewart platform centered with the cube center - Jacobian estimated at the cube center</h3> <h3 id="orgf6f7ad2"><span class="section-number-3">1.1</span> Cubic Stewart platform centered with the cube center - Jacobian estimated at the cube center</h3>
<div class="outline-text-3" id="text-1-1"> <div class="outline-text-3" id="text-1-1">
<p> <p>
We create a cubic Stewart platform (figure <a href="#org9454f54">1</a>) in such a way that the center of the cube (black dot) is located at the center of the Stewart platform (blue dot). We create a cubic Stewart platform (figure <a href="#orgaba20c8">1</a>) in such a way that the center of the cube (black star) is located at the center of the Stewart platform (blue dot).
The Jacobian matrix is estimated at the location of the center of the cube. The Jacobian matrix is estimated at the location of the center of the cube.
</p> </p>
@ -412,21 +412,14 @@ stewart = initializeCylindricalPlatforms(stewart, <span class="org-string">'Fpr'
</div> </div>
<div id="org9454f54" class="figure">
<p><img src="figs/3d-cubic-stewart-aligned.png" alt="3d-cubic-stewart-aligned.png" />
</p>
<p><span class="figure-number">Figure 1: </span>Centered cubic configuration</p>
</div>
<div id="orgaba20c8" class="figure"> <div id="orgaba20c8" class="figure">
<p><img src="figs/cubic_conf_centered_J_center.png" alt="cubic_conf_centered_J_center.png" /> <p><img src="figs/cubic_conf_centered_J_center.png" alt="cubic_conf_centered_J_center.png" />
</p> </p>
<p><span class="figure-number">Figure 2: </span>Cubic Stewart platform centered with the cube center - Jacobian estimated at the cube center (<a href="./figs/cubic_conf_centered_J_center.png">png</a>, <a href="./figs/cubic_conf_centered_J_center.pdf">pdf</a>)</p> <p><span class="figure-number">Figure 1: </span>Cubic Stewart platform centered with the cube center - Jacobian estimated at the cube center (<a href="./figs/cubic_conf_centered_J_center.png">png</a>, <a href="./figs/cubic_conf_centered_J_center.pdf">pdf</a>)</p>
</div> </div>
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides"> <table id="org4baf591" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<caption class="t-above"><span class="table-number">Table 1:</span> Stiffness Matrix</caption>
<colgroup> <colgroup>
<col class="org-right" /> <col class="org-right" />
@ -504,7 +497,7 @@ stewart = initializeCylindricalPlatforms(stewart, <span class="org-string">'Fpr'
<h3 id="orga88e79a"><span class="section-number-3">1.2</span> Cubic Stewart platform centered with the cube center - Jacobian not estimated at the cube center</h3> <h3 id="orga88e79a"><span class="section-number-3">1.2</span> Cubic Stewart platform centered with the cube center - Jacobian not estimated at the cube center</h3>
<div class="outline-text-3" id="text-1-2"> <div class="outline-text-3" id="text-1-2">
<p> <p>
We create a cubic Stewart platform with center of the cube located at the center of the Stewart platform (figure <a href="#org9454f54">1</a>). We create a cubic Stewart platform with center of the cube located at the center of the Stewart platform (figure <a href="#org47f8142">2</a>).
The Jacobian matrix is not estimated at the location of the center of the cube. The Jacobian matrix is not estimated at the location of the center of the cube.
</p> </p>
@ -531,11 +524,11 @@ stewart = initializeCylindricalPlatforms(stewart, <span class="org-string">'Fpr'
<div id="org47f8142" class="figure"> <div id="org47f8142" class="figure">
<p><img src="figs/cubic_conf_centered_J_not_center.png" alt="cubic_conf_centered_J_not_center.png" /> <p><img src="figs/cubic_conf_centered_J_not_center.png" alt="cubic_conf_centered_J_not_center.png" />
</p> </p>
<p><span class="figure-number">Figure 3: </span>Cubic Stewart platform centered with the cube center - Jacobian not estimated at the cube center (<a href="./figs/cubic_conf_centered_J_not_center.png">png</a>, <a href="./figs/cubic_conf_centered_J_not_center.pdf">pdf</a>)</p> <p><span class="figure-number">Figure 2: </span>Cubic Stewart platform centered with the cube center - Jacobian not estimated at the cube center (<a href="./figs/cubic_conf_centered_J_not_center.png">png</a>, <a href="./figs/cubic_conf_centered_J_not_center.pdf">pdf</a>)</p>
</div> </div>
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides"> <table id="org5cc2020" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<caption class="t-above"><span class="table-number">Table 2:</span> Stiffness Matrix</caption>
<colgroup> <colgroup>
<col class="org-right" /> <col class="org-right" />
@ -613,7 +606,7 @@ stewart = initializeCylindricalPlatforms(stewart, <span class="org-string">'Fpr'
<h3 id="orge02ec88"><span class="section-number-3">1.3</span> Cubic Stewart platform not centered with the cube center - Jacobian estimated at the cube center</h3> <h3 id="orge02ec88"><span class="section-number-3">1.3</span> Cubic Stewart platform not centered with the cube center - Jacobian estimated at the cube center</h3>
<div class="outline-text-3" id="text-1-3"> <div class="outline-text-3" id="text-1-3">
<p> <p>
Here, the &ldquo;center&rdquo; of the Stewart platform is not at the cube center (figure <a href="#org0235d3a">4</a>). Here, the &ldquo;center&rdquo; of the Stewart platform is not at the cube center (figure <a href="#org0235d3a">3</a>).
The Jacobian is estimated at the cube center. The Jacobian is estimated at the cube center.
</p> </p>
@ -640,11 +633,11 @@ stewart = initializeCylindricalPlatforms(stewart, <span class="org-string">'Fpr'
<div id="org0235d3a" class="figure"> <div id="org0235d3a" class="figure">
<p><img src="figs/cubic_conf_not_centered_J_center.png" alt="cubic_conf_not_centered_J_center.png" /> <p><img src="figs/cubic_conf_not_centered_J_center.png" alt="cubic_conf_not_centered_J_center.png" />
</p> </p>
<p><span class="figure-number">Figure 4: </span>Cubic Stewart platform not centered with the cube center - Jacobian estimated at the cube center (<a href="./figs/cubic_conf_not_centered_J_center.png">png</a>, <a href="./figs/cubic_conf_not_centered_J_center.pdf">pdf</a>)</p> <p><span class="figure-number">Figure 3: </span>Cubic Stewart platform not centered with the cube center - Jacobian estimated at the cube center (<a href="./figs/cubic_conf_not_centered_J_center.png">png</a>, <a href="./figs/cubic_conf_not_centered_J_center.pdf">pdf</a>)</p>
</div> </div>
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides"> <table id="org6b3d8b1" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<caption class="t-above"><span class="table-number">Table 3:</span> Stiffness Matrix</caption>
<colgroup> <colgroup>
<col class="org-right" /> <col class="org-right" />
@ -760,11 +753,11 @@ stewart = initializeCylindricalPlatforms(stewart, <span class="org-string">'Fpr'
<div id="orgbe766b3" class="figure"> <div id="orgbe766b3" class="figure">
<p><img src="figs/cubic_conf_not_centered_J_stewart_center.png" alt="cubic_conf_not_centered_J_stewart_center.png" /> <p><img src="figs/cubic_conf_not_centered_J_stewart_center.png" alt="cubic_conf_not_centered_J_stewart_center.png" />
</p> </p>
<p><span class="figure-number">Figure 5: </span>Cubic Stewart platform not centered with the cube center - Jacobian estimated at the Stewart platform center (<a href="./figs/cubic_conf_not_centered_J_stewart_center.png">png</a>, <a href="./figs/cubic_conf_not_centered_J_stewart_center.pdf">pdf</a>)</p> <p><span class="figure-number">Figure 4: </span>Cubic Stewart platform not centered with the cube center - Jacobian estimated at the Stewart platform center (<a href="./figs/cubic_conf_not_centered_J_stewart_center.png">png</a>, <a href="./figs/cubic_conf_not_centered_J_stewart_center.pdf">pdf</a>)</p>
</div> </div>
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides"> <table id="org846d51c" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<caption class="t-above"><span class="table-number">Table 4:</span> Stiffness Matrix</caption>
<colgroup> <colgroup>
<col class="org-right" /> <col class="org-right" />
@ -838,8 +831,8 @@ stewart = initializeCylindricalPlatforms(stewart, <span class="org-string">'Fpr'
</div> </div>
</div> </div>
<div id="outline-container-orgd35acc0" class="outline-3"> <div id="outline-container-org95af62e" class="outline-3">
<h3 id="orgd35acc0"><span class="section-number-3">1.5</span> Conclusion</h3> <h3 id="org95af62e"><span class="section-number-3">1.5</span> Conclusion</h3>
<div class="outline-text-3" id="text-1-5"> <div class="outline-text-3" id="text-1-5">
<div class="important"> <div class="important">
<p> <p>
@ -892,9 +885,9 @@ We find the several Cubic configuration for the Stewart platform where the cente
The differences between the configuration are the cube&rsquo;s size: The differences between the configuration are the cube&rsquo;s size:
</p> </p>
<ul class="org-ul"> <ul class="org-ul">
<li>Small Cube Size in Figure <a href="#org105635f">6</a></li> <li>Small Cube Size in Figure <a href="#org105635f">5</a></li>
<li>Medium Cube Size in Figure <a href="#org264ab9c">7</a></li> <li>Medium Cube Size in Figure <a href="#org264ab9c">6</a></li>
<li>Large Cube Size in Figure <a href="#org52254fe">8</a></li> <li>Large Cube Size in Figure <a href="#org52254fe">7</a></li>
</ul> </ul>
<p> <p>
@ -912,11 +905,11 @@ FOc = H <span class="org-type">+</span> MO_B; <span class="org-comment">% Cente
<div id="org105635f" class="figure"> <div id="org105635f" class="figure">
<p><img src="figs/stewart_cubic_conf_type_1.png" alt="stewart_cubic_conf_type_1.png" /> <p><img src="figs/stewart_cubic_conf_type_1.png" alt="stewart_cubic_conf_type_1.png" />
</p> </p>
<p><span class="figure-number">Figure 6: </span>Cubic Configuration for the Stewart Platform - Small Cube Size (<a href="./figs/stewart_cubic_conf_type_1.png">png</a>, <a href="./figs/stewart_cubic_conf_type_1.pdf">pdf</a>)</p> <p><span class="figure-number">Figure 5: </span>Cubic Configuration for the Stewart Platform - Small Cube Size (<a href="./figs/stewart_cubic_conf_type_1.png">png</a>, <a href="./figs/stewart_cubic_conf_type_1.pdf">pdf</a>)</p>
</div> </div>
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides"> <table id="org91f89e4" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<caption class="t-above"><span class="table-number">Table 5:</span> Stiffness Matrix</caption>
<colgroup> <colgroup>
<col class="org-right" /> <col class="org-right" />
@ -998,12 +991,12 @@ FOc = H <span class="org-type">+</span> MO_B; <span class="org-comment">% Cente
<div id="org264ab9c" class="figure"> <div id="org264ab9c" class="figure">
<p><img src="figs/stewart_cubic_conf_type_2.png" alt="stewart_cubic_conf_type_2.png" /> <p><img src="figs/stewart_cubic_conf_type_2.png" alt="stewart_cubic_conf_type_2.png" />
</p> </p>
<p><span class="figure-number">Figure 7: </span>Cubic Configuration for the Stewart Platform - Medium Cube Size (<a href="./figs/stewart_cubic_conf_type_2.png">png</a>, <a href="./figs/stewart_cubic_conf_type_2.pdf">pdf</a>)</p> <p><span class="figure-number">Figure 6: </span>Cubic Configuration for the Stewart Platform - Medium Cube Size (<a href="./figs/stewart_cubic_conf_type_2.png">png</a>, <a href="./figs/stewart_cubic_conf_type_2.pdf">pdf</a>)</p>
</div> </div>
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides"> <table id="orgcf84781" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<caption class="t-above"><span class="table-number">Table 6:</span> Stiffness Matrix</caption>
<colgroup> <colgroup>
<col class="org-right" /> <col class="org-right" />
@ -1085,12 +1078,12 @@ FOc = H <span class="org-type">+</span> MO_B; <span class="org-comment">% Cente
<div id="org52254fe" class="figure"> <div id="org52254fe" class="figure">
<p><img src="figs/stewart_cubic_conf_type_3.png" alt="stewart_cubic_conf_type_3.png" /> <p><img src="figs/stewart_cubic_conf_type_3.png" alt="stewart_cubic_conf_type_3.png" />
</p> </p>
<p><span class="figure-number">Figure 8: </span>Cubic Configuration for the Stewart Platform - Large Cube Size (<a href="./figs/stewart_cubic_conf_type_3.png">png</a>, <a href="./figs/stewart_cubic_conf_type_3.pdf">pdf</a>)</p> <p><span class="figure-number">Figure 7: </span>Cubic Configuration for the Stewart Platform - Large Cube Size (<a href="./figs/stewart_cubic_conf_type_3.png">png</a>, <a href="./figs/stewart_cubic_conf_type_3.pdf">pdf</a>)</p>
</div> </div>
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides"> <table id="org02f7789" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<caption class="t-above"><span class="table-number">Table 7:</span> Stiffness Matrix</caption>
<colgroup> <colgroup>
<col class="org-right" /> <col class="org-right" />
@ -1164,8 +1157,8 @@ FOc = H <span class="org-type">+</span> MO_B; <span class="org-comment">% Cente
</div> </div>
</div> </div>
<div id="outline-container-org4576402" class="outline-3"> <div id="outline-container-org7673551" class="outline-3">
<h3 id="org4576402"><span class="section-number-3">2.2</span> Conclusion</h3> <h3 id="org7673551"><span class="section-number-3">2.2</span> Conclusion</h3>
<div class="outline-text-3" id="text-2-2"> <div class="outline-text-3" id="text-2-2">
<div class="important"> <div class="important">
<p> <p>
@ -1227,20 +1220,20 @@ FOc = H <span class="org-type">+</span> MO_B; <span class="org-comment">% Cente
<p> <p>
We find that for all the cube&rsquo;s size, \(k_x = k_y = k_z = k\) where \(k\) is the strut stiffness. We find that for all the cube&rsquo;s size, \(k_x = k_y = k_z = k\) where \(k\) is the strut stiffness.
We also find that \(k_{\theta_x} = k_{\theta_y}\) and \(k_{\theta_z}\) are varying with the cube&rsquo;s size (figure <a href="#orgf5b4a80">9</a>). We also find that \(k_{\theta_x} = k_{\theta_y}\) and \(k_{\theta_z}\) are varying with the cube&rsquo;s size (figure <a href="#orgf5b4a80">8</a>).
</p> </p>
<div id="orgf5b4a80" class="figure"> <div id="orgf5b4a80" class="figure">
<p><img src="figs/stiffness_cube_size.png" alt="stiffness_cube_size.png" /> <p><img src="figs/stiffness_cube_size.png" alt="stiffness_cube_size.png" />
</p> </p>
<p><span class="figure-number">Figure 9: </span>\(k_{\theta_x} = k_{\theta_y}\) and \(k_{\theta_z}\) function of the size of the cube</p> <p><span class="figure-number">Figure 8: </span>\(k_{\theta_x} = k_{\theta_y}\) and \(k_{\theta_z}\) function of the size of the cube</p>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-org04f1ef6" class="outline-3"> <div id="outline-container-orgcad29fd" class="outline-3">
<h3 id="org04f1ef6"><span class="section-number-3">3.2</span> Conclusion</h3> <h3 id="orgcad29fd"><span class="section-number-3">3.2</span> Conclusion</h3>
<div class="outline-text-3" id="text-3-2"> <div class="outline-text-3" id="text-3-2">
<p> <p>
We observe that \(k_{\theta_x} = k_{\theta_y}\) and \(k_{\theta_z}\) increase linearly with the cube size. We observe that \(k_{\theta_x} = k_{\theta_y}\) and \(k_{\theta_z}\) increase linearly with the cube size.
@ -1271,8 +1264,8 @@ In order to maximize the rotational stiffness of the Stewart platform, the size
<h3 id="org876e05f"><span class="section-number-3">4.2</span> Dynamic decoupling between the actuators and sensors</h3> <h3 id="org876e05f"><span class="section-number-3">4.2</span> Dynamic decoupling between the actuators and sensors</h3>
</div> </div>
<div id="outline-container-org95af62e" class="outline-3"> <div id="outline-container-org213d9b9" class="outline-3">
<h3 id="org95af62e"><span class="section-number-3">4.3</span> Conclusion</h3> <h3 id="org213d9b9"><span class="section-number-3">4.3</span> Conclusion</h3>
</div> </div>
</div> </div>
@ -1330,7 +1323,7 @@ This Matlab function is accessible <a href="../src/generateCubicConfiguration.m"
<div id="org8a7f3d8" class="figure"> <div id="org8a7f3d8" class="figure">
<p><img src="figs/cubic-configuration-definition.png" alt="cubic-configuration-definition.png" /> <p><img src="figs/cubic-configuration-definition.png" alt="cubic-configuration-definition.png" />
</p> </p>
<p><span class="figure-number">Figure 10: </span>Cubic Configuration</p> <p><span class="figure-number">Figure 9: </span>Cubic Configuration</p>
</div> </div>
</div> </div>
</div> </div>
@ -1435,7 +1428,7 @@ stewart.platform_M.Mb = Mb;
</div> </div>
<div id="postamble" class="status"> <div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p> <p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2020-02-12 mer. 11:18</p> <p class="date">Created: 2020-02-12 mer. 11:23</p>
</div> </div>
</body> </body>
</html> </html>

22
org/cubic-configuration.org
View File

@ -91,7 +91,7 @@ We here study what makes the Stiffness matrix diagonal when using a cubic config
#+end_src #+end_src
** Cubic Stewart platform centered with the cube center - Jacobian estimated at the cube center ** Cubic Stewart platform centered with the cube center - Jacobian estimated at the cube center
We create a cubic Stewart platform (figure [[fig:3d-cubic-stewart-aligned]]) in such a way that the center of the cube (black dot) is located at the center of the Stewart platform (blue dot). We create a cubic Stewart platform (figure [[fig:cubic_conf_centered_J_center]]) in such a way that the center of the cube (black star) is located at the center of the Stewart platform (blue dot).
The Jacobian matrix is estimated at the location of the center of the cube. The Jacobian matrix is estimated at the location of the center of the cube.
#+begin_src matlab #+begin_src matlab
@ -111,10 +111,6 @@ The Jacobian matrix is estimated at the location of the center of the cube.
stewart = initializeCylindricalPlatforms(stewart, 'Fpr', 175e-3, 'Mpr', 150e-3); stewart = initializeCylindricalPlatforms(stewart, 'Fpr', 175e-3, 'Mpr', 150e-3);
#+end_src #+end_src
#+name: fig:3d-cubic-stewart-aligned
#+caption: Centered cubic configuration
[[file:figs/3d-cubic-stewart-aligned.png]]
#+begin_src matlab :exports none #+begin_src matlab :exports none
displayArchitecture(stewart, 'labels', false); displayArchitecture(stewart, 'labels', false);
scatter3(0, 0, FOc, 200, 'kh'); scatter3(0, 0, FOc, 200, 'kh');
@ -133,6 +129,8 @@ The Jacobian matrix is estimated at the location of the center of the cube.
data2orgtable(stewart.kinematics.K, {}, {}, ' %.2g '); data2orgtable(stewart.kinematics.K, {}, {}, ' %.2g ');
#+end_src #+end_src
#+name: tab:cubic_conf_centered_J_center
#+caption: Stiffness Matrix
#+RESULTS: #+RESULTS:
| 2 | 0 | -2.5e-16 | 0 | 2.1e-17 | 0 | | 2 | 0 | -2.5e-16 | 0 | 2.1e-17 | 0 |
| 0 | 2 | 0 | -7.8e-19 | 0 | 0 | | 0 | 2 | 0 | -7.8e-19 | 0 | 0 |
@ -142,7 +140,7 @@ The Jacobian matrix is estimated at the location of the center of the cube.
| 6.6e-18 | -3.3e-18 | 0 | 1.7e-18 | 0 | 0.06 | | 6.6e-18 | -3.3e-18 | 0 | 1.7e-18 | 0 | 0.06 |
** Cubic Stewart platform centered with the cube center - Jacobian not estimated at the cube center ** Cubic Stewart platform centered with the cube center - Jacobian not estimated at the cube center
We create a cubic Stewart platform with center of the cube located at the center of the Stewart platform (figure [[fig:3d-cubic-stewart-aligned]]). We create a cubic Stewart platform with center of the cube located at the center of the Stewart platform (figure [[fig:cubic_conf_centered_J_not_center]]).
The Jacobian matrix is not estimated at the location of the center of the cube. The Jacobian matrix is not estimated at the location of the center of the cube.
#+begin_src matlab #+begin_src matlab
@ -180,6 +178,8 @@ The Jacobian matrix is not estimated at the location of the center of the cube.
data2orgtable(stewart.kinematics.K, {}, {}, ' %.2g '); data2orgtable(stewart.kinematics.K, {}, {}, ' %.2g ');
#+end_src #+end_src
#+name: tab:cubic_conf_centered_J_not_center
#+caption: Stiffness Matrix
#+RESULTS: #+RESULTS:
| 2 | 0 | -2.5e-16 | 0 | -0.14 | 0 | | 2 | 0 | -2.5e-16 | 0 | -0.14 | 0 |
| 0 | 2 | 0 | 0.14 | 0 | 0 | | 0 | 2 | 0 | 0.14 | 0 | 0 |
@ -227,6 +227,8 @@ The Jacobian is estimated at the cube center.
data2orgtable(stewart.kinematics.K, {}, {}, ' %.2g '); data2orgtable(stewart.kinematics.K, {}, {}, ' %.2g ');
#+end_src #+end_src
#+name: tab:cubic_conf_not_centered_J_center
#+caption: Stiffness Matrix
#+RESULTS: #+RESULTS:
| 2 | 0 | -1.7e-16 | 0 | 4.9e-17 | 0 | | 2 | 0 | -1.7e-16 | 0 | 4.9e-17 | 0 |
| 0 | 2 | 0 | -2.2e-17 | 0 | 2.8e-17 | | 0 | 2 | 0 | -2.2e-17 | 0 | 2.8e-17 |
@ -281,6 +283,8 @@ The center of the cube from the top platform is at $z = 110 - 175 = -65$.
data2orgtable(stewart.kinematics.K, {}, {}, ' %.2g '); data2orgtable(stewart.kinematics.K, {}, {}, ' %.2g ');
#+end_src #+end_src
#+name: tab:cubic_conf_not_centered_J_stewart_center
#+caption: Stiffness Matrix
#+RESULTS: #+RESULTS:
| 2 | 0 | 1.5e-16 | 0 | 0.02 | 0 | | 2 | 0 | 1.5e-16 | 0 | 0.02 | 0 |
| 0 | 2 | 0 | -0.02 | 0 | 0 | | 0 | 2 | 0 | -0.02 | 0 | 0 |
@ -366,6 +370,8 @@ However, the rotational stiffnesses are increasing with the cube's size but the
data2orgtable(stewart.kinematics.K, {}, {}, ' %.2g '); data2orgtable(stewart.kinematics.K, {}, {}, ' %.2g ');
#+end_src #+end_src
#+name: tab:stewart_cubic_conf_type_1
#+caption: Stiffness Matrix
#+RESULTS: #+RESULTS:
| 2 | 0 | -2.8e-16 | 0 | 2.4e-17 | 0 | | 2 | 0 | -2.8e-16 | 0 | 2.4e-17 | 0 |
| 0 | 2 | 0 | -2.3e-17 | 0 | 0 | | 0 | 2 | 0 | -2.3e-17 | 0 | 0 |
@ -405,6 +411,8 @@ However, the rotational stiffnesses are increasing with the cube's size but the
data2orgtable(stewart.kinematics.K, {}, {}, ' %.2g '); data2orgtable(stewart.kinematics.K, {}, {}, ' %.2g ');
#+end_src #+end_src
#+name: tab:stewart_cubic_conf_type_2
#+caption: Stiffness Matrix
#+RESULTS: #+RESULTS:
| 2 | 0 | -1.9e-16 | 0 | 5.6e-17 | 0 | | 2 | 0 | -1.9e-16 | 0 | 5.6e-17 | 0 |
| 0 | 2 | 0 | -7.6e-17 | 0 | 0 | | 0 | 2 | 0 | -7.6e-17 | 0 | 0 |
@ -444,6 +452,8 @@ However, the rotational stiffnesses are increasing with the cube's size but the
data2orgtable(stewart.kinematics.K, {}, {}, ' %.2g '); data2orgtable(stewart.kinematics.K, {}, {}, ' %.2g ');
#+end_src #+end_src
#+name: tab:stewart_cubic_conf_type_3
#+caption: Stiffness Matrix
#+RESULTS: #+RESULTS:
| 2 | 0 | -3e-16 | 0 | -8.3e-17 | 0 | | 2 | 0 | -3e-16 | 0 | -8.3e-17 | 0 |
| 0 | 2 | 0 | -2.2e-17 | 0 | 5.6e-17 | | 0 | 2 | 0 | -2.2e-17 | 0 | 5.6e-17 |