Add display for each cubic configuration
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@ -4,7 +4,7 @@
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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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<!-- 2020-02-06 jeu. 18:22 -->
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<!-- 2020-02-07 ven. 17:31 -->
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<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
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<meta name="viewport" content="width=device-width, initial-scale=1" />
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<title>Cubic configuration for the Stewart Platform</title>
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@ -268,25 +268,25 @@ for the JavaScript code in this tag.
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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="#org8350a45">1. Configuration Analysis - Stiffness Matrix</a>
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<li><a href="#org16a66cd">1. Configuration Analysis - Stiffness Matrix</a>
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<ul>
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<li><a href="#org6b34363">1.1. Cubic Stewart platform centered with the cube center - Jacobian estimated at the cube center</a></li>
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<li><a href="#orgd59e9f0">1.2. Cubic Stewart platform centered with the cube center - Jacobian not estimated at the cube center</a></li>
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<li><a href="#org27bd91a">1.3. Cubic Stewart platform not centered with the cube center - Jacobian estimated at the cube center</a></li>
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<li><a href="#org4adea52">1.4. Cubic Stewart platform not centered with the cube center - Jacobian estimated at the Stewart platform center</a></li>
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<li><a href="#org5defe19">1.5. Conclusion</a></li>
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<li><a href="#org905f726">1.6. Having Cube’s center above the top platform</a></li>
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<li><a href="#orgd83749a">1.1. Cubic Stewart platform centered with the cube center - Jacobian estimated at the cube center</a></li>
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<li><a href="#org84204db">1.2. Cubic Stewart platform centered with the cube center - Jacobian not estimated at the cube center</a></li>
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<li><a href="#orgada859c">1.3. Cubic Stewart platform not centered with the cube center - Jacobian estimated at the cube center</a></li>
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<li><a href="#org8b2c367">1.4. Cubic Stewart platform not centered with the cube center - Jacobian estimated at the Stewart platform center</a></li>
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<li><a href="#org34d7a0d">1.5. Conclusion</a></li>
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<li><a href="#org265d677">1.6. Having Cube’s center above the top platform</a></li>
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</ul>
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</li>
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<li><a href="#org6746f61">2. Functions</a>
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<li><a href="#org93a8538">2. Functions</a>
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<ul>
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<li><a href="#org80fcb20">2.1. <code>generateCubicConfiguration</code>: Generate a Cubic Configuration</a>
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<li><a href="#org8786798">2.1. <code>generateCubicConfiguration</code>: Generate a Cubic Configuration</a>
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<ul>
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<li><a href="#orgd3654f4">Function description</a></li>
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<li><a href="#orgf1c4374">Documentation</a></li>
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<li><a href="#org7703a4a">Optional Parameters</a></li>
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<li><a href="#org43039c1">Position of the Cube</a></li>
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<li><a href="#orga18e804">Compute the pose</a></li>
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<li><a href="#org0b63bb1">Function description</a></li>
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<li><a href="#orgaac7da3">Documentation</a></li>
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<li><a href="#org747c61c">Optional Parameters</a></li>
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<li><a href="#orgec4e738">Position of the Cube</a></li>
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<li><a href="#org97e1d45">Compute the pose</a></li>
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</ul>
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</li>
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</ul>
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@ -313,7 +313,7 @@ According to <a class='org-ref-reference' href="#preumont07_six_axis_singl_stage
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</p>
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<p>
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To generate and study the Cubic configuration, <code>generateCubicConfiguration</code> is used (description in section <a href="#orgfe8cdfe">2.1</a>).
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To generate and study the Cubic configuration, <code>generateCubicConfiguration</code> is used (description in section <a href="#orgf3011db">2.1</a>).
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The goal is to study the benefits of using a cubic configuration:
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</p>
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<ul class="org-ul">
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@ -322,15 +322,15 @@ The goal is to study the benefits of using a cubic configuration:
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<li>Is the center of the cube an important point?</li>
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</ul>
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<div id="outline-container-org8350a45" class="outline-2">
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<h2 id="org8350a45"><span class="section-number-2">1</span> Configuration Analysis - Stiffness Matrix</h2>
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<div id="outline-container-org16a66cd" class="outline-2">
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<h2 id="org16a66cd"><span class="section-number-2">1</span> Configuration Analysis - Stiffness Matrix</h2>
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<div class="outline-text-2" id="text-1">
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</div>
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<div id="outline-container-org6b34363" class="outline-3">
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<h3 id="org6b34363"><span class="section-number-3">1.1</span> Cubic Stewart platform centered with the cube center - Jacobian estimated at the cube center</h3>
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<div id="outline-container-orgd83749a" class="outline-3">
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<h3 id="orgd83749a"><span class="section-number-3">1.1</span> Cubic Stewart platform centered with the cube center - Jacobian estimated at the cube center</h3>
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<div class="outline-text-3" id="text-1-1">
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<p>
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We create a cubic Stewart platform (figure <a href="#org964919a">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).
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We create a cubic Stewart platform (figure <a href="#org0e6176c">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).
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The Jacobian matrix is estimated at the location of the center of the cube.
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</p>
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@ -340,16 +340,24 @@ stewart = generateCubicConfiguration(stewart, <span class="org-string">'Hc'</spa
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stewart = computeJointsPose(stewart);
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stewart = initializeStrutDynamics(stewart, <span class="org-string">'Ki'</span>, ones(6,1));
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stewart = computeJacobian(stewart);
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stewart = initializeCylindricalPlatforms(stewart, <span class="org-string">'Fpr'</span>, 175e<span class="org-type">-</span>3, <span class="org-string">'Mpr'</span>, 150e<span class="org-type">-</span>3);
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</pre>
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</div>
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<div id="org964919a" class="figure">
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<div id="org0e6176c" class="figure">
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<p><img src="./figs/3d-cubic-stewart-aligned.png" alt="3d-cubic-stewart-aligned.png" />
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</p>
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<p><span class="figure-number">Figure 1: </span>Centered cubic configuration</p>
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</div>
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<div id="orgf0479ad" class="figure">
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<p><img src="figs/cubic_conf_centered_J_center.png" alt="cubic_conf_centered_J_center.png" />
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</p>
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<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>
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</div>
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<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
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@ -425,11 +433,11 @@ stewart = computeJacobian(stewart);
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</div>
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</div>
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<div id="outline-container-orgd59e9f0" class="outline-3">
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<h3 id="orgd59e9f0"><span class="section-number-3">1.2</span> Cubic Stewart platform centered with the cube center - Jacobian not estimated at the cube center</h3>
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<div id="outline-container-org84204db" class="outline-3">
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<h3 id="org84204db"><span class="section-number-3">1.2</span> Cubic Stewart platform centered with the cube center - Jacobian not estimated at the cube center</h3>
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<div class="outline-text-3" id="text-1-2">
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<p>
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We create a cubic Stewart platform with center of the cube located at the center of the Stewart platform (figure <a href="#org964919a">1</a>).
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We create a cubic Stewart platform with center of the cube located at the center of the Stewart platform (figure <a href="#org0e6176c">1</a>).
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The Jacobian matrix is not estimated at the location of the center of the cube.
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</p>
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@ -439,9 +447,17 @@ stewart = generateCubicConfiguration(stewart, <span class="org-string">'Hc'</spa
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stewart = computeJointsPose(stewart);
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stewart = initializeStrutDynamics(stewart, <span class="org-string">'Ki'</span>, ones(6,1));
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stewart = computeJacobian(stewart);
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stewart = initializeCylindricalPlatforms(stewart, <span class="org-string">'Fpr'</span>, 175e<span class="org-type">-</span>3, <span class="org-string">'Mpr'</span>, 150e<span class="org-type">-</span>3);
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</pre>
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</div>
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<div id="org7a8523c" class="figure">
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<p><img src="figs/cubic_conf_centered_J_not_center.png" alt="cubic_conf_centered_J_not_center.png" />
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</p>
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<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>
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</div>
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<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
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@ -517,19 +533,19 @@ stewart = computeJacobian(stewart);
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</div>
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</div>
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<div id="outline-container-org27bd91a" class="outline-3">
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<h3 id="org27bd91a"><span class="section-number-3">1.3</span> Cubic Stewart platform not centered with the cube center - Jacobian estimated at the cube center</h3>
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<div id="outline-container-orgada859c" class="outline-3">
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<h3 id="orgada859c"><span class="section-number-3">1.3</span> Cubic Stewart platform not centered with the cube center - Jacobian estimated at the cube center</h3>
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<div class="outline-text-3" id="text-1-3">
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<p>
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Here, the “center” of the Stewart platform is not at the cube center (figure <a href="#orgeceb55c">2</a>).
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Here, the “center” of the Stewart platform is not at the cube center (figure <a href="#org9e92807">4</a>).
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The Jacobian is estimated at the cube center.
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</p>
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<div id="orgeceb55c" class="figure">
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<div id="org9e92807" class="figure">
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<p><img src="./figs/3d-cubic-stewart-misaligned.png" alt="3d-cubic-stewart-misaligned.png" />
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</p>
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<p><span class="figure-number">Figure 2: </span>Not centered cubic configuration</p>
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<p><span class="figure-number">Figure 4: </span>Not centered cubic configuration</p>
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</div>
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<div class="org-src-container">
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@ -538,9 +554,17 @@ stewart = generateCubicConfiguration(stewart, <span class="org-string">'Hc'</spa
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stewart = computeJointsPose(stewart);
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stewart = initializeStrutDynamics(stewart, <span class="org-string">'Ki'</span>, ones(6,1));
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stewart = computeJacobian(stewart);
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stewart = initializeCylindricalPlatforms(stewart, <span class="org-string">'Fpr'</span>, 175e<span class="org-type">-</span>3, <span class="org-string">'Mpr'</span>, 150e<span class="org-type">-</span>3);
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</pre>
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</div>
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<div id="orgcc43044" class="figure">
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<p><img src="figs/cubic_conf_not_centered_J_center.png" alt="cubic_conf_not_centered_J_center.png" />
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</p>
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<p><span class="figure-number">Figure 5: </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>
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</div>
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<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
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@ -561,9 +585,9 @@ stewart = computeJacobian(stewart);
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<tr>
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<td class="org-right">2</td>
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<td class="org-right">0</td>
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<td class="org-right">-1.5e-16</td>
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<td class="org-right">-1.7e-16</td>
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<td class="org-right">0</td>
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<td class="org-right">0.04</td>
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<td class="org-right">0.02</td>
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<td class="org-right">0</td>
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</tr>
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@ -571,44 +595,44 @@ stewart = computeJacobian(stewart);
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<td class="org-right">0</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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<td class="org-right">-0.04</td>
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<td class="org-right">-0.02</td>
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<td class="org-right">0</td>
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<td class="org-right">-2.8e-17</td>
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<td class="org-right">2.8e-17</td>
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</tr>
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<tr>
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<td class="org-right">-1.5e-16</td>
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<td class="org-right">-1.7e-16</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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<td class="org-right">1.2e-18</td>
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<td class="org-right">-1e-17</td>
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<td class="org-right">0</td>
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<td class="org-right">1.2e-19</td>
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<td class="org-right">-1.4e-17</td>
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<td class="org-right">1.4e-17</td>
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</tr>
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<tr>
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<td class="org-right">0</td>
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<td class="org-right">-0.04</td>
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<td class="org-right">1.2e-18</td>
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<td class="org-right">0.016</td>
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<td class="org-right">0</td>
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<td class="org-right">8.7e-19</td>
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<td class="org-right">-0.02</td>
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<td class="org-right">1.2e-19</td>
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<td class="org-right">0.015</td>
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<td class="org-right">-4.3e-19</td>
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<td class="org-right">1.7e-18</td>
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</tr>
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<tr>
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<td class="org-right">0.04</td>
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<td class="org-right">0.02</td>
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<td class="org-right">0</td>
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<td class="org-right">-7.3e-18</td>
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<td class="org-right">-3.3e-21</td>
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<td class="org-right">0.015</td>
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<td class="org-right">0</td>
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<td class="org-right">-6.2e-18</td>
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<td class="org-right">-1.1e-19</td>
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<td class="org-right">0.016</td>
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<td class="org-right">8.7e-19</td>
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</tr>
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<tr>
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<td class="org-right">-3.7e-19</td>
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<td class="org-right">-2.5e-17</td>
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<td class="org-right">6.6e-18</td>
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<td class="org-right">2.5e-17</td>
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<td class="org-right">0</td>
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<td class="org-right">2e-18</td>
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<td class="org-right">0</td>
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<td class="org-right">1.2e-18</td>
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<td class="org-right">8.7e-19</td>
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<td class="org-right">0.06</td>
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</tr>
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</tbody>
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@ -620,8 +644,8 @@ We obtain \(k_x = k_y = k_z\) and \(k_{\theta_x} = k_{\theta_y}\), but the Stiff
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</div>
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</div>
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<div id="outline-container-org4adea52" class="outline-3">
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<h3 id="org4adea52"><span class="section-number-3">1.4</span> Cubic Stewart platform not centered with the cube center - Jacobian estimated at the Stewart platform center</h3>
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<div id="outline-container-org8b2c367" class="outline-3">
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<h3 id="org8b2c367"><span class="section-number-3">1.4</span> Cubic Stewart platform not centered with the cube center - Jacobian estimated at the Stewart platform center</h3>
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<div class="outline-text-3" id="text-1-4">
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<p>
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Here, the “center” of the Stewart platform is not at the cube center.
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@ -636,14 +660,22 @@ The center of the cube from the top platform is at \(z = 110 - 175 = -65\).
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">stewart = initializeFramesPositions(<span class="org-string">'H'</span>, 80e<span class="org-type">-</span>3, <span class="org-string">'MO_B'</span>, <span class="org-type">-</span>30e<span class="org-type">-</span>3);
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<pre class="src src-matlab">stewart = initializeFramesPositions(<span class="org-string">'H'</span>, 80e<span class="org-type">-</span>3, <span class="org-string">'MO_B'</span>, <span class="org-type">-</span>40e<span class="org-type">-</span>3);
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stewart = generateCubicConfiguration(stewart, <span class="org-string">'Hc'</span>, 100e<span class="org-type">-</span>3, <span class="org-string">'FOc'</span>, 50e<span class="org-type">-</span>3, <span class="org-string">'FHa'</span>, 0, <span class="org-string">'MHb'</span>, 0);
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stewart = computeJointsPose(stewart);
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stewart = initializeStrutDynamics(stewart, <span class="org-string">'Ki'</span>, ones(6,1));
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stewart = computeJacobian(stewart);
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stewart = initializeCylindricalPlatforms(stewart, <span class="org-string">'Fpr'</span>, 175e<span class="org-type">-</span>3, <span class="org-string">'Mpr'</span>, 150e<span class="org-type">-</span>3);
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</pre>
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</div>
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<div id="org57db017" class="figure">
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<p><img src="figs/cubic_conf_not_centered_J_stewart_center.png" alt="cubic_conf_not_centered_J_stewart_center.png" />
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</p>
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<p><span class="figure-number">Figure 6: </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>
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</div>
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<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
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@ -666,7 +698,7 @@ stewart = computeJacobian(stewart);
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<td class="org-right">0</td>
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<td class="org-right">-1.7e-16</td>
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<td class="org-right">0</td>
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<td class="org-right">4.9e-17</td>
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<td class="org-right">0.02</td>
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<td class="org-right">0</td>
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</tr>
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@ -674,7 +706,7 @@ stewart = computeJacobian(stewart);
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<td class="org-right">0</td>
|
||||
<td class="org-right">2</td>
|
||||
<td class="org-right">0</td>
|
||||
<td class="org-right">-2.2e-17</td>
|
||||
<td class="org-right">-0.02</td>
|
||||
<td class="org-right">0</td>
|
||||
<td class="org-right">2.8e-17</td>
|
||||
</tr>
|
||||
@ -683,48 +715,44 @@ stewart = computeJacobian(stewart);
|
||||
<td class="org-right">-1.7e-16</td>
|
||||
<td class="org-right">0</td>
|
||||
<td class="org-right">2</td>
|
||||
<td class="org-right">1.1e-18</td>
|
||||
<td class="org-right">1.2e-19</td>
|
||||
<td class="org-right">-1.4e-17</td>
|
||||
<td class="org-right">1.4e-17</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td class="org-right">0</td>
|
||||
<td class="org-right">-2.2e-17</td>
|
||||
<td class="org-right">1.1e-18</td>
|
||||
<td class="org-right">-0.02</td>
|
||||
<td class="org-right">1.2e-19</td>
|
||||
<td class="org-right">0.015</td>
|
||||
<td class="org-right">0</td>
|
||||
<td class="org-right">3.5e-18</td>
|
||||
<td class="org-right">-4.3e-19</td>
|
||||
<td class="org-right">1.7e-18</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td class="org-right">4.4e-17</td>
|
||||
<td class="org-right">0.02</td>
|
||||
<td class="org-right">0</td>
|
||||
<td class="org-right">-1.4e-17</td>
|
||||
<td class="org-right">-5.7e-20</td>
|
||||
<td class="org-right">-7.3e-18</td>
|
||||
<td class="org-right">-3.3e-21</td>
|
||||
<td class="org-right">0.015</td>
|
||||
<td class="org-right">-8.7e-19</td>
|
||||
<td class="org-right">0</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td class="org-right">6.6e-18</td>
|
||||
<td class="org-right">2.5e-17</td>
|
||||
<td class="org-right">0</td>
|
||||
<td class="org-right">3.5e-18</td>
|
||||
<td class="org-right">-8.7e-19</td>
|
||||
<td class="org-right">2e-18</td>
|
||||
<td class="org-right">0</td>
|
||||
<td class="org-right">0.06</td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table>
|
||||
|
||||
<p>
|
||||
We obtain \(k_x = k_y = k_z\) and \(k_{\theta_x} = k_{\theta_y}\), and the Stiffness matrix is diagonal.
|
||||
</p>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org5defe19" class="outline-3">
|
||||
<h3 id="org5defe19"><span class="section-number-3">1.5</span> Conclusion</h3>
|
||||
<div id="outline-container-org34d7a0d" class="outline-3">
|
||||
<h3 id="org34d7a0d"><span class="section-number-3">1.5</span> Conclusion</h3>
|
||||
<div class="outline-text-3" id="text-1-5">
|
||||
<div class="important">
|
||||
<ul class="org-ul">
|
||||
@ -736,8 +764,8 @@ We obtain \(k_x = k_y = k_z\) and \(k_{\theta_x} = k_{\theta_y}\), and the Stiff
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org905f726" class="outline-3">
|
||||
<h3 id="org905f726"><span class="section-number-3">1.6</span> Having Cube’s center above the top platform</h3>
|
||||
<div id="outline-container-org265d677" class="outline-3">
|
||||
<h3 id="org265d677"><span class="section-number-3">1.6</span> Having Cube’s center above the top platform</h3>
|
||||
<div class="outline-text-3" id="text-1-6">
|
||||
<p>
|
||||
Let’s say we want to have a decouple dynamics above the top platform.
|
||||
@ -785,9 +813,9 @@ stewart = initializeStewartPose(stewart);
|
||||
<tr>
|
||||
<td class="org-right">2</td>
|
||||
<td class="org-right">0</td>
|
||||
<td class="org-right">-4.6e-16</td>
|
||||
<td class="org-right">-3.2e-16</td>
|
||||
<td class="org-right">0</td>
|
||||
<td class="org-right">4e-17</td>
|
||||
<td class="org-right">3.1e-16</td>
|
||||
<td class="org-right">0</td>
|
||||
</tr>
|
||||
|
||||
@ -795,45 +823,45 @@ stewart = initializeStewartPose(stewart);
|
||||
<td class="org-right">0</td>
|
||||
<td class="org-right">2</td>
|
||||
<td class="org-right">0</td>
|
||||
<td class="org-right">-4.8e-17</td>
|
||||
<td class="org-right">-1.2e-16</td>
|
||||
<td class="org-right">0</td>
|
||||
<td class="org-right">0</td>
|
||||
<td class="org-right">-3.5e-17</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td class="org-right">-4.6e-16</td>
|
||||
<td class="org-right">-3.2e-16</td>
|
||||
<td class="org-right">0</td>
|
||||
<td class="org-right">2</td>
|
||||
<td class="org-right">1.5e-20</td>
|
||||
<td class="org-right">4e-17</td>
|
||||
<td class="org-right">5e-18</td>
|
||||
<td class="org-right">-5.6e-17</td>
|
||||
<td class="org-right">0</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td class="org-right">0</td>
|
||||
<td class="org-right">-4.8e-17</td>
|
||||
<td class="org-right">1.5e-20</td>
|
||||
<td class="org-right">0.00034</td>
|
||||
<td class="org-right">6.8e-21</td>
|
||||
<td class="org-right">4.2e-19</td>
|
||||
<td class="org-right">-1.2e-16</td>
|
||||
<td class="org-right">5e-18</td>
|
||||
<td class="org-right">0.14</td>
|
||||
<td class="org-right">3.5e-18</td>
|
||||
<td class="org-right">1.4e-17</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td class="org-right">4e-17</td>
|
||||
<td class="org-right">3e-16</td>
|
||||
<td class="org-right">0</td>
|
||||
<td class="org-right">4e-17</td>
|
||||
<td class="org-right">-3e-21</td>
|
||||
<td class="org-right">0.00034</td>
|
||||
<td class="org-right">-2.7e-20</td>
|
||||
<td class="org-right">-5.4e-17</td>
|
||||
<td class="org-right">2.1e-19</td>
|
||||
<td class="org-right">0.14</td>
|
||||
<td class="org-right">-6.9e-18</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td class="org-right">-1.7e-19</td>
|
||||
<td class="org-right">-3.6e-17</td>
|
||||
<td class="org-right">7.4e-19</td>
|
||||
<td class="org-right">-2.6e-17</td>
|
||||
<td class="org-right">0</td>
|
||||
<td class="org-right">4.2e-19</td>
|
||||
<td class="org-right">-2.7e-20</td>
|
||||
<td class="org-right">0.0014</td>
|
||||
<td class="org-right">1.3e-17</td>
|
||||
<td class="org-right">-6.9e-18</td>
|
||||
<td class="org-right">0.54</td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table>
|
||||
@ -845,19 +873,19 @@ We obtain \(k_x = k_y = k_z\) and \(k_{\theta_x} = k_{\theta_y}\), but the Stiff
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org6746f61" class="outline-2">
|
||||
<h2 id="org6746f61"><span class="section-number-2">2</span> Functions</h2>
|
||||
<div id="outline-container-org93a8538" class="outline-2">
|
||||
<h2 id="org93a8538"><span class="section-number-2">2</span> Functions</h2>
|
||||
<div class="outline-text-2" id="text-2">
|
||||
<p>
|
||||
<a id="org2a4885e"></a>
|
||||
<a id="org44c44dc"></a>
|
||||
</p>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org80fcb20" class="outline-3">
|
||||
<h3 id="org80fcb20"><span class="section-number-3">2.1</span> <code>generateCubicConfiguration</code>: Generate a Cubic Configuration</h3>
|
||||
<div id="outline-container-org8786798" class="outline-3">
|
||||
<h3 id="org8786798"><span class="section-number-3">2.1</span> <code>generateCubicConfiguration</code>: Generate a Cubic Configuration</h3>
|
||||
<div class="outline-text-3" id="text-2-1">
|
||||
<p>
|
||||
<a id="orgfe8cdfe"></a>
|
||||
<a id="orgf3011db"></a>
|
||||
</p>
|
||||
|
||||
<p>
|
||||
@ -865,9 +893,9 @@ This Matlab function is accessible <a href="src/generateCubicConfiguration.m">he
|
||||
</p>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgd3654f4" class="outline-4">
|
||||
<h4 id="orgd3654f4">Function description</h4>
|
||||
<div class="outline-text-4" id="text-orgd3654f4">
|
||||
<div id="outline-container-org0b63bb1" class="outline-4">
|
||||
<h4 id="org0b63bb1">Function description</h4>
|
||||
<div class="outline-text-4" id="text-org0b63bb1">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name">[stewart]</span> = <span class="org-function-name">generateCubicConfiguration</span>(<span class="org-variable-name">stewart</span>, <span class="org-variable-name">args</span>)
|
||||
<span class="org-comment">% generateCubicConfiguration - Generate a Cubic Configuration</span>
|
||||
@ -892,21 +920,21 @@ This Matlab function is accessible <a href="src/generateCubicConfiguration.m">he
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgf1c4374" class="outline-4">
|
||||
<h4 id="orgf1c4374">Documentation</h4>
|
||||
<div class="outline-text-4" id="text-orgf1c4374">
|
||||
<div id="outline-container-orgaac7da3" class="outline-4">
|
||||
<h4 id="orgaac7da3">Documentation</h4>
|
||||
<div class="outline-text-4" id="text-orgaac7da3">
|
||||
|
||||
<div id="org8d1a2f5" class="figure">
|
||||
<div id="orgc2715ee" class="figure">
|
||||
<p><img src="figs/cubic-configuration-definition.png" alt="cubic-configuration-definition.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 3: </span>Cubic Configuration</p>
|
||||
<p><span class="figure-number">Figure 7: </span>Cubic Configuration</p>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org7703a4a" class="outline-4">
|
||||
<h4 id="org7703a4a">Optional Parameters</h4>
|
||||
<div class="outline-text-4" id="text-org7703a4a">
|
||||
<div id="outline-container-org747c61c" class="outline-4">
|
||||
<h4 id="org747c61c">Optional Parameters</h4>
|
||||
<div class="outline-text-4" id="text-org747c61c">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">arguments
|
||||
stewart
|
||||
@ -920,9 +948,9 @@ This Matlab function is accessible <a href="src/generateCubicConfiguration.m">he
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org43039c1" class="outline-4">
|
||||
<h4 id="org43039c1">Position of the Cube</h4>
|
||||
<div class="outline-text-4" id="text-org43039c1">
|
||||
<div id="outline-container-orgec4e738" class="outline-4">
|
||||
<h4 id="orgec4e738">Position of the Cube</h4>
|
||||
<div class="outline-text-4" id="text-orgec4e738">
|
||||
<p>
|
||||
We define the useful points of the cube with respect to the Cube’s center.
|
||||
\({}^{C}C\) are the 6 vertices of the cubes expressed in a frame {C} which is
|
||||
@ -947,9 +975,9 @@ CCm = [Cc(<span class="org-type">:</span>,2), Cc(<span class="org-type">:</span>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orga18e804" class="outline-4">
|
||||
<h4 id="orga18e804">Compute the pose</h4>
|
||||
<div class="outline-text-4" id="text-orga18e804">
|
||||
<div id="outline-container-org97e1d45" class="outline-4">
|
||||
<h4 id="org97e1d45">Compute the pose</h4>
|
||||
<div class="outline-text-4" id="text-org97e1d45">
|
||||
<p>
|
||||
We can compute the vector of each leg \({}^{C}\hat{\bm{s}}_{i}\) (unit vector from \({}^{C}C_{f}\) to \({}^{C}C_{m}\)).
|
||||
</p>
|
||||
@ -982,7 +1010,7 @@ stewart.Mb = CCf <span class="org-type">+</span> [0; 0; args.FOc<span class="org
|
||||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Dehaeze Thomas</p>
|
||||
<p class="date">Created: 2020-02-06 jeu. 18:22</p>
|
||||
<p class="date">Created: 2020-02-07 ven. 17:31</p>
|
||||
</div>
|
||||
</body>
|
||||
</html>
|
||||
|
||||
@ -61,12 +61,27 @@ The Jacobian matrix is estimated at the location of the center of the cube.
|
||||
stewart = computeJointsPose(stewart);
|
||||
stewart = initializeStrutDynamics(stewart, 'Ki', ones(6,1));
|
||||
stewart = computeJacobian(stewart);
|
||||
stewart = initializeCylindricalPlatforms(stewart, 'Fpr', 175e-3, 'Mpr', 150e-3);
|
||||
#+end_src
|
||||
|
||||
#+name: fig:3d-cubic-stewart-aligned
|
||||
#+caption: Centered cubic configuration
|
||||
[[file:./figs/3d-cubic-stewart-aligned.png]]
|
||||
|
||||
#+begin_src matlab :exports none
|
||||
displayArchitecture(stewart, 'labels', false);
|
||||
scatter3(0, 0, 50e-3, 200, 'kh');
|
||||
#+end_src
|
||||
|
||||
#+header: :tangle no :exports results :results none :noweb yes
|
||||
#+begin_src matlab :var filepath="figs/cubic_conf_centered_J_center.pdf" :var figsize="wide-tall" :post pdf2svg(file=*this*, ext="png")
|
||||
<<plt-matlab>>
|
||||
#+end_src
|
||||
|
||||
#+name: fig:cubic_conf_centered_J_center
|
||||
#+caption: Cubic Stewart platform centered with the cube center - Jacobian estimated at the cube center ([[./figs/cubic_conf_centered_J_center.png][png]], [[./figs/cubic_conf_centered_J_center.pdf][pdf]])
|
||||
[[file:figs/cubic_conf_centered_J_center.png]]
|
||||
|
||||
#+begin_src matlab :exports results :results value table replace :tangle no
|
||||
data2orgtable(stewart.K, {}, {}, ' %.2g ');
|
||||
#+end_src
|
||||
@ -89,8 +104,23 @@ The Jacobian matrix is not estimated at the location of the center of the cube.
|
||||
stewart = computeJointsPose(stewart);
|
||||
stewart = initializeStrutDynamics(stewart, 'Ki', ones(6,1));
|
||||
stewart = computeJacobian(stewart);
|
||||
stewart = initializeCylindricalPlatforms(stewart, 'Fpr', 175e-3, 'Mpr', 150e-3);
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :exports none
|
||||
displayArchitecture(stewart, 'labels', false);
|
||||
scatter3(0, 0, 50e-3, 200, 'kh');
|
||||
#+end_src
|
||||
|
||||
#+header: :tangle no :exports results :results none :noweb yes
|
||||
#+begin_src matlab :var filepath="figs/cubic_conf_centered_J_not_center.pdf" :var figsize="wide-tall" :post pdf2svg(file=*this*, ext="png")
|
||||
<<plt-matlab>>
|
||||
#+end_src
|
||||
|
||||
#+name: fig:cubic_conf_centered_J_not_center
|
||||
#+caption: Cubic Stewart platform centered with the cube center - Jacobian not estimated at the cube center ([[./figs/cubic_conf_centered_J_not_center.png][png]], [[./figs/cubic_conf_centered_J_not_center.pdf][pdf]])
|
||||
[[file:figs/cubic_conf_centered_J_not_center.png]]
|
||||
|
||||
#+begin_src matlab :exports results :results value table replace :tangle no
|
||||
data2orgtable(stewart.K, {}, {}, ' %.2g ');
|
||||
#+end_src
|
||||
@ -117,19 +147,34 @@ The Jacobian is estimated at the cube center.
|
||||
stewart = computeJointsPose(stewart);
|
||||
stewart = initializeStrutDynamics(stewart, 'Ki', ones(6,1));
|
||||
stewart = computeJacobian(stewart);
|
||||
stewart = initializeCylindricalPlatforms(stewart, 'Fpr', 175e-3, 'Mpr', 150e-3);
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :exports none
|
||||
displayArchitecture(stewart, 'labels', false);
|
||||
scatter3(0, 0, 50e-3, 200, 'kh');
|
||||
#+end_src
|
||||
|
||||
#+header: :tangle no :exports results :results none :noweb yes
|
||||
#+begin_src matlab :var filepath="figs/cubic_conf_not_centered_J_center.pdf" :var figsize="wide-tall" :post pdf2svg(file=*this*, ext="png")
|
||||
<<plt-matlab>>
|
||||
#+end_src
|
||||
|
||||
#+name: fig:cubic_conf_not_centered_J_center
|
||||
#+caption: Cubic Stewart platform not centered with the cube center - Jacobian estimated at the cube center ([[./figs/cubic_conf_not_centered_J_center.png][png]], [[./figs/cubic_conf_not_centered_J_center.pdf][pdf]])
|
||||
[[file:figs/cubic_conf_not_centered_J_center.png]]
|
||||
|
||||
#+begin_src matlab :exports results :results value table replace :tangle no
|
||||
data2orgtable(stewart.K, {}, {}, ' %.2g ');
|
||||
#+end_src
|
||||
|
||||
#+RESULTS:
|
||||
| 2 | 0 | -1.5e-16 | 0 | 0.04 | 0 |
|
||||
| 0 | 2 | 0 | -0.04 | 0 | -2.8e-17 |
|
||||
| -1.5e-16 | 0 | 2 | 1.2e-18 | -1e-17 | 0 |
|
||||
| 0 | -0.04 | 1.2e-18 | 0.016 | 0 | 8.7e-19 |
|
||||
| 0.04 | 0 | -6.2e-18 | -1.1e-19 | 0.016 | 8.7e-19 |
|
||||
| -3.7e-19 | -2.5e-17 | 0 | 1.2e-18 | 8.7e-19 | 0.06 |
|
||||
| 2 | 0 | -1.7e-16 | 0 | 0.02 | 0 |
|
||||
| 0 | 2 | 0 | -0.02 | 0 | 2.8e-17 |
|
||||
| -1.7e-16 | 0 | 2 | 1.2e-19 | -1.4e-17 | 1.4e-17 |
|
||||
| 0 | -0.02 | 1.2e-19 | 0.015 | -4.3e-19 | 1.7e-18 |
|
||||
| 0.02 | 0 | -7.3e-18 | -3.3e-21 | 0.015 | 0 |
|
||||
| 6.6e-18 | 2.5e-17 | 0 | 2e-18 | 0 | 0.06 |
|
||||
|
||||
We obtain $k_x = k_y = k_z$ and $k_{\theta_x} = k_{\theta_y}$, but the Stiffness matrix is not diagonal.
|
||||
|
||||
@ -143,26 +188,39 @@ The center height of the Stewart platform is then at $z = \frac{175-75}{2} = 50$
|
||||
The center of the cube from the top platform is at $z = 110 - 175 = -65$.
|
||||
|
||||
#+begin_src matlab
|
||||
stewart = initializeFramesPositions('H', 80e-3, 'MO_B', -30e-3);
|
||||
stewart = initializeFramesPositions('H', 80e-3, 'MO_B', -40e-3);
|
||||
stewart = generateCubicConfiguration(stewart, 'Hc', 100e-3, 'FOc', 50e-3, 'FHa', 0, 'MHb', 0);
|
||||
stewart = computeJointsPose(stewart);
|
||||
stewart = initializeStrutDynamics(stewart, 'Ki', ones(6,1));
|
||||
stewart = computeJacobian(stewart);
|
||||
stewart = initializeCylindricalPlatforms(stewart, 'Fpr', 175e-3, 'Mpr', 150e-3);
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :exports none
|
||||
displayArchitecture(stewart, 'labels', false);
|
||||
scatter3(0, 0, 50e-3, 200, 'kh');
|
||||
#+end_src
|
||||
|
||||
#+header: :tangle no :exports results :results none :noweb yes
|
||||
#+begin_src matlab :var filepath="figs/cubic_conf_not_centered_J_stewart_center.pdf" :var figsize="wide-tall" :post pdf2svg(file=*this*, ext="png")
|
||||
<<plt-matlab>>
|
||||
#+end_src
|
||||
|
||||
#+name: fig:cubic_conf_not_centered_J_stewart_center
|
||||
#+caption: Cubic Stewart platform not centered with the cube center - Jacobian estimated at the Stewart platform center ([[./figs/cubic_conf_not_centered_J_stewart_center.png][png]], [[./figs/cubic_conf_not_centered_J_stewart_center.pdf][pdf]])
|
||||
[[file:figs/cubic_conf_not_centered_J_stewart_center.png]]
|
||||
|
||||
#+begin_src matlab :exports results :results value table replace :tangle no
|
||||
data2orgtable(stewart.K, {}, {}, ' %.2g ');
|
||||
#+end_src
|
||||
|
||||
#+RESULTS:
|
||||
| 2 | 0 | -1.7e-16 | 0 | 4.9e-17 | 0 |
|
||||
| 0 | 2 | 0 | -2.2e-17 | 0 | 2.8e-17 |
|
||||
| -1.7e-16 | 0 | 2 | 1.1e-18 | -1.4e-17 | 1.4e-17 |
|
||||
| 0 | -2.2e-17 | 1.1e-18 | 0.015 | 0 | 3.5e-18 |
|
||||
| 4.4e-17 | 0 | -1.4e-17 | -5.7e-20 | 0.015 | -8.7e-19 |
|
||||
| 6.6e-18 | 2.5e-17 | 0 | 3.5e-18 | -8.7e-19 | 0.06 |
|
||||
|
||||
We obtain $k_x = k_y = k_z$ and $k_{\theta_x} = k_{\theta_y}$, and the Stiffness matrix is diagonal.
|
||||
| 2 | 0 | -1.7e-16 | 0 | 0.02 | 0 |
|
||||
| 0 | 2 | 0 | -0.02 | 0 | 2.8e-17 |
|
||||
| -1.7e-16 | 0 | 2 | 1.2e-19 | -1.4e-17 | 1.4e-17 |
|
||||
| 0 | -0.02 | 1.2e-19 | 0.015 | -4.3e-19 | 1.7e-18 |
|
||||
| 0.02 | 0 | -7.3e-18 | -3.3e-21 | 0.015 | 0 |
|
||||
| 6.6e-18 | 2.5e-17 | 0 | 2e-18 | 0 | 0.06 |
|
||||
|
||||
** Conclusion
|
||||
#+begin_important
|
||||
@ -192,17 +250,22 @@ This is possible, to do so:
|
||||
stewart = initializeStewartPose(stewart);
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :exports none
|
||||
displayArchitecture(stewart, 'labels', false);
|
||||
scatter3(0, 0, 50e-3, 200, 'kh');
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :exports results :results value table replace :tangle no
|
||||
data2orgtable(stewart.K, {}, {}, ' %.2g ');
|
||||
#+end_src
|
||||
|
||||
#+RESULTS:
|
||||
| 2 | 0 | -4.6e-16 | 0 | 4e-17 | 0 |
|
||||
| 0 | 2 | 0 | -4.8e-17 | 0 | -3.5e-17 |
|
||||
| -4.6e-16 | 0 | 2 | 1.5e-20 | 4e-17 | 0 |
|
||||
| 0 | -4.8e-17 | 1.5e-20 | 0.00034 | 6.8e-21 | 4.2e-19 |
|
||||
| 4e-17 | 0 | 4e-17 | -3e-21 | 0.00034 | -2.7e-20 |
|
||||
| -1.7e-19 | -3.6e-17 | 0 | 4.2e-19 | -2.7e-20 | 0.0014 |
|
||||
| 2 | 0 | -3.2e-16 | 0 | 3.1e-16 | 0 |
|
||||
| 0 | 2 | 0 | -1.2e-16 | 0 | 0 |
|
||||
| -3.2e-16 | 0 | 2 | 5e-18 | -5.6e-17 | 0 |
|
||||
| 0 | -1.2e-16 | 5e-18 | 0.14 | 3.5e-18 | 1.4e-17 |
|
||||
| 3e-16 | 0 | -5.4e-17 | 2.1e-19 | 0.14 | -6.9e-18 |
|
||||
| 7.4e-19 | -2.6e-17 | 0 | 1.3e-17 | -6.9e-18 | 0.54 |
|
||||
|
||||
We obtain $k_x = k_y = k_z$ and $k_{\theta_x} = k_{\theta_y}$, but the Stiffness matrix is not diagonal.
|
||||
|
||||
|
||||
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Reference in New Issue
Block a user