Reworked index.org: better filenames
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<title>Cubic configuration for the Stewart Platform</title>
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<meta name="author" content="Thomas Dehaeze" />
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<h2>Table of Contents</h2>
|
||||
<div id="text-table-of-contents">
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||||
<ul>
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||||
<li><a href="#org4a16be2">1. Questions we wish to answer with this analysis</a></li>
|
||||
<li><a href="#org289931f">2. Configuration Analysis - Stiffness Matrix</a>
|
||||
<li><a href="#org86c83bf">1. Questions we wish to answer with this analysis</a></li>
|
||||
<li><a href="#org0b05973">2. <span class="todo TODO">TODO</span> Configuration Analysis - Stiffness Matrix</a>
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||||
<ul>
|
||||
<li><a href="#orgc378f8a">2.1. Cubic Stewart platform centered with the cube center - Jacobian estimated at the cube center</a></li>
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||||
<li><a href="#org608174e">2.2. Cubic Stewart platform centered with the cube center - Jacobian not estimated at the cube center</a></li>
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||||
<li><a href="#orgbd736ef">2.3. Cubic Stewart platform not centered with the cube center - Jacobian estimated at the cube center</a></li>
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||||
<li><a href="#org6fbeda1">2.4. 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="#org18633d3">2.5. Conclusion</a></li>
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||||
<li><a href="#org3f035e8">2.1. Cubic Stewart platform centered with the cube center - Jacobian estimated at the cube center</a></li>
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||||
<li><a href="#org77ecb36">2.2. Cubic Stewart platform centered with the cube center - Jacobian not estimated at the cube center</a></li>
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||||
<li><a href="#org42ea8ad">2.3. Cubic Stewart platform not centered with the cube center - Jacobian estimated at the cube center</a></li>
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||||
<li><a href="#org38870ce">2.4. 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="#org08c7461">2.5. Conclusion</a></li>
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||||
</ul>
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||||
</li>
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||||
<li><a href="#orgf0ba2d0">3. Cubic size analysis</a></li>
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||||
<li><a href="#org97dffbc">4. initializeCubicConfiguration</a>
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||||
<li><a href="#orgc4c2abd">3. <span class="todo TODO">TODO</span> Cubic size analysis</a></li>
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||||
<li><a href="#org36a27e6">4. <span class="todo TODO">TODO</span> initializeCubicConfiguration</a>
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<ul>
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<li><a href="#org4eb8b23">4.1. Function description</a></li>
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||||
<li><a href="#orga42cb17">4.2. Optional Parameters</a></li>
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<li><a href="#orgc281f60">4.3. Cube Creation</a></li>
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||||
<li><a href="#orgfed01f0">4.4. Vectors of each leg</a></li>
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<li><a href="#org21db1ef">4.5. Verification of Height of the Stewart Platform</a></li>
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<li><a href="#org9578c3c">4.6. Determinate the location of the joints</a></li>
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<li><a href="#org71c9d4e">4.7. Returns Stewart Structure</a></li>
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<li><a href="#orgf299c5c">4.1. Function description</a></li>
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<li><a href="#org46c8589">4.2. Optional Parameters</a></li>
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||||
<li><a href="#orgd8d9b14">4.3. Cube Creation</a></li>
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||||
<li><a href="#org181d1d8">4.4. Vectors of each leg</a></li>
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||||
<li><a href="#orgb396e98">4.5. Verification of Height of the Stewart Platform</a></li>
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||||
<li><a href="#orgf38af83">4.6. Determinate the location of the joints</a></li>
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||||
<li><a href="#orgdf9e3cf">4.7. Returns Stewart Structure</a></li>
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||||
</ul>
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||||
</li>
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||||
<li><a href="#orgb2d1742">5. Tests</a>
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||||
<li><a href="#orgf8fb731">5. <span class="todo TODO">TODO</span> Tests</a>
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||||
<ul>
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||||
<li><a href="#org6e933c9">5.1. First attempt to parametrisation</a></li>
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<li><a href="#org60486ce">5.2. Second attempt</a></li>
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||||
<li><a href="#orge571873">5.3. Generate the Stewart platform for a Cubic configuration</a></li>
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||||
<li><a href="#org4434fe5">5.1. First attempt to parametrisation</a></li>
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||||
<li><a href="#org723e6eb">5.2. Second attempt</a></li>
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<li><a href="#orgcc173ac">5.3. Generate the Stewart platform for a Cubic configuration</a></li>
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</ul>
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||||
</li>
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||||
</ul>
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@@ -326,15 +331,15 @@ The specificity of the Cubic configuration is that each actuator is orthogonal w
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</p>
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<p>
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To generate and study the Cubic configuration, <code>initializeCubicConfiguration</code> is used (description in section <a href="#org38614bc">4</a>).
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||||
To generate and study the Cubic configuration, <code>initializeCubicConfiguration</code> is used (description in section <a href="#org8b1f609">4</a>).
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</p>
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<p>
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According to <a class='org-ref-reference' href="#preumont07_six_axis_singl_stage_activ">preumont07_six_axis_singl_stage_activ</a>, the cubic configuration provides a uniform stiffness in all directions and <b>minimizes the crosscoupling</b> from actuator to sensor of different legs (being orthogonal to each other).
|
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</p>
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||||
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||||
<div id="outline-container-org4a16be2" class="outline-2">
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||||
<h2 id="org4a16be2"><span class="section-number-2">1</span> Questions we wish to answer with this analysis</h2>
|
||||
<div id="outline-container-org86c83bf" class="outline-2">
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||||
<h2 id="org86c83bf"><span class="section-number-2">1</span> Questions we wish to answer with this analysis</h2>
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||||
<div class="outline-text-2" id="text-1">
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||||
<p>
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||||
The goal is to study the benefits of using a cubic configuration:
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||||
@@ -347,40 +352,40 @@ The goal is to study the benefits of using a cubic configuration:
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||||
</div>
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||||
</div>
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||||
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||||
<div id="outline-container-org289931f" class="outline-2">
|
||||
<h2 id="org289931f"><span class="section-number-2">2</span> Configuration Analysis - Stiffness Matrix</h2>
|
||||
<div id="outline-container-org0b05973" class="outline-2">
|
||||
<h2 id="org0b05973"><span class="section-number-2">2</span> <span class="todo TODO">TODO</span> Configuration Analysis - Stiffness Matrix</h2>
|
||||
<div class="outline-text-2" id="text-2">
|
||||
</div>
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||||
<div id="outline-container-orgc378f8a" class="outline-3">
|
||||
<h3 id="orgc378f8a"><span class="section-number-3">2.1</span> Cubic Stewart platform centered with the cube center - Jacobian estimated at the cube center</h3>
|
||||
<div id="outline-container-org3f035e8" class="outline-3">
|
||||
<h3 id="org3f035e8"><span class="section-number-3">2.1</span> Cubic Stewart platform centered with the cube center - Jacobian estimated at the cube center</h3>
|
||||
<div class="outline-text-3" id="text-2-1">
|
||||
<p>
|
||||
We create a cubic Stewart platform (figure <a href="#org8e23773">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="#org1effc0f">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).
|
||||
The Jacobian matrix is estimated at the location of the center of the cube.
|
||||
</p>
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||||
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||||
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||||
<div id="org8e23773" class="figure">
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||||
<div id="org1effc0f" 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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||||
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||||
<div class="org-src-container">
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||||
<pre class="src src-matlab">opts = struct<span class="org-rainbow-delimiters-depth-1">(</span>...
|
||||
<span class="org-string">'H_tot'</span>, <span class="org-highlight-numbers-number">100</span>, ...<span class="org-comment"> % Total height of the Hexapod [mm]</span>
|
||||
<span class="org-string">'L'</span>, <span class="org-highlight-numbers-number">200</span><span class="org-type">/</span>sqrt<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, ...<span class="org-comment"> % Size of the Cube [mm]</span>
|
||||
<span class="org-string">'H'</span>, <span class="org-highlight-numbers-number">60</span>, ...<span class="org-comment"> % Height between base joints and platform joints [mm]</span>
|
||||
<span class="org-string">'H0'</span>, <span class="org-highlight-numbers-number">200</span><span class="org-type">/</span><span class="org-highlight-numbers-number">2</span><span class="org-type">-</span><span class="org-highlight-numbers-number">60</span><span class="org-type">/</span><span class="org-highlight-numbers-number">2</span> ...<span class="org-comment"> % Height between the corner of the cube and the plane containing the base joints [mm]</span>
|
||||
<span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
stewart = initializeCubicConfiguration<span class="org-rainbow-delimiters-depth-1">(</span>opts<span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
opts = struct<span class="org-rainbow-delimiters-depth-1">(</span>...
|
||||
<span class="org-string">'Jd_pos'</span>, <span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">0</span>, <span class="org-type">-</span><span class="org-highlight-numbers-number">50</span><span class="org-rainbow-delimiters-depth-2">]</span>, ...<span class="org-comment"> % Position of the Jacobian for displacement estimation from the top of the mobile platform [mm]</span>
|
||||
<span class="org-string">'Jf_pos'</span>, <span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">0</span>, <span class="org-type">-</span><span class="org-highlight-numbers-number">50</span><span class="org-rainbow-delimiters-depth-2">]</span> ...<span class="org-comment"> % Position of the Jacobian for force location from the top of the mobile platform [mm]</span>
|
||||
<span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
stewart = computeGeometricalProperties<span class="org-rainbow-delimiters-depth-1">(</span>stewart, opts<span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
<pre class="src src-matlab">opts = struct(...
|
||||
<span class="org-string">'H_tot'</span>, 100, ...<span class="org-comment"> % Total height of the Hexapod [mm]</span>
|
||||
<span class="org-string">'L'</span>, 200<span class="org-type">/</span>sqrt(3), ...<span class="org-comment"> % Size of the Cube [mm]</span>
|
||||
<span class="org-string">'H'</span>, 60, ...<span class="org-comment"> % Height between base joints and platform joints [mm]</span>
|
||||
<span class="org-string">'H0'</span>, 200<span class="org-type">/</span>2<span class="org-type">-</span>60<span class="org-type">/</span>2 ...<span class="org-comment"> % Height between the corner of the cube and the plane containing the base joints [mm]</span>
|
||||
);
|
||||
stewart = initializeCubicConfiguration(opts);
|
||||
opts = struct(...
|
||||
<span class="org-string">'Jd_pos'</span>, [0, 0, <span class="org-type">-</span>50], ...<span class="org-comment"> % Position of the Jacobian for displacement estimation from the top of the mobile platform [mm]</span>
|
||||
<span class="org-string">'Jf_pos'</span>, [0, 0, <span class="org-type">-</span>50] ...<span class="org-comment"> % Position of the Jacobian for force location from the top of the mobile platform [mm]</span>
|
||||
);
|
||||
stewart = computeGeometricalProperties(stewart, opts);
|
||||
|
||||
save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./mat/stewart.mat'</span>, <span class="org-string">'stewart'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
save(<span class="org-string">'./mat/stewart.mat'</span>, <span class="org-string">'stewart'</span>);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -464,27 +469,27 @@ save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org608174e" class="outline-3">
|
||||
<h3 id="org608174e"><span class="section-number-3">2.2</span> Cubic Stewart platform centered with the cube center - Jacobian not estimated at the cube center</h3>
|
||||
<div id="outline-container-org77ecb36" class="outline-3">
|
||||
<h3 id="org77ecb36"><span class="section-number-3">2.2</span> Cubic Stewart platform centered with the cube center - Jacobian not estimated at the cube center</h3>
|
||||
<div class="outline-text-3" id="text-2-2">
|
||||
<p>
|
||||
We create a cubic Stewart platform with center of the cube located at the center of the Stewart platform (figure <a href="#org8e23773">1</a>).
|
||||
We create a cubic Stewart platform with center of the cube located at the center of the Stewart platform (figure <a href="#org1effc0f">1</a>).
|
||||
The Jacobian matrix is not estimated at the location of the center of the cube.
|
||||
</p>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">opts = struct<span class="org-rainbow-delimiters-depth-1">(</span>...
|
||||
<span class="org-string">'H_tot'</span>, <span class="org-highlight-numbers-number">100</span>, ...<span class="org-comment"> % Total height of the Hexapod [mm]</span>
|
||||
<span class="org-string">'L'</span>, <span class="org-highlight-numbers-number">200</span><span class="org-type">/</span>sqrt<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, ...<span class="org-comment"> % Size of the Cube [mm]</span>
|
||||
<span class="org-string">'H'</span>, <span class="org-highlight-numbers-number">60</span>, ...<span class="org-comment"> % Height between base joints and platform joints [mm]</span>
|
||||
<span class="org-string">'H0'</span>, <span class="org-highlight-numbers-number">200</span><span class="org-type">/</span><span class="org-highlight-numbers-number">2</span><span class="org-type">-</span><span class="org-highlight-numbers-number">60</span><span class="org-type">/</span><span class="org-highlight-numbers-number">2</span> ...<span class="org-comment"> % Height between the corner of the cube and the plane containing the base joints [mm]</span>
|
||||
<span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
stewart = initializeCubicConfiguration<span class="org-rainbow-delimiters-depth-1">(</span>opts<span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
opts = struct<span class="org-rainbow-delimiters-depth-1">(</span>...
|
||||
<span class="org-string">'Jd_pos'</span>, <span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">0</span><span class="org-rainbow-delimiters-depth-2">]</span>, ...<span class="org-comment"> % Position of the Jacobian for displacement estimation from the top of the mobile platform [mm]</span>
|
||||
<span class="org-string">'Jf_pos'</span>, <span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">0</span><span class="org-rainbow-delimiters-depth-2">]</span> ...<span class="org-comment"> % Position of the Jacobian for force location from the top of the mobile platform [mm]</span>
|
||||
<span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
stewart = computeGeometricalProperties<span class="org-rainbow-delimiters-depth-1">(</span>stewart, opts<span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
<pre class="src src-matlab">opts = struct(...
|
||||
<span class="org-string">'H_tot'</span>, 100, ...<span class="org-comment"> % Total height of the Hexapod [mm]</span>
|
||||
<span class="org-string">'L'</span>, 200<span class="org-type">/</span>sqrt(3), ...<span class="org-comment"> % Size of the Cube [mm]</span>
|
||||
<span class="org-string">'H'</span>, 60, ...<span class="org-comment"> % Height between base joints and platform joints [mm]</span>
|
||||
<span class="org-string">'H0'</span>, 200<span class="org-type">/</span>2<span class="org-type">-</span>60<span class="org-type">/</span>2 ...<span class="org-comment"> % Height between the corner of the cube and the plane containing the base joints [mm]</span>
|
||||
);
|
||||
stewart = initializeCubicConfiguration(opts);
|
||||
opts = struct(...
|
||||
<span class="org-string">'Jd_pos'</span>, [0, 0, 0], ...<span class="org-comment"> % Position of the Jacobian for displacement estimation from the top of the mobile platform [mm]</span>
|
||||
<span class="org-string">'Jf_pos'</span>, [0, 0, 0] ...<span class="org-comment"> % Position of the Jacobian for force location from the top of the mobile platform [mm]</span>
|
||||
);
|
||||
stewart = computeGeometricalProperties(stewart, opts);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -568,16 +573,16 @@ stewart = computeGeometricalProperties<span class="org-rainbow-delimiters-depth-
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgbd736ef" class="outline-3">
|
||||
<h3 id="orgbd736ef"><span class="section-number-3">2.3</span> Cubic Stewart platform not centered with the cube center - Jacobian estimated at the cube center</h3>
|
||||
<div id="outline-container-org42ea8ad" class="outline-3">
|
||||
<h3 id="org42ea8ad"><span class="section-number-3">2.3</span> Cubic Stewart platform not centered with the cube center - Jacobian estimated at the cube center</h3>
|
||||
<div class="outline-text-3" id="text-2-3">
|
||||
<p>
|
||||
Here, the "center" of the Stewart platform is not at the cube center (figure <a href="#org3982eac">2</a>).
|
||||
Here, the “center” of the Stewart platform is not at the cube center (figure <a href="#org3f10bc2">2</a>).
|
||||
The Jacobian is estimated at the cube center.
|
||||
</p>
|
||||
|
||||
|
||||
<div id="org3982eac" class="figure">
|
||||
<div id="org3f10bc2" class="figure">
|
||||
<p><img src="./figs/3d-cubic-stewart-misaligned.png" alt="3d-cubic-stewart-misaligned.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 2: </span>Not centered cubic configuration</p>
|
||||
@@ -591,18 +596,18 @@ The center of the cube from the top platform is at \(z = 110 - 175 = -65\).
|
||||
</p>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">opts = struct<span class="org-rainbow-delimiters-depth-1">(</span>...
|
||||
<span class="org-string">'H_tot'</span>, <span class="org-highlight-numbers-number">100</span>, ...<span class="org-comment"> % Total height of the Hexapod [mm]</span>
|
||||
<span class="org-string">'L'</span>, <span class="org-highlight-numbers-number">220</span><span class="org-type">/</span>sqrt<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, ...<span class="org-comment"> % Size of the Cube [mm]</span>
|
||||
<span class="org-string">'H'</span>, <span class="org-highlight-numbers-number">60</span>, ...<span class="org-comment"> % Height between base joints and platform joints [mm]</span>
|
||||
<span class="org-string">'H0'</span>, <span class="org-highlight-numbers-number">75</span> ...<span class="org-comment"> % Height between the corner of the cube and the plane containing the base joints [mm]</span>
|
||||
<span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
stewart = initializeCubicConfiguration<span class="org-rainbow-delimiters-depth-1">(</span>opts<span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
opts = struct<span class="org-rainbow-delimiters-depth-1">(</span>...
|
||||
<span class="org-string">'Jd_pos'</span>, <span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">0</span>, <span class="org-type">-</span><span class="org-highlight-numbers-number">65</span><span class="org-rainbow-delimiters-depth-2">]</span>, ...<span class="org-comment"> % Position of the Jacobian for displacement estimation from the top of the mobile platform [mm]</span>
|
||||
<span class="org-string">'Jf_pos'</span>, <span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">0</span>, <span class="org-type">-</span><span class="org-highlight-numbers-number">65</span><span class="org-rainbow-delimiters-depth-2">]</span> ...<span class="org-comment"> % Position of the Jacobian for force location from the top of the mobile platform [mm]</span>
|
||||
<span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
stewart = computeGeometricalProperties<span class="org-rainbow-delimiters-depth-1">(</span>stewart, opts<span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
<pre class="src src-matlab">opts = struct(...
|
||||
<span class="org-string">'H_tot'</span>, 100, ...<span class="org-comment"> % Total height of the Hexapod [mm]</span>
|
||||
<span class="org-string">'L'</span>, 220<span class="org-type">/</span>sqrt(3), ...<span class="org-comment"> % Size of the Cube [mm]</span>
|
||||
<span class="org-string">'H'</span>, 60, ...<span class="org-comment"> % Height between base joints and platform joints [mm]</span>
|
||||
<span class="org-string">'H0'</span>, 75 ...<span class="org-comment"> % Height between the corner of the cube and the plane containing the base joints [mm]</span>
|
||||
);
|
||||
stewart = initializeCubicConfiguration(opts);
|
||||
opts = struct(...
|
||||
<span class="org-string">'Jd_pos'</span>, [0, 0, <span class="org-type">-</span>65], ...<span class="org-comment"> % Position of the Jacobian for displacement estimation from the top of the mobile platform [mm]</span>
|
||||
<span class="org-string">'Jf_pos'</span>, [0, 0, <span class="org-type">-</span>65] ...<span class="org-comment"> % Position of the Jacobian for force location from the top of the mobile platform [mm]</span>
|
||||
);
|
||||
stewart = computeGeometricalProperties(stewart, opts);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -690,11 +695,11 @@ We obtain \(k_x = k_y = k_z\) and \(k_{\theta_x} = k_{\theta_y}\), but the Stiff
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org6fbeda1" class="outline-3">
|
||||
<h3 id="org6fbeda1"><span class="section-number-3">2.4</span> Cubic Stewart platform not centered with the cube center - Jacobian estimated at the Stewart platform center</h3>
|
||||
<div id="outline-container-org38870ce" class="outline-3">
|
||||
<h3 id="org38870ce"><span class="section-number-3">2.4</span> Cubic Stewart platform not centered with the cube center - Jacobian estimated at the Stewart platform center</h3>
|
||||
<div class="outline-text-3" id="text-2-4">
|
||||
<p>
|
||||
Here, the "center" of the Stewart platform is not at the cube center.
|
||||
Here, the “center” of the Stewart platform is not at the cube center.
|
||||
The Jacobian is estimated at the center of the Stewart platform.
|
||||
</p>
|
||||
|
||||
@@ -706,18 +711,18 @@ The center of the cube from the top platform is at \(z = 110 - 175 = -65\).
|
||||
</p>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">opts = struct<span class="org-rainbow-delimiters-depth-1">(</span>...
|
||||
<span class="org-string">'H_tot'</span>, <span class="org-highlight-numbers-number">100</span>, ...<span class="org-comment"> % Total height of the Hexapod [mm]</span>
|
||||
<span class="org-string">'L'</span>, <span class="org-highlight-numbers-number">220</span><span class="org-type">/</span>sqrt<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, ...<span class="org-comment"> % Size of the Cube [mm]</span>
|
||||
<span class="org-string">'H'</span>, <span class="org-highlight-numbers-number">60</span>, ...<span class="org-comment"> % Height between base joints and platform joints [mm]</span>
|
||||
<span class="org-string">'H0'</span>, <span class="org-highlight-numbers-number">75</span> ...<span class="org-comment"> % Height between the corner of the cube and the plane containing the base joints [mm]</span>
|
||||
<span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
stewart = initializeCubicConfiguration<span class="org-rainbow-delimiters-depth-1">(</span>opts<span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
opts = struct<span class="org-rainbow-delimiters-depth-1">(</span>...
|
||||
<span class="org-string">'Jd_pos'</span>, <span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">0</span>, <span class="org-type">-</span><span class="org-highlight-numbers-number">60</span><span class="org-rainbow-delimiters-depth-2">]</span>, ...<span class="org-comment"> % Position of the Jacobian for displacement estimation from the top of the mobile platform [mm]</span>
|
||||
<span class="org-string">'Jf_pos'</span>, <span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">0</span>, <span class="org-type">-</span><span class="org-highlight-numbers-number">60</span><span class="org-rainbow-delimiters-depth-2">]</span> ...<span class="org-comment"> % Position of the Jacobian for force location from the top of the mobile platform [mm]</span>
|
||||
<span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
stewart = computeGeometricalProperties<span class="org-rainbow-delimiters-depth-1">(</span>stewart, opts<span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
<pre class="src src-matlab">opts = struct(...
|
||||
<span class="org-string">'H_tot'</span>, 100, ...<span class="org-comment"> % Total height of the Hexapod [mm]</span>
|
||||
<span class="org-string">'L'</span>, 220<span class="org-type">/</span>sqrt(3), ...<span class="org-comment"> % Size of the Cube [mm]</span>
|
||||
<span class="org-string">'H'</span>, 60, ...<span class="org-comment"> % Height between base joints and platform joints [mm]</span>
|
||||
<span class="org-string">'H0'</span>, 75 ...<span class="org-comment"> % Height between the corner of the cube and the plane containing the base joints [mm]</span>
|
||||
);
|
||||
stewart = initializeCubicConfiguration(opts);
|
||||
opts = struct(...
|
||||
<span class="org-string">'Jd_pos'</span>, [0, 0, <span class="org-type">-</span>60], ...<span class="org-comment"> % Position of the Jacobian for displacement estimation from the top of the mobile platform [mm]</span>
|
||||
<span class="org-string">'Jf_pos'</span>, [0, 0, <span class="org-type">-</span>60] ...<span class="org-comment"> % Position of the Jacobian for force location from the top of the mobile platform [mm]</span>
|
||||
);
|
||||
stewart = computeGeometricalProperties(stewart, opts);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -805,8 +810,8 @@ We obtain \(k_x = k_y = k_z\) and \(k_{\theta_x} = k_{\theta_y}\), but the Stiff
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org18633d3" class="outline-3">
|
||||
<h3 id="org18633d3"><span class="section-number-3">2.5</span> Conclusion</h3>
|
||||
<div id="outline-container-org08c7461" class="outline-3">
|
||||
<h3 id="org08c7461"><span class="section-number-3">2.5</span> Conclusion</h3>
|
||||
<div class="outline-text-3" id="text-2-5">
|
||||
<div class="important">
|
||||
<ul class="org-ul">
|
||||
@@ -819,8 +824,8 @@ We obtain \(k_x = k_y = k_z\) and \(k_{\theta_x} = k_{\theta_y}\), but the Stiff
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgf0ba2d0" class="outline-2">
|
||||
<h2 id="orgf0ba2d0"><span class="section-number-2">3</span> Cubic size analysis</h2>
|
||||
<div id="outline-container-orgc4c2abd" class="outline-2">
|
||||
<h2 id="orgc4c2abd"><span class="section-number-2">3</span> <span class="todo TODO">TODO</span> Cubic size analysis</h2>
|
||||
<div class="outline-text-2" id="text-3">
|
||||
<p>
|
||||
We here study the effect of the size of the cube used for the Stewart configuration.
|
||||
@@ -835,31 +840,31 @@ We only vary the size of the cube.
|
||||
</p>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">H_cubes = <span class="org-highlight-numbers-number">250</span><span class="org-type">:</span><span class="org-highlight-numbers-number">20</span><span class="org-type">:</span><span class="org-highlight-numbers-number">350</span>;
|
||||
stewarts = <span class="org-rainbow-delimiters-depth-1">{</span>zeros<span class="org-rainbow-delimiters-depth-2">(</span>length<span class="org-rainbow-delimiters-depth-3">(</span>H_cubes<span class="org-rainbow-delimiters-depth-3">)</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">}</span>;
|
||||
<pre class="src src-matlab">H_cubes = 250<span class="org-type">:</span>20<span class="org-type">:</span>350;
|
||||
stewarts = {zeros(length(H_cubes), 1)};
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"><span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant"><span class="org-highlight-numbers-number">1</span></span><span class="org-constant">:length</span><span class="org-constant"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-constant">H_cubes</span><span class="org-constant"><span class="org-rainbow-delimiters-depth-1">)</span></span>
|
||||
H_cube = H_cubes<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-constant">i</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
H_tot = <span class="org-highlight-numbers-number">100</span>;
|
||||
H = <span class="org-highlight-numbers-number">80</span>;
|
||||
<pre class="src src-matlab"><span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant">1:length(H_cubes)</span>
|
||||
H_cube = H_cubes(<span class="org-constant">i</span>);
|
||||
H_tot = 100;
|
||||
H = 80;
|
||||
|
||||
opts = struct<span class="org-rainbow-delimiters-depth-1">(</span>...
|
||||
opts = struct(...
|
||||
<span class="org-string">'H_tot'</span>, H_tot, ...<span class="org-comment"> % Total height of the Hexapod [mm]</span>
|
||||
<span class="org-string">'L'</span>, H_cube<span class="org-type">/</span>sqrt<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, ...<span class="org-comment"> % Size of the Cube [mm]</span>
|
||||
<span class="org-string">'L'</span>, H_cube<span class="org-type">/</span>sqrt(3), ...<span class="org-comment"> % Size of the Cube [mm]</span>
|
||||
<span class="org-string">'H'</span>, H, ...<span class="org-comment"> % Height between base joints and platform joints [mm]</span>
|
||||
<span class="org-string">'H0'</span>, H_cube<span class="org-type">/</span><span class="org-highlight-numbers-number">2</span><span class="org-type">-</span>H<span class="org-type">/</span><span class="org-highlight-numbers-number">2</span> ...<span class="org-comment"> % Height between the corner of the cube and the plane containing the base joints [mm]</span>
|
||||
<span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
stewart = initializeCubicConfiguration<span class="org-rainbow-delimiters-depth-1">(</span>opts<span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
<span class="org-string">'H0'</span>, H_cube<span class="org-type">/</span>2<span class="org-type">-</span>H<span class="org-type">/</span>2 ...<span class="org-comment"> % Height between the corner of the cube and the plane containing the base joints [mm]</span>
|
||||
);
|
||||
stewart = initializeCubicConfiguration(opts);
|
||||
|
||||
opts = struct<span class="org-rainbow-delimiters-depth-1">(</span>...
|
||||
<span class="org-string">'Jd_pos'</span>, <span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">0</span>, H_cube<span class="org-type">/</span><span class="org-highlight-numbers-number">2</span><span class="org-type">-</span>opts.H0<span class="org-type">-</span>opts.H_tot<span class="org-rainbow-delimiters-depth-2">]</span>, ...<span class="org-comment"> % Position of the Jacobian for displacement estimation from the top of the mobile platform [mm]</span>
|
||||
<span class="org-string">'Jf_pos'</span>, <span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">0</span>, H_cube<span class="org-type">/</span><span class="org-highlight-numbers-number">2</span><span class="org-type">-</span>opts.H0<span class="org-type">-</span>opts.H_tot<span class="org-rainbow-delimiters-depth-2">]</span> ...<span class="org-comment"> % Position of the Jacobian for force location from the top of the mobile platform [mm]</span>
|
||||
<span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
stewart = computeGeometricalProperties<span class="org-rainbow-delimiters-depth-1">(</span>stewart, opts<span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
stewarts<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-constant">i</span><span class="org-rainbow-delimiters-depth-1">)</span> = <span class="org-rainbow-delimiters-depth-1">{</span>stewart<span class="org-rainbow-delimiters-depth-1">}</span>;
|
||||
opts = struct(...
|
||||
<span class="org-string">'Jd_pos'</span>, [0, 0, H_cube<span class="org-type">/</span>2<span class="org-type">-</span>opts.H0<span class="org-type">-</span>opts.H_tot], ...<span class="org-comment"> % Position of the Jacobian for displacement estimation from the top of the mobile platform [mm]</span>
|
||||
<span class="org-string">'Jf_pos'</span>, [0, 0, H_cube<span class="org-type">/</span>2<span class="org-type">-</span>opts.H0<span class="org-type">-</span>opts.H_tot] ...<span class="org-comment"> % Position of the Jacobian for force location from the top of the mobile platform [mm]</span>
|
||||
);
|
||||
stewart = computeGeometricalProperties(stewart, opts);
|
||||
stewarts(<span class="org-constant">i</span>) = {stewart};
|
||||
<span class="org-keyword">end</span>
|
||||
</pre>
|
||||
</div>
|
||||
@@ -869,9 +874,9 @@ stewarts = <span class="org-rainbow-delimiters-depth-1">{</span>zeros<span class
|
||||
The Stiffness matrix is computed for all generated Stewart platforms.
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">Ks = zeros<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">6</span>, <span class="org-highlight-numbers-number">6</span>, length<span class="org-rainbow-delimiters-depth-2">(</span>H_cube<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
<span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant"><span class="org-highlight-numbers-number">1</span></span><span class="org-constant">:length</span><span class="org-constant"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-constant">H_cubes</span><span class="org-constant"><span class="org-rainbow-delimiters-depth-1">)</span></span>
|
||||
Ks<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-type">:</span>, <span class="org-constant">i</span><span class="org-rainbow-delimiters-depth-1">)</span> = stewarts<span class="org-rainbow-delimiters-depth-1">{</span><span class="org-constant">i</span><span class="org-rainbow-delimiters-depth-1">}</span>.Jd<span class="org-type">'*</span>stewarts<span class="org-rainbow-delimiters-depth-1">{</span><span class="org-constant">i</span><span class="org-rainbow-delimiters-depth-1">}</span>.Jd;
|
||||
<pre class="src src-matlab">Ks = zeros(6, 6, length(H_cube));
|
||||
<span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant">1:length(H_cubes)</span>
|
||||
Ks(<span class="org-type">:</span>, <span class="org-type">:</span>, <span class="org-constant">i</span>) = stewarts{<span class="org-constant">i</span>}.Jd<span class="org-type">'*</span>stewarts{<span class="org-constant">i</span>}.Jd;
|
||||
<span class="org-keyword">end</span>
|
||||
</pre>
|
||||
</div>
|
||||
@@ -886,16 +891,16 @@ Finally, we plot \(k_{\theta_x} = k_{\theta_y}\) and \(k_{\theta_z}\)
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
||||
hold on;
|
||||
plot<span class="org-rainbow-delimiters-depth-1">(</span>H_cubes, squeeze<span class="org-rainbow-delimiters-depth-2">(</span>Ks<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">4</span>, <span class="org-highlight-numbers-number">4</span>, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, <span class="org-string">'$k_</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">{</span></span><span class="org-string">\theta_x</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">}</span></span><span class="org-string">$'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
plot<span class="org-rainbow-delimiters-depth-1">(</span>H_cubes, squeeze<span class="org-rainbow-delimiters-depth-2">(</span>Ks<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">6</span>, <span class="org-highlight-numbers-number">6</span>, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, <span class="org-string">'$k_</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">{</span></span><span class="org-string">\theta_z</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">}</span></span><span class="org-string">$'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
plot(H_cubes, squeeze(Ks(4, 4, <span class="org-type">:</span>)), <span class="org-string">'DisplayName'</span>, <span class="org-string">'$k_{\theta_x}$'</span>);
|
||||
plot(H_cubes, squeeze(Ks(6, 6, <span class="org-type">:</span>)), <span class="org-string">'DisplayName'</span>, <span class="org-string">'$k_{\theta_z}$'</span>);
|
||||
hold off;
|
||||
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'location'</span>, <span class="org-string">'northwest'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Cube Size </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">mm</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; ylabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Rotational stiffnes </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">normalized</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
legend(<span class="org-string">'location'</span>, <span class="org-string">'northwest'</span>);
|
||||
xlabel(<span class="org-string">'Cube Size [mm]'</span>); ylabel(<span class="org-string">'Rotational stiffnes [normalized]'</span>);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org7d4f005" class="figure">
|
||||
<div id="org659a01f" class="figure">
|
||||
<p><img src="figs/stiffness_cube_size.png" alt="stiffness_cube_size.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 3: </span>\(k_{\theta_x} = k_{\theta_y}\) and \(k_{\theta_z}\) function of the size of the cube</p>
|
||||
@@ -916,37 +921,37 @@ In that case, the legs will the further separated. Size of the cube is then limi
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org97dffbc" class="outline-2">
|
||||
<h2 id="org97dffbc"><span class="section-number-2">4</span> initializeCubicConfiguration</h2>
|
||||
<div id="outline-container-org36a27e6" class="outline-2">
|
||||
<h2 id="org36a27e6"><span class="section-number-2">4</span> <span class="todo TODO">TODO</span> initializeCubicConfiguration</h2>
|
||||
<div class="outline-text-2" id="text-4">
|
||||
<p>
|
||||
<a id="org38614bc"></a>
|
||||
<a id="org8b1f609"></a>
|
||||
</p>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org4eb8b23" class="outline-3">
|
||||
<h3 id="org4eb8b23"><span class="section-number-3">4.1</span> Function description</h3>
|
||||
<div id="outline-container-orgf299c5c" class="outline-3">
|
||||
<h3 id="orgf299c5c"><span class="section-number-3">4.1</span> Function description</h3>
|
||||
<div class="outline-text-3" id="text-4-1">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name"><span class="org-rainbow-delimiters-depth-1">[</span></span><span class="org-variable-name">stewart</span><span class="org-variable-name"><span class="org-rainbow-delimiters-depth-1">]</span></span> = <span class="org-function-name">initializeCubicConfiguration</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">opts_param</span><span class="org-rainbow-delimiters-depth-1">)</span>
|
||||
<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name">[stewart]</span> = <span class="org-function-name">initializeCubicConfiguration</span>(<span class="org-variable-name">opts_param</span>)
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orga42cb17" class="outline-3">
|
||||
<h3 id="orga42cb17"><span class="section-number-3">4.2</span> Optional Parameters</h3>
|
||||
<div id="outline-container-org46c8589" class="outline-3">
|
||||
<h3 id="org46c8589"><span class="section-number-3">4.2</span> Optional Parameters</h3>
|
||||
<div class="outline-text-3" id="text-4-2">
|
||||
<p>
|
||||
Default values for opts.
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">opts = struct<span class="org-rainbow-delimiters-depth-1">(</span>...
|
||||
<span class="org-string">'H_tot'</span>, <span class="org-highlight-numbers-number">90</span>, ...<span class="org-comment"> % Total height of the Hexapod [mm]</span>
|
||||
<span class="org-string">'L'</span>, <span class="org-highlight-numbers-number">110</span>, ...<span class="org-comment"> % Size of the Cube [mm]</span>
|
||||
<span class="org-string">'H'</span>, <span class="org-highlight-numbers-number">40</span>, ...<span class="org-comment"> % Height between base joints and platform joints [mm]</span>
|
||||
<span class="org-string">'H0'</span>, <span class="org-highlight-numbers-number">75</span> ...<span class="org-comment"> % Height between the corner of the cube and the plane containing the base joints [mm]</span>
|
||||
<span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
<pre class="src src-matlab">opts = struct(...
|
||||
<span class="org-string">'H_tot'</span>, 90, ...<span class="org-comment"> % Total height of the Hexapod [mm]</span>
|
||||
<span class="org-string">'L'</span>, 110, ...<span class="org-comment"> % Size of the Cube [mm]</span>
|
||||
<span class="org-string">'H'</span>, 40, ...<span class="org-comment"> % Height between base joints and platform joints [mm]</span>
|
||||
<span class="org-string">'H0'</span>, 75 ...<span class="org-comment"> % Height between the corner of the cube and the plane containing the base joints [mm]</span>
|
||||
);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -954,9 +959,9 @@ Default values for opts.
|
||||
Populate opts with input parameters
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"><span class="org-keyword">if</span> exist<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'opts_param'</span>,<span class="org-string">'var'</span><span class="org-rainbow-delimiters-depth-1">)</span>
|
||||
<span class="org-keyword">for</span> <span class="org-variable-name">opt</span> = <span class="org-constant">fieldnames</span><span class="org-constant"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-constant">opts_param</span><span class="org-constant"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-constant">'</span>
|
||||
opts.<span class="org-rainbow-delimiters-depth-1">(</span>opt<span class="org-rainbow-delimiters-depth-2">{</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">}</span><span class="org-rainbow-delimiters-depth-1">)</span> = opts_param.<span class="org-rainbow-delimiters-depth-1">(</span>opt<span class="org-rainbow-delimiters-depth-2">{</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">}</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
<pre class="src src-matlab"><span class="org-keyword">if</span> exist(<span class="org-string">'opts_param'</span>,<span class="org-string">'var'</span>)
|
||||
<span class="org-keyword">for</span> <span class="org-variable-name">opt</span> = <span class="org-constant">fieldnames(opts_param)'</span>
|
||||
opts.(opt{1}) = opts_param.(opt{1});
|
||||
<span class="org-keyword">end</span>
|
||||
<span class="org-keyword">end</span>
|
||||
</pre>
|
||||
@@ -964,18 +969,18 @@ Populate opts with input parameters
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgc281f60" class="outline-3">
|
||||
<h3 id="orgc281f60"><span class="section-number-3">4.3</span> Cube Creation</h3>
|
||||
<div id="outline-container-orgd8d9b14" class="outline-3">
|
||||
<h3 id="orgd8d9b14"><span class="section-number-3">4.3</span> Cube Creation</h3>
|
||||
<div class="outline-text-3" id="text-4-3">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">points = <span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">0</span>; ...
|
||||
<span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">1</span>; ...
|
||||
<span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">0</span>; ...
|
||||
<span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">1</span>; ...
|
||||
<span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">0</span>; ...
|
||||
<span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">1</span>; ...
|
||||
<span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">0</span>; ...
|
||||
<span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">]</span>;
|
||||
<pre class="src src-matlab">points = [0, 0, 0; ...
|
||||
0, 0, 1; ...
|
||||
0, 1, 0; ...
|
||||
0, 1, 1; ...
|
||||
1, 0, 0; ...
|
||||
1, 0, 1; ...
|
||||
1, 1, 0; ...
|
||||
1, 1, 1];
|
||||
points = opts.L<span class="org-type">*</span>points;
|
||||
</pre>
|
||||
</div>
|
||||
@@ -984,16 +989,16 @@ points = opts.L<span class="org-type">*</span>points;
|
||||
We create the rotation matrix to rotate the cube
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">sx = cross<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">1</span> <span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">0</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
sx = sx<span class="org-type">/</span>norm<span class="org-rainbow-delimiters-depth-1">(</span>sx<span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
<pre class="src src-matlab">sx = cross([1, 1, 1], [1 0 0]);
|
||||
sx = sx<span class="org-type">/</span>norm(sx);
|
||||
|
||||
sy = <span class="org-type">-</span>cross<span class="org-rainbow-delimiters-depth-1">(</span>sx, <span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
sy = sy<span class="org-type">/</span>norm<span class="org-rainbow-delimiters-depth-1">(</span>sy<span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
sy = <span class="org-type">-</span>cross(sx, [1, 1, 1]);
|
||||
sy = sy<span class="org-type">/</span>norm(sy);
|
||||
|
||||
sz = <span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">]</span>;
|
||||
sz = sz<span class="org-type">/</span>norm<span class="org-rainbow-delimiters-depth-1">(</span>sz<span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
sz = [1, 1, 1];
|
||||
sz = sz<span class="org-type">/</span>norm(sz);
|
||||
|
||||
R = <span class="org-rainbow-delimiters-depth-1">[</span>sx<span class="org-type">'</span>, sy<span class="org-type">'</span>, sz<span class="org-type">'</span><span class="org-rainbow-delimiters-depth-1">]</span><span class="org-type">'</span>;
|
||||
R = [sx<span class="org-type">'</span>, sy<span class="org-type">'</span>, sz<span class="org-type">'</span>]<span class="org-type">'</span>;
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -1001,25 +1006,25 @@ R = <span class="org-rainbow-delimiters-depth-1">[</span>sx<span class="org-type
|
||||
We use to rotation matrix to rotate the cube
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">cube = zeros<span class="org-rainbow-delimiters-depth-1">(</span>size<span class="org-rainbow-delimiters-depth-2">(</span>points<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
<span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant"><span class="org-highlight-numbers-number">1</span></span><span class="org-constant">:size</span><span class="org-constant"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-constant">points, </span><span class="org-constant"><span class="org-highlight-numbers-number">1</span></span><span class="org-constant"><span class="org-rainbow-delimiters-depth-1">)</span></span>
|
||||
cube<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-constant">i</span>, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-1">)</span> = R <span class="org-type">*</span> points<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-constant">i</span>, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">'</span>;
|
||||
<pre class="src src-matlab">cube = zeros(size(points));
|
||||
<span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant">1:size(points, 1)</span>
|
||||
cube(<span class="org-constant">i</span>, <span class="org-type">:</span>) = R <span class="org-type">*</span> points(<span class="org-constant">i</span>, <span class="org-type">:</span>)<span class="org-type">'</span>;
|
||||
<span class="org-keyword">end</span>
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgfed01f0" class="outline-3">
|
||||
<h3 id="orgfed01f0"><span class="section-number-3">4.4</span> Vectors of each leg</h3>
|
||||
<div id="outline-container-org181d1d8" class="outline-3">
|
||||
<h3 id="org181d1d8"><span class="section-number-3">4.4</span> Vectors of each leg</h3>
|
||||
<div class="outline-text-3" id="text-4-4">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">leg_indices = <span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">3</span>, <span class="org-highlight-numbers-number">4</span>; ...
|
||||
<span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">4</span>; ...
|
||||
<span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">6</span>; ...
|
||||
<span class="org-highlight-numbers-number">5</span>, <span class="org-highlight-numbers-number">6</span>; ...
|
||||
<span class="org-highlight-numbers-number">5</span>, <span class="org-highlight-numbers-number">7</span>; ...
|
||||
<span class="org-highlight-numbers-number">3</span>, <span class="org-highlight-numbers-number">7</span><span class="org-rainbow-delimiters-depth-1">]</span>;
|
||||
<pre class="src src-matlab">leg_indices = [3, 4; ...
|
||||
2, 4; ...
|
||||
2, 6; ...
|
||||
5, 6; ...
|
||||
5, 7; ...
|
||||
3, 7];
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -1027,50 +1032,50 @@ We use to rotation matrix to rotate the cube
|
||||
Vectors are:
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">legs = zeros<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">6</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
legs_start = zeros<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">6</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
<pre class="src src-matlab">legs = zeros(6, 3);
|
||||
legs_start = zeros(6, 3);
|
||||
|
||||
<span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant"><span class="org-highlight-numbers-number">1</span></span><span class="org-constant">:</span><span class="org-constant"><span class="org-highlight-numbers-number">6</span></span>
|
||||
legs<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-constant">i</span>, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-1">)</span> = cube<span class="org-rainbow-delimiters-depth-1">(</span>leg_indices<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-constant">i</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type">-</span> cube<span class="org-rainbow-delimiters-depth-1">(</span>leg_indices<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-constant">i</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
legs_start<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-constant">i</span>, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-1">)</span> = cube<span class="org-rainbow-delimiters-depth-1">(</span>leg_indices<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-constant">i</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
<span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant">1:6</span>
|
||||
legs(<span class="org-constant">i</span>, <span class="org-type">:</span>) = cube(leg_indices(<span class="org-constant">i</span>, 2), <span class="org-type">:</span>) <span class="org-type">-</span> cube(leg_indices(<span class="org-constant">i</span>, 1), <span class="org-type">:</span>);
|
||||
legs_start(<span class="org-constant">i</span>, <span class="org-type">:</span>) = cube(leg_indices(<span class="org-constant">i</span>, 1), <span class="org-type">:</span>);
|
||||
<span class="org-keyword">end</span>
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org21db1ef" class="outline-3">
|
||||
<h3 id="org21db1ef"><span class="section-number-3">4.5</span> Verification of Height of the Stewart Platform</h3>
|
||||
<div id="outline-container-orgb396e98" class="outline-3">
|
||||
<h3 id="orgb396e98"><span class="section-number-3">4.5</span> Verification of Height of the Stewart Platform</h3>
|
||||
<div class="outline-text-3" id="text-4-5">
|
||||
<p>
|
||||
If the Stewart platform is not contained in the cube, throw an error.
|
||||
</p>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">Hmax = cube<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">4</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type">-</span> cube<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
<span class="org-keyword">if</span> opts.H0 <span class="org-type"><</span> cube<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>
|
||||
error<span class="org-rainbow-delimiters-depth-1">(</span>sprintf<span class="org-rainbow-delimiters-depth-2">(</span>'H0 is not high enought. Minimum H0 = %.<span class="org-highlight-numbers-number">1f</span><span class="org-type">'</span>, cube(<span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">3</span>)));
|
||||
<span class="org-keyword">else</span> <span class="org-keyword">if</span> opts.H0 <span class="org-type">+</span> opts.H <span class="org-type">></span> cube<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">4</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-3">)</span>
|
||||
error<span class="org-rainbow-delimiters-depth-3">(</span>sprintf<span class="org-rainbow-delimiters-depth-4">(</span>'H0<span class="org-type">+</span>H is too high. Maximum H0<span class="org-type">+</span>H = %.<span class="org-highlight-numbers-number">1f</span><span class="org-type">'</span>, cube(<span class="org-highlight-numbers-number">4</span>, <span class="org-highlight-numbers-number">3</span>)));
|
||||
error<span class="org-rainbow-delimiters-depth-5">(</span><span class="org-string">'H0+H is too high'</span><span class="org-rainbow-delimiters-depth-5">)</span>;
|
||||
<pre class="src src-matlab">Hmax = cube(4, 3) <span class="org-type">-</span> cube(2, 3);
|
||||
<span class="org-keyword">if</span> opts.H0 <span class="org-type"><</span> cube(2, 3)
|
||||
error(sprintf(<span class="org-string">'H0 is not high enought. Minimum H0 = %.1f'</span>, cube(2, 3)));
|
||||
<span class="org-keyword">else</span> <span class="org-keyword">if</span> opts.H0 <span class="org-type">+</span> opts.H <span class="org-type">></span> cube(4, 3)
|
||||
error(sprintf(<span class="org-string">'H0+H is too high. Maximum H0+H = %.1f'</span>, cube(4, 3)));
|
||||
error(<span class="org-string">'H0+H is too high'</span>);
|
||||
<span class="org-keyword">end</span>
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org9578c3c" class="outline-3">
|
||||
<h3 id="org9578c3c"><span class="section-number-3">4.6</span> Determinate the location of the joints</h3>
|
||||
<div id="outline-container-orgf38af83" class="outline-3">
|
||||
<h3 id="orgf38af83"><span class="section-number-3">4.6</span> Determinate the location of the joints</h3>
|
||||
<div class="outline-text-3" id="text-4-6">
|
||||
<p>
|
||||
We now determine the location of the joints on the fixed platform w.r.t the fixed frame \(\{A\}\).
|
||||
\(\{A\}\) is fixed to the bottom of the base.
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">Aa = zeros<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">6</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
<span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant"><span class="org-highlight-numbers-number">1</span></span><span class="org-constant">:</span><span class="org-constant"><span class="org-highlight-numbers-number">6</span></span>
|
||||
t = <span class="org-rainbow-delimiters-depth-1">(</span>opts.H0<span class="org-type">-</span>legs_start<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-constant">i</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">/</span><span class="org-rainbow-delimiters-depth-1">(</span>legs<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-constant">i</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
Aa<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-constant">i</span>, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-1">)</span> = legs_start<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-constant">i</span>, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type">+</span> t<span class="org-type">*</span>legs<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-constant">i</span>, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
<pre class="src src-matlab">Aa = zeros(6, 3);
|
||||
<span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant">1:6</span>
|
||||
t = (opts.H0<span class="org-type">-</span>legs_start(<span class="org-constant">i</span>, 3))<span class="org-type">/</span>(legs(<span class="org-constant">i</span>, 3));
|
||||
Aa(<span class="org-constant">i</span>, <span class="org-type">:</span>) = legs_start(<span class="org-constant">i</span>, <span class="org-type">:</span>) <span class="org-type">+</span> t<span class="org-type">*</span>legs(<span class="org-constant">i</span>, <span class="org-type">:</span>);
|
||||
<span class="org-keyword">end</span>
|
||||
</pre>
|
||||
</div>
|
||||
@@ -1079,10 +1084,10 @@ We now determine the location of the joints on the fixed platform w.r.t the fixe
|
||||
And the location of the joints on the mobile platform with respect to \(\{A\}\).
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">Ab = zeros<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">6</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
<span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant"><span class="org-highlight-numbers-number">1</span></span><span class="org-constant">:</span><span class="org-constant"><span class="org-highlight-numbers-number">6</span></span>
|
||||
t = <span class="org-rainbow-delimiters-depth-1">(</span>opts.H0<span class="org-type">+</span>opts.H<span class="org-type">-</span>legs_start<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-constant">i</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">/</span><span class="org-rainbow-delimiters-depth-1">(</span>legs<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-constant">i</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
Ab<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-constant">i</span>, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-1">)</span> = legs_start<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-constant">i</span>, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type">+</span> t<span class="org-type">*</span>legs<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-constant">i</span>, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
<pre class="src src-matlab">Ab = zeros(6, 3);
|
||||
<span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant">1:6</span>
|
||||
t = (opts.H0<span class="org-type">+</span>opts.H<span class="org-type">-</span>legs_start(<span class="org-constant">i</span>, 3))<span class="org-type">/</span>(legs(<span class="org-constant">i</span>, 3));
|
||||
Ab(<span class="org-constant">i</span>, <span class="org-type">:</span>) = legs_start(<span class="org-constant">i</span>, <span class="org-type">:</span>) <span class="org-type">+</span> t<span class="org-type">*</span>legs(<span class="org-constant">i</span>, <span class="org-type">:</span>);
|
||||
<span class="org-keyword">end</span>
|
||||
</pre>
|
||||
</div>
|
||||
@@ -1091,25 +1096,25 @@ And the location of the joints on the mobile platform with respect to \(\{A\}\).
|
||||
And the location of the joints on the mobile platform with respect to \(\{B\}\).
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">Bb = zeros<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">6</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
Bb = Ab <span class="org-type">-</span> <span class="org-rainbow-delimiters-depth-1">(</span>opts.H0 <span class="org-type">+</span> opts.H_tot<span class="org-type">/</span><span class="org-highlight-numbers-number">2</span> <span class="org-type">+</span> opts.H<span class="org-type">/</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">*</span><span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">]</span>;
|
||||
<pre class="src src-matlab">Bb = zeros(6, 3);
|
||||
Bb = Ab <span class="org-type">-</span> (opts.H0 <span class="org-type">+</span> opts.H_tot<span class="org-type">/</span>2 <span class="org-type">+</span> opts.H<span class="org-type">/</span>2)<span class="org-type">*</span>[0, 0, 1];
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">h = opts.H0 <span class="org-type">+</span> opts.H<span class="org-type">/</span><span class="org-highlight-numbers-number">2</span> <span class="org-type">-</span> opts.H_tot<span class="org-type">/</span><span class="org-highlight-numbers-number">2</span>;
|
||||
Aa = Aa <span class="org-type">-</span> h<span class="org-type">*</span><span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">]</span>;
|
||||
Ab = Ab <span class="org-type">-</span> h<span class="org-type">*</span><span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">]</span>;
|
||||
<pre class="src src-matlab">h = opts.H0 <span class="org-type">+</span> opts.H<span class="org-type">/</span>2 <span class="org-type">-</span> opts.H_tot<span class="org-type">/</span>2;
|
||||
Aa = Aa <span class="org-type">-</span> h<span class="org-type">*</span>[0, 0, 1];
|
||||
Ab = Ab <span class="org-type">-</span> h<span class="org-type">*</span>[0, 0, 1];
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org71c9d4e" class="outline-3">
|
||||
<h3 id="org71c9d4e"><span class="section-number-3">4.7</span> Returns Stewart Structure</h3>
|
||||
<div id="outline-container-orgdf9e3cf" class="outline-3">
|
||||
<h3 id="orgdf9e3cf"><span class="section-number-3">4.7</span> Returns Stewart Structure</h3>
|
||||
<div class="outline-text-3" id="text-4-7">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> stewart = struct<span class="org-rainbow-delimiters-depth-1">()</span>;
|
||||
<pre class="src src-matlab"> stewart = struct();
|
||||
stewart.Aa = Aa;
|
||||
stewart.Ab = Ab;
|
||||
stewart.Bb = Bb;
|
||||
@@ -1121,15 +1126,15 @@ Ab = Ab <span class="org-type">-</span> h<span class="org-type">*</span><span cl
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgb2d1742" class="outline-2">
|
||||
<h2 id="orgb2d1742"><span class="section-number-2">5</span> Tests</h2>
|
||||
<div id="outline-container-orgf8fb731" class="outline-2">
|
||||
<h2 id="orgf8fb731"><span class="section-number-2">5</span> <span class="todo TODO">TODO</span> Tests</h2>
|
||||
<div class="outline-text-2" id="text-5">
|
||||
</div>
|
||||
<div id="outline-container-org6e933c9" class="outline-3">
|
||||
<h3 id="org6e933c9"><span class="section-number-3">5.1</span> First attempt to parametrisation</h3>
|
||||
<div id="outline-container-org4434fe5" class="outline-3">
|
||||
<h3 id="org4434fe5"><span class="section-number-3">5.1</span> First attempt to parametrisation</h3>
|
||||
<div class="outline-text-3" id="text-5-1">
|
||||
|
||||
<div id="org94bcd9c" class="figure">
|
||||
<div id="org8dfcb96" class="figure">
|
||||
<p><img src="./figs/stewart_bottom_plate.png" alt="stewart_bottom_plate.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 4: </span>Schematic of the bottom plates with all the parameters</p>
|
||||
@@ -1164,8 +1169,8 @@ Lets express \(a_i\), \(b_i\) and \(a_j\):
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org60486ce" class="outline-3">
|
||||
<h3 id="org60486ce"><span class="section-number-3">5.2</span> Second attempt</h3>
|
||||
<div id="outline-container-org723e6eb" class="outline-3">
|
||||
<h3 id="org723e6eb"><span class="section-number-3">5.2</span> Second attempt</h3>
|
||||
<div class="outline-text-3" id="text-5-2">
|
||||
<p>
|
||||
We start with the point of a cube in space:
|
||||
@@ -1184,41 +1189,41 @@ Then we have the direction of all the vectors expressed in the frame of the hexa
|
||||
</p>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">points = <span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">0</span>; ...
|
||||
<span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">1</span>; ...
|
||||
<span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">0</span>; ...
|
||||
<span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">1</span>; ...
|
||||
<span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">0</span>; ...
|
||||
<span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">1</span>; ...
|
||||
<span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">0</span>; ...
|
||||
<span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">]</span>;
|
||||
<pre class="src src-matlab">points = [0, 0, 0; ...
|
||||
0, 0, 1; ...
|
||||
0, 1, 0; ...
|
||||
0, 1, 1; ...
|
||||
1, 0, 0; ...
|
||||
1, 0, 1; ...
|
||||
1, 1, 0; ...
|
||||
1, 1, 1];
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
||||
plot3<span class="org-rainbow-delimiters-depth-1">(</span>points<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>,<span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, points<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>,<span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, points<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>,<span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'ko'</span><span class="org-rainbow-delimiters-depth-1">)</span>
|
||||
plot3(points(<span class="org-type">:</span>,1), points(<span class="org-type">:</span>,2), points(<span class="org-type">:</span>,3), <span class="org-string">'ko'</span>)
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">sx = cross<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">1</span> <span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">0</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
sx = sx<span class="org-type">/</span>norm<span class="org-rainbow-delimiters-depth-1">(</span>sx<span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
<pre class="src src-matlab">sx = cross([1, 1, 1], [1 0 0]);
|
||||
sx = sx<span class="org-type">/</span>norm(sx);
|
||||
|
||||
sy = <span class="org-type">-</span>cross<span class="org-rainbow-delimiters-depth-1">(</span>sx, <span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
sy = sy<span class="org-type">/</span>norm<span class="org-rainbow-delimiters-depth-1">(</span>sy<span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
sy = <span class="org-type">-</span>cross(sx, [1, 1, 1]);
|
||||
sy = sy<span class="org-type">/</span>norm(sy);
|
||||
|
||||
sz = <span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">]</span>;
|
||||
sz = sz<span class="org-type">/</span>norm<span class="org-rainbow-delimiters-depth-1">(</span>sz<span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
sz = [1, 1, 1];
|
||||
sz = sz<span class="org-type">/</span>norm(sz);
|
||||
|
||||
R = <span class="org-rainbow-delimiters-depth-1">[</span>sx<span class="org-type">'</span>, sy<span class="org-type">'</span>, sz<span class="org-type">'</span><span class="org-rainbow-delimiters-depth-1">]</span><span class="org-type">'</span>;
|
||||
R = [sx<span class="org-type">'</span>, sy<span class="org-type">'</span>, sz<span class="org-type">'</span>]<span class="org-type">'</span>;
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">cube = zeros<span class="org-rainbow-delimiters-depth-1">(</span>size<span class="org-rainbow-delimiters-depth-2">(</span>points<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
<span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant"><span class="org-highlight-numbers-number">1</span></span><span class="org-constant">:size</span><span class="org-constant"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-constant">points, </span><span class="org-constant"><span class="org-highlight-numbers-number">1</span></span><span class="org-constant"><span class="org-rainbow-delimiters-depth-1">)</span></span>
|
||||
cube<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-constant">i</span>, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-1">)</span> = R <span class="org-type">*</span> points<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-constant">i</span>, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">'</span>;
|
||||
<pre class="src src-matlab">cube = zeros(size(points));
|
||||
<span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant">1:size(points, 1)</span>
|
||||
cube(<span class="org-constant">i</span>, <span class="org-type">:</span>) = R <span class="org-type">*</span> points(<span class="org-constant">i</span>, <span class="org-type">:</span>)<span class="org-type">'</span>;
|
||||
<span class="org-keyword">end</span>
|
||||
</pre>
|
||||
</div>
|
||||
@@ -1226,8 +1231,8 @@ R = <span class="org-rainbow-delimiters-depth-1">[</span>sx<span class="org-type
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
||||
hold on;
|
||||
plot3<span class="org-rainbow-delimiters-depth-1">(</span>points<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>,<span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, points<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>,<span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, points<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>,<span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'ko'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
plot3<span class="org-rainbow-delimiters-depth-1">(</span>cube<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>,<span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, cube<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>,<span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, cube<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>,<span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'ro'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
plot3(points(<span class="org-type">:</span>,1), points(<span class="org-type">:</span>,2), points(<span class="org-type">:</span>,3), <span class="org-string">'ko'</span>);
|
||||
plot3(cube(<span class="org-type">:</span>,1), cube(<span class="org-type">:</span>,2), cube(<span class="org-type">:</span>,3), <span class="org-string">'ro'</span>);
|
||||
hold off;
|
||||
</pre>
|
||||
</div>
|
||||
@@ -1236,17 +1241,17 @@ hold off;
|
||||
Now we plot the legs of the hexapod.
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">leg_indices = <span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">3</span>, <span class="org-highlight-numbers-number">4</span>; ...
|
||||
<span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">4</span>; ...
|
||||
<span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">6</span>; ...
|
||||
<span class="org-highlight-numbers-number">5</span>, <span class="org-highlight-numbers-number">6</span>; ...
|
||||
<span class="org-highlight-numbers-number">5</span>, <span class="org-highlight-numbers-number">7</span>; ...
|
||||
<span class="org-highlight-numbers-number">3</span>, <span class="org-highlight-numbers-number">7</span><span class="org-rainbow-delimiters-depth-1">]</span>
|
||||
<pre class="src src-matlab">leg_indices = [3, 4; ...
|
||||
2, 4; ...
|
||||
2, 6; ...
|
||||
5, 6; ...
|
||||
5, 7; ...
|
||||
3, 7]
|
||||
|
||||
<span class="org-type">figure</span>;
|
||||
hold on;
|
||||
<span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant"><span class="org-highlight-numbers-number">1</span></span><span class="org-constant">:</span><span class="org-constant"><span class="org-highlight-numbers-number">6</span></span>
|
||||
plot3<span class="org-rainbow-delimiters-depth-1">(</span>cube<span class="org-rainbow-delimiters-depth-2">(</span>leg_indices<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-constant">i</span>, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-3">)</span>,<span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, cube<span class="org-rainbow-delimiters-depth-2">(</span>leg_indices<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-constant">i</span>, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-3">)</span>,<span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, cube<span class="org-rainbow-delimiters-depth-2">(</span>leg_indices<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-constant">i</span>, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-3">)</span>,<span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'-'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
<span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant">1:6</span>
|
||||
plot3(cube(leg_indices(<span class="org-constant">i</span>, <span class="org-type">:</span>),1), cube(leg_indices(<span class="org-constant">i</span>, <span class="org-type">:</span>),2), cube(leg_indices(<span class="org-constant">i</span>, <span class="org-type">:</span>),3), <span class="org-string">'-'</span>);
|
||||
<span class="org-keyword">end</span>
|
||||
hold off;
|
||||
</pre>
|
||||
@@ -1256,12 +1261,12 @@ hold off;
|
||||
Vectors are:
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">legs = zeros<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">6</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
legs_start = zeros<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">6</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
<pre class="src src-matlab">legs = zeros(6, 3);
|
||||
legs_start = zeros(6, 3);
|
||||
|
||||
<span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant"><span class="org-highlight-numbers-number">1</span></span><span class="org-constant">:</span><span class="org-constant"><span class="org-highlight-numbers-number">6</span></span>
|
||||
legs<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-constant">i</span>, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-1">)</span> = cube<span class="org-rainbow-delimiters-depth-1">(</span>leg_indices<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-constant">i</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type">-</span> cube<span class="org-rainbow-delimiters-depth-1">(</span>leg_indices<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-constant">i</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
legs_start<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-constant">i</span>, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-1">)</span> = cube<span class="org-rainbow-delimiters-depth-1">(</span>leg_indices<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-constant">i</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-1">)</span>
|
||||
<span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant">1:6</span>
|
||||
legs(<span class="org-constant">i</span>, <span class="org-type">:</span>) = cube(leg_indices(<span class="org-constant">i</span>, 2), <span class="org-type">:</span>) <span class="org-type">-</span> cube(leg_indices(<span class="org-constant">i</span>, 1), <span class="org-type">:</span>);
|
||||
legs_start(<span class="org-constant">i</span>, <span class="org-type">:</span>) = cube(leg_indices(<span class="org-constant">i</span>, 1), <span class="org-type">:</span>)
|
||||
<span class="org-keyword">end</span>
|
||||
</pre>
|
||||
</div>
|
||||
@@ -1271,40 +1276,40 @@ We now have the orientation of each leg.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
We here want to see if the position of the "slice" changes something.
|
||||
We here want to see if the position of the “slice” changes something.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
Let's first estimate the maximum height of the Stewart platform.
|
||||
Let’s first estimate the maximum height of the Stewart platform.
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">Hmax = cube<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">4</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type">-</span> cube<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
<pre class="src src-matlab">Hmax = cube(4, 3) <span class="org-type">-</span> cube(2, 3);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
Let's then estimate the middle position of the platform
|
||||
Let’s then estimate the middle position of the platform
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">Hmid = cube<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">8</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">/</span><span class="org-highlight-numbers-number">2</span>;
|
||||
<pre class="src src-matlab">Hmid = cube(8, 3)<span class="org-type">/</span>2;
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orge571873" class="outline-3">
|
||||
<h3 id="orge571873"><span class="section-number-3">5.3</span> Generate the Stewart platform for a Cubic configuration</h3>
|
||||
<div id="outline-container-orgcc173ac" class="outline-3">
|
||||
<h3 id="orgcc173ac"><span class="section-number-3">5.3</span> Generate the Stewart platform for a Cubic configuration</h3>
|
||||
<div class="outline-text-3" id="text-5-3">
|
||||
<p>
|
||||
First we defined the height of the Hexapod.
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">H = Hmax<span class="org-type">/</span><span class="org-highlight-numbers-number">2</span>;
|
||||
<pre class="src src-matlab">H = Hmax<span class="org-type">/</span>2;
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">Zs = <span class="org-highlight-numbers-number">1</span>.<span class="org-highlight-numbers-number">2</span><span class="org-type">*</span>cube<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Height of the fixed platform</span>
|
||||
<pre class="src src-matlab">Zs = 1.2<span class="org-type">*</span>cube(2, 3); <span class="org-comment">% Height of the fixed platform</span>
|
||||
Ze = Zs <span class="org-type">+</span> H; <span class="org-comment">% Height of the mobile platform</span>
|
||||
</pre>
|
||||
</div>
|
||||
@@ -1313,10 +1318,10 @@ Ze = Zs <span class="org-type">+</span> H; <span class="org-comment">% Height of
|
||||
We now determine the location of the joints on the fixed platform.
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">Aa = zeros<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">6</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
<span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant"><span class="org-highlight-numbers-number">1</span></span><span class="org-constant">:</span><span class="org-constant"><span class="org-highlight-numbers-number">6</span></span>
|
||||
t = <span class="org-rainbow-delimiters-depth-1">(</span>Zs<span class="org-type">-</span>legs_start<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-constant">i</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">/</span><span class="org-rainbow-delimiters-depth-1">(</span>legs<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-constant">i</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
Aa<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-constant">i</span>, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-1">)</span> = legs_start<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-constant">i</span>, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type">+</span> t<span class="org-type">*</span>legs<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-constant">i</span>, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
<pre class="src src-matlab">Aa = zeros(6, 3);
|
||||
<span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant">1:6</span>
|
||||
t = (Zs<span class="org-type">-</span>legs_start(<span class="org-constant">i</span>, 3))<span class="org-type">/</span>(legs(<span class="org-constant">i</span>, 3));
|
||||
Aa(<span class="org-constant">i</span>, <span class="org-type">:</span>) = legs_start(<span class="org-constant">i</span>, <span class="org-type">:</span>) <span class="org-type">+</span> t<span class="org-type">*</span>legs(<span class="org-constant">i</span>, <span class="org-type">:</span>);
|
||||
<span class="org-keyword">end</span>
|
||||
</pre>
|
||||
</div>
|
||||
@@ -1325,10 +1330,10 @@ We now determine the location of the joints on the fixed platform.
|
||||
And the location of the joints on the mobile platform
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">Ab = zeros<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">6</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
<span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant"><span class="org-highlight-numbers-number">1</span></span><span class="org-constant">:</span><span class="org-constant"><span class="org-highlight-numbers-number">6</span></span>
|
||||
t = <span class="org-rainbow-delimiters-depth-1">(</span>Ze<span class="org-type">-</span>legs_start<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-constant">i</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">/</span><span class="org-rainbow-delimiters-depth-1">(</span>legs<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-constant">i</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
Ab<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-constant">i</span>, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-1">)</span> = legs_start<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-constant">i</span>, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type">+</span> t<span class="org-type">*</span>legs<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-constant">i</span>, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
<pre class="src src-matlab">Ab = zeros(6, 3);
|
||||
<span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant">1:6</span>
|
||||
t = (Ze<span class="org-type">-</span>legs_start(<span class="org-constant">i</span>, 3))<span class="org-type">/</span>(legs(<span class="org-constant">i</span>, 3));
|
||||
Ab(<span class="org-constant">i</span>, <span class="org-type">:</span>) = legs_start(<span class="org-constant">i</span>, <span class="org-type">:</span>) <span class="org-type">+</span> t<span class="org-type">*</span>legs(<span class="org-constant">i</span>, <span class="org-type">:</span>);
|
||||
<span class="org-keyword">end</span>
|
||||
</pre>
|
||||
</div>
|
||||
@@ -1339,13 +1344,13 @@ And we plot the legs.
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
||||
hold on;
|
||||
<span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant"><span class="org-highlight-numbers-number">1</span></span><span class="org-constant">:</span><span class="org-constant"><span class="org-highlight-numbers-number">6</span></span>
|
||||
plot3<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>Ab<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-constant">i</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-3">)</span>,Aa<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-constant">i</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-rainbow-delimiters-depth-2">[</span>Ab<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-constant">i</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-3">)</span>,Aa<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-constant">i</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-rainbow-delimiters-depth-2">[</span>Ab<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-constant">i</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-3">)</span>,Aa<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-constant">i</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-string">'k-'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
<span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant">1:6</span>
|
||||
plot3([Ab(<span class="org-constant">i</span>, 1),Aa(<span class="org-constant">i</span>, 1)], [Ab(<span class="org-constant">i</span>, 2),Aa(<span class="org-constant">i</span>, 2)], [Ab(<span class="org-constant">i</span>, 3),Aa(<span class="org-constant">i</span>, 3)], <span class="org-string">'k-'</span>);
|
||||
<span class="org-keyword">end</span>
|
||||
hold off;
|
||||
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">-</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
ylim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">-</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
zlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
xlim([<span class="org-type">-</span>1, 1]);
|
||||
ylim([<span class="org-type">-</span>1, 1]);
|
||||
zlim([0, 2]);
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1362,9 +1367,8 @@ zlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
|
||||
</p>
|
||||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Thomas Dehaeze</p>
|
||||
<p class="date">Created: 2019-12-12 jeu. 20:10</p>
|
||||
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||
<p class="author">Author: Dehaeze Thomas</p>
|
||||
<p class="date">Created: 2020-01-27 lun. 17:41</p>
|
||||
</div>
|
||||
</body>
|
||||
</html>
|
||||
|
||||
Reference in New Issue
Block a user