From 8197bb4eb88c52f83d03c6bb4490f981c42bc9a3 Mon Sep 17 00:00:00 2001
From: Thomas Dehaeze <dehaeze.thomas@gmail.com>
Date: Thu, 6 Feb 2020 18:23:01 +0100
Subject: [PATCH] Update the cubic configuration analysis

---
 cubic-configuration.html         | 700 +++++++++++++++----------------
 cubic-configuration.org          | 226 +++++-----
 src/generateCubicConfiguration.m |   4 +-
 3 files changed, 432 insertions(+), 498 deletions(-)
diff --git a/cubic-configuration.html b/cubic-configuration.html
index 96cc75a..a0f2463 100644
--- a/cubic-configuration.html
+++ b/cubic-configuration.html
@@ -4,7 +4,7 @@
 "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
 <html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
 <head>
-<!-- 2020-02-06 jeu. 17:29 -->
+<!-- 2020-02-06 jeu. 18:22 -->
 <meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
 <meta name="viewport" content="width=device-width, initial-scale=1" />
 <title>Cubic configuration for the Stewart Platform</title>
@@ -268,25 +268,25 @@ for the JavaScript code in this tag.
 <h2>Table of Contents</h2>
 <div id="text-table-of-contents">
 <ul>
-<li><a href="#org75c6951">1. <span class="todo TODO">TODO</span> Configuration Analysis - Stiffness Matrix</a>
+<li><a href="#org8350a45">1. Configuration Analysis - Stiffness Matrix</a>
 <ul>
-<li><a href="#orga823f72">1.1. Cubic Stewart platform centered with the cube center - Jacobian estimated at the cube center</a></li>
-<li><a href="#org4261310">1.2. Cubic Stewart platform centered with the cube center - Jacobian not estimated at the cube center</a></li>
-<li><a href="#orgf297eb8">1.3. Cubic Stewart platform not centered with the cube center - Jacobian estimated at the cube center</a></li>
-<li><a href="#orgfeaf9c1">1.4. Cubic Stewart platform not centered with the cube center - Jacobian estimated at the Stewart platform center</a></li>
-<li><a href="#org24bdf29">1.5. Conclusion</a></li>
+<li><a href="#org6b34363">1.1. Cubic Stewart platform centered with the cube center - Jacobian estimated at the cube center</a></li>
+<li><a href="#orgd59e9f0">1.2. Cubic Stewart platform centered with the cube center - Jacobian not estimated at the cube center</a></li>
+<li><a href="#org27bd91a">1.3. Cubic Stewart platform not centered with the cube center - Jacobian estimated at the cube center</a></li>
+<li><a href="#org4adea52">1.4. Cubic Stewart platform not centered with the cube center - Jacobian estimated at the Stewart platform center</a></li>
+<li><a href="#org5defe19">1.5. Conclusion</a></li>
+<li><a href="#org905f726">1.6. Having Cube&rsquo;s center above the top platform</a></li>
 </ul>
 </li>
-<li><a href="#org2cb2ab0">2. <span class="todo TODO">TODO</span> Cubic size analysis</a></li>
-<li><a href="#orgeec7b47">3. Functions</a>
+<li><a href="#org6746f61">2. Functions</a>
 <ul>
-<li><a href="#org92224ef">3.1. <code>generateCubicConfiguration</code>: Generate a Cubic Configuration</a>
+<li><a href="#org80fcb20">2.1. <code>generateCubicConfiguration</code>: Generate a Cubic Configuration</a>
 <ul>
-<li><a href="#org715472d">Function description</a></li>
-<li><a href="#orgbab37f8">Documentation</a></li>
-<li><a href="#orgddbe42e">Optional Parameters</a></li>
-<li><a href="#org66dd074">Position of the Cube</a></li>
-<li><a href="#org388f35d">Compute the pose</a></li>
+<li><a href="#orgd3654f4">Function description</a></li>
+<li><a href="#orgf1c4374">Documentation</a></li>
+<li><a href="#org7703a4a">Optional Parameters</a></li>
+<li><a href="#org43039c1">Position of the Cube</a></li>
+<li><a href="#orga18e804">Compute the pose</a></li>
 </ul>
 </li>
 </ul>
@@ -313,7 +313,7 @@ According to <a class='org-ref-reference' href="#preumont07_six_axis_singl_stage
 </p>
 
 <p>
-To generate and study the Cubic configuration, <code>generateCubicConfiguration</code> is used (description in section <a href="#orgb0ae4eb">3.1</a>).
+To generate and study the Cubic configuration, <code>generateCubicConfiguration</code> is used (description in section <a href="#orgfe8cdfe">2.1</a>).
 The goal is to study the benefits of using a cubic configuration:
 </p>
 <ul class="org-ul">
@@ -322,48 +322,34 @@ The goal is to study the benefits of using a cubic configuration:
 <li>Is the center of the cube an important point?</li>
 </ul>
 
-<div id="outline-container-org75c6951" class="outline-2">
-<h2 id="org75c6951"><span class="section-number-2">1</span> <span class="todo TODO">TODO</span> Configuration Analysis - Stiffness Matrix</h2>
+<div id="outline-container-org8350a45" class="outline-2">
+<h2 id="org8350a45"><span class="section-number-2">1</span> Configuration Analysis - Stiffness Matrix</h2>
 <div class="outline-text-2" id="text-1">
 </div>
-<div id="outline-container-orga823f72" class="outline-3">
-<h3 id="orga823f72"><span class="section-number-3">1.1</span> Cubic Stewart platform centered with the cube center - Jacobian estimated at the cube center</h3>
+<div id="outline-container-org6b34363" class="outline-3">
+<h3 id="org6b34363"><span class="section-number-3">1.1</span> Cubic Stewart platform centered with the cube center - Jacobian estimated at the cube center</h3>
 <div class="outline-text-3" id="text-1-1">
 <p>
-We create a cubic Stewart platform (figure <a href="#org66ade8d">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="#org964919a">1</a>) in such a way that the center of the cube (black dot) is located at the center of the Stewart platform (blue dot).
 The Jacobian matrix is estimated at the location of the center of the cube.
 </p>
 
+<div class="org-src-container">
+<pre class="src src-matlab">stewart = initializeFramesPositions(<span class="org-string">'H'</span>, 100e<span class="org-type">-</span>3, <span class="org-string">'MO_B'</span>, <span class="org-type">-</span>50e<span class="org-type">-</span>3);
+stewart = generateCubicConfiguration(stewart, <span class="org-string">'Hc'</span>, 100e<span class="org-type">-</span>3, <span class="org-string">'FOc'</span>, 50e<span class="org-type">-</span>3, <span class="org-string">'FHa'</span>, 0, <span class="org-string">'MHb'</span>, 0);
+stewart = computeJointsPose(stewart);
+stewart = initializeStrutDynamics(stewart, <span class="org-string">'Ki'</span>, ones(6,1));
+stewart = computeJacobian(stewart);
+</pre>
+</div>
 
-<div id="org66ade8d" class="figure">
+
+<div id="org964919a" class="figure">
 <p><img src="./figs/3d-cubic-stewart-aligned.png" alt="3d-cubic-stewart-aligned.png" />
 </p>
 <p><span class="figure-number">Figure 1: </span>Centered cubic configuration</p>
 </div>
 
-<div class="org-src-container">
-<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-string">'./mat/stewart.mat'</span>, <span class="org-string">'stewart'</span>);
-</pre>
-</div>
-
-<div class="org-src-container">
-<pre class="src src-matlab">K = stewart.Jf<span class="org-type">'*</span>stewart.Jf;
-</pre>
-</div>
-
 <table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
 
 
@@ -383,88 +369,76 @@ save(<span class="org-string">'./mat/stewart.mat'</span>, <span class="org-strin
 <tbody>
 <tr>
 <td class="org-right">2</td>
-<td class="org-right">1.9e-18</td>
-<td class="org-right">-2.3e-17</td>
-<td class="org-right">1.8e-18</td>
-<td class="org-right">5.5e-17</td>
-<td class="org-right">-1.5e-17</td>
+<td class="org-right">0</td>
+<td class="org-right">-2.5e-16</td>
+<td class="org-right">0</td>
+<td class="org-right">2.1e-17</td>
+<td class="org-right">0</td>
 </tr>
 
 <tr>
-<td class="org-right">1.9e-18</td>
+<td class="org-right">0</td>
 <td class="org-right">2</td>
-<td class="org-right">6.8e-18</td>
-<td class="org-right">-6.1e-17</td>
-<td class="org-right">-1.6e-18</td>
-<td class="org-right">4.8e-18</td>
+<td class="org-right">0</td>
+<td class="org-right">-7.8e-19</td>
+<td class="org-right">0</td>
+<td class="org-right">0</td>
 </tr>
 
 <tr>
-<td class="org-right">-2.3e-17</td>
-<td class="org-right">6.8e-18</td>
+<td class="org-right">-2.5e-16</td>
+<td class="org-right">0</td>
 <td class="org-right">2</td>
-<td class="org-right">-6.7e-18</td>
-<td class="org-right">4.9e-18</td>
-<td class="org-right">5.3e-19</td>
+<td class="org-right">-2.4e-18</td>
+<td class="org-right">-1.4e-17</td>
+<td class="org-right">0</td>
 </tr>
 
 <tr>
-<td class="org-right">1.8e-18</td>
-<td class="org-right">-6.1e-17</td>
-<td class="org-right">-6.7e-18</td>
-<td class="org-right">0.0067</td>
-<td class="org-right">-2.3e-20</td>
-<td class="org-right">-6.1e-20</td>
+<td class="org-right">0</td>
+<td class="org-right">-7.8e-19</td>
+<td class="org-right">-2.4e-18</td>
+<td class="org-right">0.015</td>
+<td class="org-right">-4.3e-19</td>
+<td class="org-right">1.7e-18</td>
 </tr>
 
 <tr>
-<td class="org-right">5.5e-17</td>
-<td class="org-right">-1.6e-18</td>
-<td class="org-right">4.9e-18</td>
-<td class="org-right">-2.3e-20</td>
-<td class="org-right">0.0067</td>
-<td class="org-right">1e-18</td>
+<td class="org-right">1.8e-17</td>
+<td class="org-right">0</td>
+<td class="org-right">-1.1e-17</td>
+<td class="org-right">0</td>
+<td class="org-right">0.015</td>
+<td class="org-right">0</td>
 </tr>
 
 <tr>
-<td class="org-right">-1.5e-17</td>
-<td class="org-right">4.8e-18</td>
-<td class="org-right">5.3e-19</td>
-<td class="org-right">-6.1e-20</td>
-<td class="org-right">1e-18</td>
-<td class="org-right">0.027</td>
+<td class="org-right">6.6e-18</td>
+<td class="org-right">-3.3e-18</td>
+<td class="org-right">0</td>
+<td class="org-right">1.7e-18</td>
+<td class="org-right">0</td>
+<td class="org-right">0.06</td>
 </tr>
 </tbody>
 </table>
 </div>
 </div>
 
-<div id="outline-container-org4261310" class="outline-3">
-<h3 id="org4261310"><span class="section-number-3">1.2</span> Cubic Stewart platform centered with the cube center - Jacobian not estimated at the cube center</h3>
+<div id="outline-container-orgd59e9f0" class="outline-3">
+<h3 id="orgd59e9f0"><span class="section-number-3">1.2</span> Cubic Stewart platform centered with the cube center - Jacobian not estimated at the cube center</h3>
 <div class="outline-text-3" id="text-1-2">
 <p>
-We create a cubic Stewart platform with center of the cube located at the center of the Stewart platform (figure <a href="#org66ade8d">1</a>).
+We create a cubic Stewart platform with center of the cube located at the center of the Stewart platform (figure <a href="#org964919a">1</a>).
 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-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>
-
-<div class="org-src-container">
-<pre class="src src-matlab">K = stewart.Jf<span class="org-type">'*</span>stewart.Jf;
+<pre class="src src-matlab">stewart = initializeFramesPositions(<span class="org-string">'H'</span>, 100e<span class="org-type">-</span>3, <span class="org-string">'MO_B'</span>, 0);
+stewart = generateCubicConfiguration(stewart, <span class="org-string">'Hc'</span>, 100e<span class="org-type">-</span>3, <span class="org-string">'FOc'</span>, 50e<span class="org-type">-</span>3, <span class="org-string">'FHa'</span>, 0, <span class="org-string">'MHb'</span>, 0);
+stewart = computeJointsPose(stewart);
+stewart = initializeStrutDynamics(stewart, <span class="org-string">'Ki'</span>, ones(6,1));
+stewart = computeJacobian(stewart);
 </pre>
 </div>
 
@@ -487,102 +461,83 @@ stewart = computeGeometricalProperties(stewart, opts);
 <tbody>
 <tr>
 <td class="org-right">2</td>
-<td class="org-right">1.9e-18</td>
-<td class="org-right">-2.3e-17</td>
-<td class="org-right">1.5e-18</td>
+<td class="org-right">0</td>
+<td class="org-right">-2.5e-16</td>
+<td class="org-right">1.4e-17</td>
 <td class="org-right">-0.1</td>
-<td class="org-right">-1.5e-17</td>
+<td class="org-right">0</td>
 </tr>
 
 <tr>
-<td class="org-right">1.9e-18</td>
+<td class="org-right">0</td>
 <td class="org-right">2</td>
-<td class="org-right">6.8e-18</td>
+<td class="org-right">0</td>
 <td class="org-right">0.1</td>
-<td class="org-right">-1.6e-18</td>
-<td class="org-right">4.8e-18</td>
+<td class="org-right">0</td>
+<td class="org-right">0</td>
 </tr>
 
 <tr>
-<td class="org-right">-2.3e-17</td>
-<td class="org-right">6.8e-18</td>
+<td class="org-right">-2.5e-16</td>
+<td class="org-right">0</td>
 <td class="org-right">2</td>
-<td class="org-right">-5.1e-19</td>
-<td class="org-right">-5.5e-18</td>
-<td class="org-right">5.3e-19</td>
+<td class="org-right">3.4e-18</td>
+<td class="org-right">-1.4e-17</td>
+<td class="org-right">0</td>
 </tr>
 
 <tr>
-<td class="org-right">1.5e-18</td>
+<td class="org-right">1.4e-17</td>
 <td class="org-right">0.1</td>
-<td class="org-right">-5.1e-19</td>
-<td class="org-right">0.012</td>
-<td class="org-right">-3e-19</td>
-<td class="org-right">3.1e-19</td>
+<td class="org-right">3.4e-18</td>
+<td class="org-right">0.02</td>
+<td class="org-right">1.1e-20</td>
+<td class="org-right">3.4e-18</td>
 </tr>
 
 <tr>
 <td class="org-right">-0.1</td>
-<td class="org-right">-1.6e-18</td>
-<td class="org-right">-5.5e-18</td>
-<td class="org-right">-3e-19</td>
-<td class="org-right">0.012</td>
-<td class="org-right">1.9e-18</td>
+<td class="org-right">0</td>
+<td class="org-right">-1.4e-17</td>
+<td class="org-right">1.4e-19</td>
+<td class="org-right">0.02</td>
+<td class="org-right">-1.7e-18</td>
 </tr>
 
 <tr>
-<td class="org-right">-1.5e-17</td>
-<td class="org-right">4.8e-18</td>
-<td class="org-right">5.3e-19</td>
-<td class="org-right">3.1e-19</td>
-<td class="org-right">1.9e-18</td>
-<td class="org-right">0.027</td>
+<td class="org-right">6.6e-18</td>
+<td class="org-right">-3.3e-18</td>
+<td class="org-right">0</td>
+<td class="org-right">3.6e-18</td>
+<td class="org-right">-1.7e-18</td>
+<td class="org-right">0.06</td>
 </tr>
 </tbody>
 </table>
 </div>
 </div>
 
-<div id="outline-container-orgf297eb8" class="outline-3">
-<h3 id="orgf297eb8"><span class="section-number-3">1.3</span> Cubic Stewart platform not centered with the cube center - Jacobian estimated at the cube center</h3>
+<div id="outline-container-org27bd91a" class="outline-3">
+<h3 id="org27bd91a"><span class="section-number-3">1.3</span> Cubic Stewart platform not centered with the cube center - Jacobian estimated at the cube center</h3>
 <div class="outline-text-3" id="text-1-3">
 <p>
-Here, the &ldquo;center&rdquo; of the Stewart platform is not at the cube center (figure <a href="#org4492663">2</a>).
+Here, the &ldquo;center&rdquo; of the Stewart platform is not at the cube center (figure <a href="#orgeceb55c">2</a>).
 The Jacobian is estimated at the cube center.
 </p>
 
 
-<div id="org4492663" class="figure">
+<div id="orgeceb55c" 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>
 </div>
 
-<p>
-The center of the cube is at \(z = 110\).
-The Stewart platform is from \(z = H_0 = 75\) to \(z = H_0 + H_{tot} = 175\).
-The center height of the Stewart platform is then at \(z = \frac{175-75}{2} = 50\).
-The center of the cube from the top platform is at \(z = 110 - 175 = -65\).
-</p>
-
 <div class="org-src-container">
-<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>
-
-<div class="org-src-container">
-<pre class="src src-matlab">K = stewart.Jf<span class="org-type">'*</span>stewart.Jf;
+<pre class="src src-matlab">stewart = initializeFramesPositions(<span class="org-string">'H'</span>, 80e<span class="org-type">-</span>3, <span class="org-string">'MO_B'</span>, <span class="org-type">-</span>40e<span class="org-type">-</span>3);
+stewart = generateCubicConfiguration(stewart, <span class="org-string">'Hc'</span>, 100e<span class="org-type">-</span>3, <span class="org-string">'FOc'</span>, 50e<span class="org-type">-</span>3, <span class="org-string">'FHa'</span>, 0, <span class="org-string">'MHb'</span>, 0);
+stewart = computeJointsPose(stewart);
+stewart = initializeStrutDynamics(stewart, <span class="org-string">'Ki'</span>, ones(6,1));
+stewart = computeJacobian(stewart);
 </pre>
 </div>
 
@@ -605,56 +560,56 @@ stewart = computeGeometricalProperties(stewart, opts);
 <tbody>
 <tr>
 <td class="org-right">2</td>
-<td class="org-right">-1.8e-17</td>
-<td class="org-right">2.6e-17</td>
-<td class="org-right">3.3e-18</td>
+<td class="org-right">0</td>
+<td class="org-right">-1.5e-16</td>
+<td class="org-right">0</td>
 <td class="org-right">0.04</td>
-<td class="org-right">1.7e-19</td>
+<td class="org-right">0</td>
 </tr>
 
 <tr>
-<td class="org-right">-1.8e-17</td>
+<td class="org-right">0</td>
 <td class="org-right">2</td>
-<td class="org-right">1.9e-16</td>
+<td class="org-right">0</td>
 <td class="org-right">-0.04</td>
-<td class="org-right">2.2e-19</td>
-<td class="org-right">-5.3e-19</td>
+<td class="org-right">0</td>
+<td class="org-right">-2.8e-17</td>
 </tr>
 
 <tr>
-<td class="org-right">2.6e-17</td>
-<td class="org-right">1.9e-16</td>
+<td class="org-right">-1.5e-16</td>
+<td class="org-right">0</td>
 <td class="org-right">2</td>
-<td class="org-right">-8.9e-18</td>
-<td class="org-right">6.5e-19</td>
-<td class="org-right">-5.8e-19</td>
+<td class="org-right">1.2e-18</td>
+<td class="org-right">-1e-17</td>
+<td class="org-right">0</td>
 </tr>
 
 <tr>
-<td class="org-right">3.3e-18</td>
+<td class="org-right">0</td>
 <td class="org-right">-0.04</td>
-<td class="org-right">-8.9e-18</td>
-<td class="org-right">0.0089</td>
-<td class="org-right">-9.3e-20</td>
-<td class="org-right">9.8e-20</td>
+<td class="org-right">1.2e-18</td>
+<td class="org-right">0.016</td>
+<td class="org-right">0</td>
+<td class="org-right">8.7e-19</td>
 </tr>
 
 <tr>
 <td class="org-right">0.04</td>
-<td class="org-right">2.2e-19</td>
-<td class="org-right">6.5e-19</td>
-<td class="org-right">-9.3e-20</td>
-<td class="org-right">0.0089</td>
-<td class="org-right">-2.4e-18</td>
+<td class="org-right">0</td>
+<td class="org-right">-6.2e-18</td>
+<td class="org-right">-1.1e-19</td>
+<td class="org-right">0.016</td>
+<td class="org-right">8.7e-19</td>
 </tr>
 
 <tr>
-<td class="org-right">1.7e-19</td>
-<td class="org-right">-5.3e-19</td>
-<td class="org-right">-5.8e-19</td>
-<td class="org-right">9.8e-20</td>
-<td class="org-right">-2.4e-18</td>
-<td class="org-right">0.032</td>
+<td class="org-right">-3.7e-19</td>
+<td class="org-right">-2.5e-17</td>
+<td class="org-right">0</td>
+<td class="org-right">1.2e-18</td>
+<td class="org-right">8.7e-19</td>
+<td class="org-right">0.06</td>
 </tr>
 </tbody>
 </table>
@@ -665,8 +620,8 @@ We obtain \(k_x = k_y = k_z\) and \(k_{\theta_x} = k_{\theta_y}\), but the Stiff
 </div>
 </div>
 
-<div id="outline-container-orgfeaf9c1" class="outline-3">
-<h3 id="orgfeaf9c1"><span class="section-number-3">1.4</span> Cubic Stewart platform not centered with the cube center - Jacobian estimated at the Stewart platform center</h3>
+<div id="outline-container-org4adea52" class="outline-3">
+<h3 id="org4adea52"><span class="section-number-3">1.4</span> Cubic Stewart platform not centered with the cube center - Jacobian estimated at the Stewart platform center</h3>
 <div class="outline-text-3" id="text-1-4">
 <p>
 Here, the &ldquo;center&rdquo; of the Stewart platform is not at the cube center.
@@ -681,23 +636,11 @@ 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-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>
-
-<div class="org-src-container">
-<pre class="src src-matlab">K = stewart.Jf<span class="org-type">'*</span>stewart.Jf;
+<pre class="src src-matlab">stewart = initializeFramesPositions(<span class="org-string">'H'</span>, 80e<span class="org-type">-</span>3, <span class="org-string">'MO_B'</span>, <span class="org-type">-</span>30e<span class="org-type">-</span>3);
+stewart = generateCubicConfiguration(stewart, <span class="org-string">'Hc'</span>, 100e<span class="org-type">-</span>3, <span class="org-string">'FOc'</span>, 50e<span class="org-type">-</span>3, <span class="org-string">'FHa'</span>, 0, <span class="org-string">'MHb'</span>, 0);
+stewart = computeJointsPose(stewart);
+stewart = initializeStrutDynamics(stewart, <span class="org-string">'Ki'</span>, ones(6,1));
+stewart = computeJacobian(stewart);
 </pre>
 </div>
 
@@ -720,56 +663,177 @@ stewart = computeGeometricalProperties(stewart, opts);
 <tbody>
 <tr>
 <td class="org-right">2</td>
-<td class="org-right">-1.8e-17</td>
-<td class="org-right">2.6e-17</td>
-<td class="org-right">-5.7e-19</td>
-<td class="org-right">0.03</td>
-<td class="org-right">1.7e-19</td>
+<td class="org-right">0</td>
+<td class="org-right">-1.7e-16</td>
+<td class="org-right">0</td>
+<td class="org-right">4.9e-17</td>
+<td class="org-right">0</td>
 </tr>
 
 <tr>
-<td class="org-right">-1.8e-17</td>
+<td class="org-right">0</td>
 <td class="org-right">2</td>
-<td class="org-right">1.9e-16</td>
-<td class="org-right">-0.03</td>
-<td class="org-right">2.2e-19</td>
-<td class="org-right">-5.3e-19</td>
+<td class="org-right">0</td>
+<td class="org-right">-2.2e-17</td>
+<td class="org-right">0</td>
+<td class="org-right">2.8e-17</td>
 </tr>
 
 <tr>
-<td class="org-right">2.6e-17</td>
-<td class="org-right">1.9e-16</td>
+<td class="org-right">-1.7e-16</td>
+<td class="org-right">0</td>
 <td class="org-right">2</td>
-<td class="org-right">-1.5e-17</td>
-<td class="org-right">6.5e-19</td>
-<td class="org-right">-5.8e-19</td>
+<td class="org-right">1.1e-18</td>
+<td class="org-right">-1.4e-17</td>
+<td class="org-right">1.4e-17</td>
 </tr>
 
 <tr>
-<td class="org-right">-5.7e-19</td>
-<td class="org-right">-0.03</td>
-<td class="org-right">-1.5e-17</td>
-<td class="org-right">0.0085</td>
-<td class="org-right">4.9e-20</td>
-<td class="org-right">1.7e-19</td>
+<td class="org-right">0</td>
+<td class="org-right">-2.2e-17</td>
+<td class="org-right">1.1e-18</td>
+<td class="org-right">0.015</td>
+<td class="org-right">0</td>
+<td class="org-right">3.5e-18</td>
 </tr>
 
 <tr>
-<td class="org-right">0.03</td>
-<td class="org-right">2.2e-19</td>
-<td class="org-right">6.5e-19</td>
-<td class="org-right">4.9e-20</td>
-<td class="org-right">0.0085</td>
-<td class="org-right">-1.1e-18</td>
+<td class="org-right">4.4e-17</td>
+<td class="org-right">0</td>
+<td class="org-right">-1.4e-17</td>
+<td class="org-right">-5.7e-20</td>
+<td class="org-right">0.015</td>
+<td class="org-right">-8.7e-19</td>
 </tr>
 
 <tr>
-<td class="org-right">1.7e-19</td>
-<td class="org-right">-5.3e-19</td>
-<td class="org-right">-5.8e-19</td>
-<td class="org-right">1.7e-19</td>
-<td class="org-right">-1.1e-18</td>
-<td class="org-right">0.032</td>
+<td class="org-right">6.6e-18</td>
+<td class="org-right">2.5e-17</td>
+<td class="org-right">0</td>
+<td class="org-right">3.5e-18</td>
+<td class="org-right">-8.7e-19</td>
+<td class="org-right">0.06</td>
+</tr>
+</tbody>
+</table>
+
+<p>
+We obtain \(k_x = k_y = k_z\) and \(k_{\theta_x} = k_{\theta_y}\), and the Stiffness matrix is diagonal.
+</p>
+</div>
+</div>
+
+<div id="outline-container-org5defe19" class="outline-3">
+<h3 id="org5defe19"><span class="section-number-3">1.5</span> Conclusion</h3>
+<div class="outline-text-3" id="text-1-5">
+<div class="important">
+<ul class="org-ul">
+<li>The cubic configuration permits to have \(k_x = k_y = k_z\) and \(k_{\theta_x} = k_{\theta_y}\)</li>
+<li>The stiffness matrix \(K\) is diagonal for the cubic configuration if the Jacobian is estimated at the cube center.</li>
+</ul>
+
+</div>
+</div>
+</div>
+
+<div id="outline-container-org905f726" class="outline-3">
+<h3 id="org905f726"><span class="section-number-3">1.6</span> Having Cube&rsquo;s center above the top platform</h3>
+<div class="outline-text-3" id="text-1-6">
+<p>
+Let&rsquo;s say we want to have a decouple dynamics above the top platform.
+Thus, we want the cube&rsquo;s center to be located above the top center.
+This is possible, to do so:
+</p>
+<ul class="org-ul">
+<li>The position of the center of the cube should be positioned at A</li>
+<li>The Height of the &ldquo;useful&rdquo; part of the cube should be at least equal to two times the distance from F to A.
+It is possible to have small cube, but then to configuration is a little bit strange.</li>
+</ul>
+
+<div class="org-src-container">
+<pre class="src src-matlab">stewart = initializeFramesPositions(<span class="org-string">'H'</span>, 100e<span class="org-type">-</span>3, <span class="org-string">'MO_B'</span>, 50e<span class="org-type">-</span>3);
+FOc = stewart.H <span class="org-type">+</span> stewart.MO_B(3);
+Hc = 2<span class="org-type">*</span>(stewart.H <span class="org-type">+</span> stewart.MO_B(3));
+stewart = generateCubicConfiguration(stewart, <span class="org-string">'Hc'</span>, Hc, <span class="org-string">'FOc'</span>, FOc, <span class="org-string">'FHa'</span>, 10e<span class="org-type">-</span>3, <span class="org-string">'MHb'</span>, 10e<span class="org-type">-</span>3);
+stewart = computeJointsPose(stewart);
+stewart = initializeStrutDynamics(stewart, <span class="org-string">'Ki'</span>, ones(6,1));
+stewart = initializeJointDynamics(stewart, <span class="org-string">'disable'</span>, <span class="org-constant">true</span>);
+stewart = initializeCylindricalPlatforms(stewart);
+stewart = initializeCylindricalStruts(stewart);
+stewart = computeJacobian(stewart);
+stewart = initializeStewartPose(stewart);
+</pre>
+</div>
+
+<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
+
+
+<colgroup>
+<col  class="org-right" />
+
+<col  class="org-right" />
+
+<col  class="org-right" />
+
+<col  class="org-right" />
+
+<col  class="org-right" />
+
+<col  class="org-right" />
+</colgroup>
+<tbody>
+<tr>
+<td class="org-right">2</td>
+<td class="org-right">0</td>
+<td class="org-right">-4.6e-16</td>
+<td class="org-right">0</td>
+<td class="org-right">4e-17</td>
+<td class="org-right">0</td>
+</tr>
+
+<tr>
+<td class="org-right">0</td>
+<td class="org-right">2</td>
+<td class="org-right">0</td>
+<td class="org-right">-4.8e-17</td>
+<td class="org-right">0</td>
+<td class="org-right">-3.5e-17</td>
+</tr>
+
+<tr>
+<td class="org-right">-4.6e-16</td>
+<td class="org-right">0</td>
+<td class="org-right">2</td>
+<td class="org-right">1.5e-20</td>
+<td class="org-right">4e-17</td>
+<td class="org-right">0</td>
+</tr>
+
+<tr>
+<td class="org-right">0</td>
+<td class="org-right">-4.8e-17</td>
+<td class="org-right">1.5e-20</td>
+<td class="org-right">0.00034</td>
+<td class="org-right">6.8e-21</td>
+<td class="org-right">4.2e-19</td>
+</tr>
+
+<tr>
+<td class="org-right">4e-17</td>
+<td class="org-right">0</td>
+<td class="org-right">4e-17</td>
+<td class="org-right">-3e-21</td>
+<td class="org-right">0.00034</td>
+<td class="org-right">-2.7e-20</td>
+</tr>
+
+<tr>
+<td class="org-right">-1.7e-19</td>
+<td class="org-right">-3.6e-17</td>
+<td class="org-right">0</td>
+<td class="org-right">4.2e-19</td>
+<td class="org-right">-2.7e-20</td>
+<td class="org-right">0.0014</td>
 </tr>
 </tbody>
 </table>
@@ -779,131 +843,21 @@ We obtain \(k_x = k_y = k_z\) and \(k_{\theta_x} = k_{\theta_y}\), but the Stiff
 </p>
 </div>
 </div>
-
-<div id="outline-container-org24bdf29" class="outline-3">
-<h3 id="org24bdf29"><span class="section-number-3">1.5</span> Conclusion</h3>
-<div class="outline-text-3" id="text-1-5">
-<div class="important">
-<ul class="org-ul">
-<li>The cubic configuration permits to have \(k_x = k_y = k_z\) and \(k_{\theta\x} = k_{\theta_y}\)</li>
-<li>The stiffness matrix \(K\) is diagonal for the cubic configuration if the Stewart platform and the cube are centered <b>and</b> the Jacobian is estimated at the cube center</li>
-</ul>
-
-</div>
-</div>
-</div>
 </div>
 
-<div id="outline-container-org2cb2ab0" class="outline-2">
-<h2 id="org2cb2ab0"><span class="section-number-2">2</span> <span class="todo TODO">TODO</span> Cubic size analysis</h2>
+<div id="outline-container-org6746f61" class="outline-2">
+<h2 id="org6746f61"><span class="section-number-2">2</span> Functions</h2>
 <div class="outline-text-2" id="text-2">
 <p>
-We here study the effect of the size of the cube used for the Stewart configuration.
-</p>
-
-<p>
-We fix the height of the Stewart platform, the center of the cube is at the center of the Stewart platform.
-</p>
-
-<p>
-We only vary the size of the cube.
-</p>
-
-<div class="org-src-container">
-<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">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-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(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>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-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>
-
-
-<p>
-The Stiffness matrix is computed for all generated Stewart platforms.
-</p>
-<div class="org-src-container">
-<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>
-
-<p>
-The only elements of \(K\) that vary are \(k_{\theta_x} = k_{\theta_y}\) and \(k_{\theta_z}\).
-</p>
-
-<p>
-Finally, we plot \(k_{\theta_x} = k_{\theta_y}\) and \(k_{\theta_z}\)
-</p>
-<div class="org-src-container">
-<pre class="src src-matlab"><span class="org-type">figure</span>;
-hold on;
-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-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="org009489e" 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>
-</div>
-
-
-<p>
-We observe that \(k_{\theta_x} = k_{\theta_y}\) and \(k_{\theta_z}\) increase linearly with the cube size.
-</p>
-
-<div class="important">
-<p>
-In order to maximize the rotational stiffness of the Stewart platform, the size of the cube should be the highest possible.
-In that case, the legs will the further separated. Size of the cube is then limited by allowed space.
-</p>
-
-</div>
-</div>
-</div>
-
-<div id="outline-container-orgeec7b47" class="outline-2">
-<h2 id="orgeec7b47"><span class="section-number-2">3</span> Functions</h2>
-<div class="outline-text-2" id="text-3">
-<p>
-<a id="orgb108018"></a>
+<a id="org2a4885e"></a>
 </p>
 </div>
 
-<div id="outline-container-org92224ef" class="outline-3">
-<h3 id="org92224ef"><span class="section-number-3">3.1</span> <code>generateCubicConfiguration</code>: Generate a Cubic Configuration</h3>
-<div class="outline-text-3" id="text-3-1">
+<div id="outline-container-org80fcb20" class="outline-3">
+<h3 id="org80fcb20"><span class="section-number-3">2.1</span> <code>generateCubicConfiguration</code>: Generate a Cubic Configuration</h3>
+<div class="outline-text-3" id="text-2-1">
 <p>
-<a id="orgb0ae4eb"></a>
+<a id="orgfe8cdfe"></a>
 </p>
 
 <p>
@@ -911,9 +865,9 @@ This Matlab function is accessible <a href="src/generateCubicConfiguration.m">he
 </p>
 </div>
 
-<div id="outline-container-org715472d" class="outline-4">
-<h4 id="org715472d">Function description</h4>
-<div class="outline-text-4" id="text-org715472d">
+<div id="outline-container-orgd3654f4" class="outline-4">
+<h4 id="orgd3654f4">Function description</h4>
+<div class="outline-text-4" id="text-orgd3654f4">
 <div class="org-src-container">
 <pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name">[stewart]</span> = <span class="org-function-name">generateCubicConfiguration</span>(<span class="org-variable-name">stewart</span>, <span class="org-variable-name">args</span>)
 <span class="org-comment">% generateCubicConfiguration - Generate a Cubic Configuration</span>
@@ -938,37 +892,37 @@ This Matlab function is accessible <a href="src/generateCubicConfiguration.m">he
 </div>
 </div>
 
-<div id="outline-container-orgbab37f8" class="outline-4">
-<h4 id="orgbab37f8">Documentation</h4>
-<div class="outline-text-4" id="text-orgbab37f8">
+<div id="outline-container-orgf1c4374" class="outline-4">
+<h4 id="orgf1c4374">Documentation</h4>
+<div class="outline-text-4" id="text-orgf1c4374">
 
-<div id="org946a873" class="figure">
+<div id="org8d1a2f5" class="figure">
 <p><img src="figs/cubic-configuration-definition.png" alt="cubic-configuration-definition.png" />
 </p>
-<p><span class="figure-number">Figure 4: </span>Cubic Configuration</p>
+<p><span class="figure-number">Figure 3: </span>Cubic Configuration</p>
 </div>
 </div>
 </div>
 
-<div id="outline-container-orgddbe42e" class="outline-4">
-<h4 id="orgddbe42e">Optional Parameters</h4>
-<div class="outline-text-4" id="text-orgddbe42e">
+<div id="outline-container-org7703a4a" class="outline-4">
+<h4 id="org7703a4a">Optional Parameters</h4>
+<div class="outline-text-4" id="text-org7703a4a">
 <div class="org-src-container">
 <pre class="src src-matlab">arguments
     stewart
     args.Hc  (1,1) double {mustBeNumeric, mustBePositive} = 60e<span class="org-type">-</span>3
     args.FOc (1,1) double {mustBeNumeric} = 50e<span class="org-type">-</span>3
-    args.FHa (1,1) double {mustBeNumeric, mustBePositive} = 15e<span class="org-type">-</span>3
-    args.MHb (1,1) double {mustBeNumeric, mustBePositive} = 15e<span class="org-type">-</span>3
+    args.FHa (1,1) double {mustBeNumeric, mustBeNonnegative} = 15e<span class="org-type">-</span>3
+    args.MHb (1,1) double {mustBeNumeric, mustBeNonnegative} = 15e<span class="org-type">-</span>3
 <span class="org-keyword">end</span>
 </pre>
 </div>
 </div>
 </div>
 
-<div id="outline-container-org66dd074" class="outline-4">
-<h4 id="org66dd074">Position of the Cube</h4>
-<div class="outline-text-4" id="text-org66dd074">
+<div id="outline-container-org43039c1" class="outline-4">
+<h4 id="org43039c1">Position of the Cube</h4>
+<div class="outline-text-4" id="text-org43039c1">
 <p>
 We define the useful points of the cube with respect to the Cube&rsquo;s center.
 \({}^{C}C\) are the 6 vertices of the cubes expressed in a frame {C} which is
@@ -993,9 +947,9 @@ CCm = [Cc(<span class="org-type">:</span>,2), Cc(<span class="org-type">:</span>
 </div>
 </div>
 
-<div id="outline-container-org388f35d" class="outline-4">
-<h4 id="org388f35d">Compute the pose</h4>
-<div class="outline-text-4" id="text-org388f35d">
+<div id="outline-container-orga18e804" class="outline-4">
+<h4 id="orga18e804">Compute the pose</h4>
+<div class="outline-text-4" id="text-orga18e804">
 <p>
 We can compute the vector of each leg \({}^{C}\hat{\bm{s}}_{i}\) (unit vector from \({}^{C}C_{f}\) to \({}^{C}C_{m}\)).
 </p>
@@ -1028,7 +982,7 @@ stewart.Mb = CCf <span class="org-type">+</span> [0; 0; args.FOc<span class="org
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Dehaeze Thomas</p>
-<p class="date">Created: 2020-02-06 jeu. 17:29</p>
+<p class="date">Created: 2020-02-06 jeu. 18:22</p>
 </div>
 </body>
 </html>
diff --git a/cubic-configuration.org b/cubic-configuration.org
index 9a92416..262caf2 100644
--- a/cubic-configuration.org
+++ b/cubic-configuration.org
@@ -21,7 +21,7 @@
 #+PROPERTY: header-args:matlab+ :output-dir figs
 :END:
 
-* Introduction                                                       :ignore:
+* Introduction                                                        :ignore:
 The discovery of the Cubic configuration is done in cite:geng94_six_degree_of_freed_activ.
 Further analysis is conducted in
 
@@ -37,7 +37,8 @@ The goal is to study the benefits of using a cubic configuration:
 - No coupling between the actuators?
 - Is the center of the cube an important point?
 
-* Matlab Init                                                :noexport:ignore:
+* Configuration Analysis - Stiffness Matrix
+** Matlab Init                                              :noexport:ignore:
 #+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
   <<matlab-dir>>
 #+end_src
@@ -50,84 +51,57 @@ The goal is to study the benefits of using a cubic configuration:
   simulinkproject('./');
 #+end_src
 
-* TODO Configuration Analysis - Stiffness Matrix
 ** Cubic Stewart platform centered with the cube center - Jacobian estimated at the cube center
 We create a cubic Stewart platform (figure [[fig:3d-cubic-stewart-aligned]]) in such a way that the center of the cube (black dot) is located at the center of the Stewart platform (blue dot).
 The Jacobian matrix is estimated at the location of the center of the cube.
 
+#+begin_src matlab
+  stewart = initializeFramesPositions('H', 100e-3, 'MO_B', -50e-3);
+  stewart = generateCubicConfiguration(stewart, 'Hc', 100e-3, 'FOc', 50e-3, 'FHa', 0, 'MHb', 0);
+  stewart = computeJointsPose(stewart);
+  stewart = initializeStrutDynamics(stewart, 'Ki', ones(6,1));
+  stewart = computeJacobian(stewart);
+#+end_src
+
 #+name: fig:3d-cubic-stewart-aligned
 #+caption: Centered cubic configuration
 [[file:./figs/3d-cubic-stewart-aligned.png]]
 
-#+begin_src matlab :results silent
-  opts = struct(...
-      'H_tot', 100, ... % Total height of the Hexapod [mm]
-      'L',     200/sqrt(3), ... % Size of the Cube [mm]
-      'H',     60, ... % Height between base joints and platform joints [mm]
-      'H0',    200/2-60/2 ... % Height between the corner of the cube and the plane containing the base joints [mm]
-      );
-  stewart = initializeCubicConfiguration(opts);
-  opts = struct(...
-      'Jd_pos', [0, 0, -50], ... % Position of the Jacobian for displacement estimation from the top of the mobile platform [mm]
-      'Jf_pos', [0, 0, -50]  ... % Position of the Jacobian for force location from the top of the mobile platform [mm]
-      );
-  stewart = computeGeometricalProperties(stewart, opts);
-
-  save('./mat/stewart.mat', 'stewart');
-#+end_src
-
-#+begin_src matlab :results none :exports code
-  K = stewart.Jf'*stewart.Jf;
-#+end_src
-
-#+begin_src matlab :results value table :exports results
-  data = K;
-  data2orgtable(data, {}, {}, ' %.2g ');
+#+begin_src matlab :exports results :results value table replace :tangle no
+  data2orgtable(stewart.K, {}, {}, ' %.2g ');
 #+end_src
 
 #+RESULTS:
-|        2 |  1.9e-18 | -2.3e-17 |  1.8e-18 |  5.5e-17 | -1.5e-17 |
-|  1.9e-18 |        2 |  6.8e-18 | -6.1e-17 | -1.6e-18 |  4.8e-18 |
-| -2.3e-17 |  6.8e-18 |        2 | -6.7e-18 |  4.9e-18 |  5.3e-19 |
-|  1.8e-18 | -6.1e-17 | -6.7e-18 |   0.0067 | -2.3e-20 | -6.1e-20 |
-|  5.5e-17 | -1.6e-18 |  4.9e-18 | -2.3e-20 |   0.0067 |    1e-18 |
-| -1.5e-17 |  4.8e-18 |  5.3e-19 | -6.1e-20 |    1e-18 |    0.027 |
+|        2 |        0 | -2.5e-16 |        0 |  2.1e-17 |       0 |
+|        0 |        2 |        0 | -7.8e-19 |        0 |       0 |
+| -2.5e-16 |        0 |        2 | -2.4e-18 | -1.4e-17 |       0 |
+|        0 | -7.8e-19 | -2.4e-18 |    0.015 | -4.3e-19 | 1.7e-18 |
+|  1.8e-17 |        0 | -1.1e-17 |        0 |    0.015 |       0 |
+|  6.6e-18 | -3.3e-18 |        0 |  1.7e-18 |        0 |    0.06 |
 
 ** Cubic Stewart platform centered with the cube center - Jacobian not estimated at the cube center
 We create a cubic Stewart platform with center of the cube located at the center of the Stewart platform (figure [[fig:3d-cubic-stewart-aligned]]).
 The Jacobian matrix is not estimated at the location of the center of the cube.
 
-#+begin_src matlab :results silent
-  opts = struct(...
-      'H_tot', 100, ... % Total height of the Hexapod [mm]
-      'L',     200/sqrt(3), ... % Size of the Cube [mm]
-      'H',     60, ... % Height between base joints and platform joints [mm]
-      'H0',    200/2-60/2 ... % Height between the corner of the cube and the plane containing the base joints [mm]
-      );
-  stewart = initializeCubicConfiguration(opts);
-  opts = struct(...
-      'Jd_pos', [0, 0, 0], ... % Position of the Jacobian for displacement estimation from the top of the mobile platform [mm]
-      'Jf_pos', [0, 0, 0]  ... % Position of the Jacobian for force location from the top of the mobile platform [mm]
-      );
-  stewart = computeGeometricalProperties(stewart, opts);
+#+begin_src matlab
+  stewart = initializeFramesPositions('H', 100e-3, 'MO_B', 0);
+  stewart = generateCubicConfiguration(stewart, 'Hc', 100e-3, 'FOc', 50e-3, 'FHa', 0, 'MHb', 0);
+  stewart = computeJointsPose(stewart);
+  stewart = initializeStrutDynamics(stewart, 'Ki', ones(6,1));
+  stewart = computeJacobian(stewart);
 #+end_src
 
-#+begin_src matlab :results none :exports code
-  K = stewart.Jf'*stewart.Jf;
-#+end_src
-
-#+begin_src matlab :results value table :exports results
-  data = K;
-  data2orgtable(data', {}, {}, ' %.2g ');
+#+begin_src matlab :exports results :results value table replace :tangle no
+  data2orgtable(stewart.K, {}, {}, ' %.2g ');
 #+end_src
 
 #+RESULTS:
-|        2 |  1.9e-18 | -2.3e-17 |  1.5e-18 |     -0.1 | -1.5e-17 |
-|  1.9e-18 |        2 |  6.8e-18 |      0.1 | -1.6e-18 |  4.8e-18 |
-| -2.3e-17 |  6.8e-18 |        2 | -5.1e-19 | -5.5e-18 |  5.3e-19 |
-|  1.5e-18 |      0.1 | -5.1e-19 |    0.012 |   -3e-19 |  3.1e-19 |
-|     -0.1 | -1.6e-18 | -5.5e-18 |   -3e-19 |    0.012 |  1.9e-18 |
-| -1.5e-17 |  4.8e-18 |  5.3e-19 |  3.1e-19 |  1.9e-18 |    0.027 |
+|        2 |        0 | -2.5e-16 | 1.4e-17 |     -0.1 |        0 |
+|        0 |        2 |        0 |     0.1 |        0 |        0 |
+| -2.5e-16 |        0 |        2 | 3.4e-18 | -1.4e-17 |        0 |
+|  1.4e-17 |      0.1 |  3.4e-18 |    0.02 |  1.1e-20 |  3.4e-18 |
+|     -0.1 |        0 | -1.4e-17 | 1.4e-19 |     0.02 | -1.7e-18 |
+|  6.6e-18 | -3.3e-18 |        0 | 3.6e-18 | -1.7e-18 |     0.06 |
 
 ** Cubic Stewart platform not centered with the cube center - Jacobian estimated at the cube center
 Here, the "center" of the Stewart platform is not at the cube center (figure [[fig:3d-cubic-stewart-misaligned]]).
@@ -137,42 +111,25 @@ The Jacobian is estimated at the cube center.
 #+caption: Not centered cubic configuration
 [[file:./figs/3d-cubic-stewart-misaligned.png]]
 
-The center of the cube is at $z = 110$.
-The Stewart platform is from $z = H_0 = 75$ to $z = H_0 + H_{tot} = 175$.
-The center height of the Stewart platform is then at $z = \frac{175-75}{2} = 50$.
-The center of the cube from the top platform is at $z = 110 - 175 = -65$.
-
-#+begin_src matlab :results silent
-  opts = struct(...
-      'H_tot', 100,         ... % Total height of the Hexapod [mm]
-      'L',     220/sqrt(3), ... % Size of the Cube [mm]
-      'H',     60,          ... % Height between base joints and platform joints [mm]
-      'H0',    75           ... % Height between the corner of the cube and the plane containing the base joints [mm]
-      );
-  stewart = initializeCubicConfiguration(opts);
-  opts = struct(...
-      'Jd_pos', [0, 0, -65], ... % Position of the Jacobian for displacement estimation from the top of the mobile platform [mm]
-      'Jf_pos', [0, 0, -65]  ... % Position of the Jacobian for force location from the top of the mobile platform [mm]
-      );
-  stewart = computeGeometricalProperties(stewart, opts);
+#+begin_src matlab
+  stewart = initializeFramesPositions('H', 80e-3, 'MO_B', -40e-3);
+  stewart = generateCubicConfiguration(stewart, 'Hc', 100e-3, 'FOc', 50e-3, 'FHa', 0, 'MHb', 0);
+  stewart = computeJointsPose(stewart);
+  stewart = initializeStrutDynamics(stewart, 'Ki', ones(6,1));
+  stewart = computeJacobian(stewart);
 #+end_src
 
-#+begin_src matlab :results none :exports code
-  K = stewart.Jf'*stewart.Jf;
-#+end_src
-
-#+begin_src matlab :results value table :exports results
-  data = K;
-  data2orgtable(data', {}, {}, ' %.2g ');
+#+begin_src matlab :exports results :results value table replace :tangle no
+  data2orgtable(stewart.K, {}, {}, ' %.2g ');
 #+end_src
 
 #+RESULTS:
-|        2 | -1.8e-17 |  2.6e-17 |  3.3e-18 |     0.04 |  1.7e-19 |
-| -1.8e-17 |        2 |  1.9e-16 |    -0.04 |  2.2e-19 | -5.3e-19 |
-|  2.6e-17 |  1.9e-16 |        2 | -8.9e-18 |  6.5e-19 | -5.8e-19 |
-|  3.3e-18 |    -0.04 | -8.9e-18 |   0.0089 | -9.3e-20 |  9.8e-20 |
-|     0.04 |  2.2e-19 |  6.5e-19 | -9.3e-20 |   0.0089 | -2.4e-18 |
-|  1.7e-19 | -5.3e-19 | -5.8e-19 |  9.8e-20 | -2.4e-18 |    0.032 |
+|        2 |        0 | -1.5e-16 |        0 |    0.04 |        0 |
+|        0 |        2 |        0 |    -0.04 |       0 | -2.8e-17 |
+| -1.5e-16 |        0 |        2 |  1.2e-18 |  -1e-17 |        0 |
+|        0 |    -0.04 |  1.2e-18 |    0.016 |       0 |  8.7e-19 |
+|     0.04 |        0 | -6.2e-18 | -1.1e-19 |   0.016 |  8.7e-19 |
+| -3.7e-19 | -2.5e-17 |        0 |  1.2e-18 | 8.7e-19 |     0.06 |
 
 We obtain $k_x = k_y = k_z$ and $k_{\theta_x} = k_{\theta_y}$, but the Stiffness matrix is not diagonal.
 
@@ -185,47 +142,71 @@ The Stewart platform is from $z = H_0 = 75$ to $z = H_0 + H_{tot} = 175$.
 The center height of the Stewart platform is then at $z = \frac{175-75}{2} = 50$.
 The center of the cube from the top platform is at $z = 110 - 175 = -65$.
 
-#+begin_src matlab :results silent
-  opts = struct(...
-      'H_tot', 100, ... % Total height of the Hexapod [mm]
-      'L',     220/sqrt(3), ... % Size of the Cube [mm]
-      'H',     60, ... % Height between base joints and platform joints [mm]
-      'H0',    75 ... % Height between the corner of the cube and the plane containing the base joints [mm]
-      );
-  stewart = initializeCubicConfiguration(opts);
-  opts = struct(...
-      'Jd_pos', [0, 0, -60], ... % Position of the Jacobian for displacement estimation from the top of the mobile platform [mm]
-      'Jf_pos', [0, 0, -60]  ... % Position of the Jacobian for force location from the top of the mobile platform [mm]
-      );
-  stewart = computeGeometricalProperties(stewart, opts);
+#+begin_src matlab
+  stewart = initializeFramesPositions('H', 80e-3, 'MO_B', -30e-3);
+  stewart = generateCubicConfiguration(stewart, 'Hc', 100e-3, 'FOc', 50e-3, 'FHa', 0, 'MHb', 0);
+  stewart = computeJointsPose(stewart);
+  stewart = initializeStrutDynamics(stewart, 'Ki', ones(6,1));
+  stewart = computeJacobian(stewart);
 #+end_src
 
-#+begin_src matlab :results none :exports code
-  K = stewart.Jf'*stewart.Jf;
-#+end_src
-
-#+begin_src matlab :results value table :exports results
-  data = K;
-  data2orgtable(data', {}, {}, ' %.2g ');
+#+begin_src matlab :exports results :results value table replace :tangle no
+  data2orgtable(stewart.K, {}, {}, ' %.2g ');
 #+end_src
 
 #+RESULTS:
-|        2 | -1.8e-17 |  2.6e-17 | -5.7e-19 |     0.03 |  1.7e-19 |
-| -1.8e-17 |        2 |  1.9e-16 |    -0.03 |  2.2e-19 | -5.3e-19 |
-|  2.6e-17 |  1.9e-16 |        2 | -1.5e-17 |  6.5e-19 | -5.8e-19 |
-| -5.7e-19 |    -0.03 | -1.5e-17 |   0.0085 |  4.9e-20 |  1.7e-19 |
-|     0.03 |  2.2e-19 |  6.5e-19 |  4.9e-20 |   0.0085 | -1.1e-18 |
-|  1.7e-19 | -5.3e-19 | -5.8e-19 |  1.7e-19 | -1.1e-18 |    0.032 |
+|        2 |        0 | -1.7e-16 |        0 |  4.9e-17 |        0 |
+|        0 |        2 |        0 | -2.2e-17 |        0 |  2.8e-17 |
+| -1.7e-16 |        0 |        2 |  1.1e-18 | -1.4e-17 |  1.4e-17 |
+|        0 | -2.2e-17 |  1.1e-18 |    0.015 |        0 |  3.5e-18 |
+|  4.4e-17 |        0 | -1.4e-17 | -5.7e-20 |    0.015 | -8.7e-19 |
+|  6.6e-18 |  2.5e-17 |        0 |  3.5e-18 | -8.7e-19 |     0.06 |
 
-We obtain $k_x = k_y = k_z$ and $k_{\theta_x} = k_{\theta_y}$, but the Stiffness matrix is not diagonal.
+We obtain $k_x = k_y = k_z$ and $k_{\theta_x} = k_{\theta_y}$, and the Stiffness matrix is diagonal.
 
 ** Conclusion
 #+begin_important
-  - The cubic configuration permits to have $k_x = k_y = k_z$ and $k_{\theta\x} = k_{\theta_y}$
-  - The stiffness matrix $K$ is diagonal for the cubic configuration if the Stewart platform and the cube are centered *and* the Jacobian is estimated at the cube center
+  - The cubic configuration permits to have $k_x = k_y = k_z$ and $k_{\theta_x} = k_{\theta_y}$
+  - The stiffness matrix $K$ is diagonal for the cubic configuration if the Jacobian is estimated at the cube center.
 #+end_important
 
-* TODO Cubic size analysis
+** Having Cube's center above the top platform
+Let's say we want to have a decouple dynamics above the top platform.
+Thus, we want the cube's center to be located above the top center.
+This is possible, to do so:
+- The position of the center of the cube should be positioned at A
+- The Height of the "useful" part of the cube should be at least equal to two times the distance from F to A.
+  It is possible to have small cube, but then to configuration is a little bit strange.
+
+#+begin_src matlab
+  stewart = initializeFramesPositions('H', 100e-3, 'MO_B', 50e-3);
+  FOc = stewart.H + stewart.MO_B(3);
+  Hc = 2*(stewart.H + stewart.MO_B(3));
+  stewart = generateCubicConfiguration(stewart, 'Hc', Hc, 'FOc', FOc, 'FHa', 10e-3, 'MHb', 10e-3);
+  stewart = computeJointsPose(stewart);
+  stewart = initializeStrutDynamics(stewart, 'Ki', ones(6,1));
+  stewart = initializeJointDynamics(stewart, 'disable', true);
+  stewart = initializeCylindricalPlatforms(stewart);
+  stewart = initializeCylindricalStruts(stewart);
+  stewart = computeJacobian(stewart);
+  stewart = initializeStewartPose(stewart);
+#+end_src
+
+#+begin_src matlab :exports results :results value table replace :tangle no
+  data2orgtable(stewart.K, {}, {}, ' %.2g ');
+#+end_src
+
+#+RESULTS:
+|        2 |        0 | -4.6e-16 |        0 |    4e-17 |        0 |
+|        0 |        2 |        0 | -4.8e-17 |        0 | -3.5e-17 |
+| -4.6e-16 |        0 |        2 |  1.5e-20 |    4e-17 |        0 |
+|        0 | -4.8e-17 |  1.5e-20 |  0.00034 |  6.8e-21 |  4.2e-19 |
+|    4e-17 |        0 |    4e-17 |   -3e-21 |  0.00034 | -2.7e-20 |
+| -1.7e-19 | -3.6e-17 |        0 |  4.2e-19 | -2.7e-20 |   0.0014 |
+
+We obtain $k_x = k_y = k_z$ and $k_{\theta_x} = k_{\theta_y}$, but the Stiffness matrix is not diagonal.
+
+* TODO Cubic size analysis                                          :noexport:
 We here study the effect of the size of the cube used for the Stewart configuration.
 
 We fix the height of the Stewart platform, the center of the cube is at the center of the Stewart platform.
@@ -260,7 +241,6 @@ We only vary the size of the cube.
   end
 #+end_src
 
-
 The Stiffness matrix is computed for all generated Stewart platforms.
 #+begin_src matlab :results none :exports code
   Ks = zeros(6, 6, length(H_cube));
@@ -355,8 +335,8 @@ This Matlab function is accessible [[file:src/generateCubicConfiguration.m][here
       stewart
       args.Hc  (1,1) double {mustBeNumeric, mustBePositive} = 60e-3
       args.FOc (1,1) double {mustBeNumeric} = 50e-3
-      args.FHa (1,1) double {mustBeNumeric, mustBePositive} = 15e-3
-      args.MHb (1,1) double {mustBeNumeric, mustBePositive} = 15e-3
+      args.FHa (1,1) double {mustBeNumeric, mustBeNonnegative} = 15e-3
+      args.MHb (1,1) double {mustBeNumeric, mustBeNonnegative} = 15e-3
   end
 #+end_src
 
diff --git a/src/generateCubicConfiguration.m b/src/generateCubicConfiguration.m
index 8bc48dc..920cfdf 100644
--- a/src/generateCubicConfiguration.m
+++ b/src/generateCubicConfiguration.m
@@ -21,8 +21,8 @@ arguments
     stewart
     args.Hc  (1,1) double {mustBeNumeric, mustBePositive} = 60e-3
     args.FOc (1,1) double {mustBeNumeric} = 50e-3
-    args.FHa (1,1) double {mustBeNumeric, mustBePositive} = 15e-3
-    args.MHb (1,1) double {mustBeNumeric, mustBePositive} = 15e-3
+    args.FHa (1,1) double {mustBeNumeric, mustBeNonnegative} = 15e-3
+    args.MHb (1,1) double {mustBeNumeric, mustBeNonnegative} = 15e-3
 end
 
 sx = [ 2; -1; -1];

1.9e-18	-2.3e-17	1.8e-18	5.5e-17	-1.5e-17	0	-2.5e-16	0	2.1e-17	0
1.9e-18	0	2	6.8e-18	-6.1e-17	-1.6e-18	4.8e-18	0	-7.8e-19	0	0
-2.3e-17	6.8e-18	-2.5e-16	0	2	-6.7e-18	4.9e-18	5.3e-19	-2.4e-18	-1.4e-17	0
1.8e-18	-6.1e-17	-6.7e-18	0.0067	-2.3e-20	-6.1e-20	0	-7.8e-19	-2.4e-18	0.015	-4.3e-19	1.7e-18
5.5e-17	-1.6e-18	4.9e-18	-2.3e-20	0.0067	1e-18	1.8e-17	0	-1.1e-17	0	0.015	0
-1.5e-17	4.8e-18	5.3e-19	-6.1e-20	1e-18	0.027	6.6e-18	-3.3e-18	0	1.7e-18	0	0.06
2	0	-4.6e-16	0	4e-17	0
0	2	0	-4.8e-17	0	-3.5e-17
-4.6e-16	0	2	1.5e-20	4e-17	0
0	-4.8e-17	1.5e-20	0.00034	6.8e-21	4.2e-19
4e-17	0	4e-17	-3e-21	0.00034	-2.7e-20
-1.7e-19	-3.6e-17	0	4.2e-19	-2.7e-20	0.0014