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Thomas Dehaeze 2020-06-22 14:45:27 +02:00
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commit 441d036bd9
18 changed files with 1738 additions and 250 deletions
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<div id="org-div-home-and-up">
@ -232,14 +22,432 @@
<a accesskey="H" href="../index.html"> HOME </a>
</div><div id="content">
<h1 class="title">Tikz Figures</h1>
<div id="table-of-contents">
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#orgfc691a5">1. X-Y Rotating Positioning Platform</a></li>
<li><a href="#org221a454">2. X-Y Rotating Positioning Platform with Force Sensors</a></li>
<li><a href="#org7cc7ccb">3. Decentralized Integral Force Feedback</a></li>
<li><a href="#orgbd891cf">4. Decentralized Direct Velocity Feedback</a></li>
<li><a href="#orgedc1f23">5. Springs in parallel</a></li>
</ul>
</div>
</div>
<p>
Configuration file is accessible <a href="config.html">here</a>.
</p>
<div id="outline-container-orgfc691a5" class="outline-2">
<h2 id="orgfc691a5"><span class="section-number-2">1</span> X-Y Rotating Positioning Platform</h2>
<div class="outline-text-2" id="text-1">
<div class="org-src-container">
<pre class="src src-latex">\begin{tikzpicture}
% Angle
\def\thetau{25}
% Rotational Stage
\draw[fill=black!60!white] (0, 0) circle (4.3);
\draw[fill=black!40!white] (0, 0) circle (3.8);
% Label
\node[anchor=north west, rotate=\thetau] at (-2.5, 2.5) {\small Rotating Stage};
% Rotating Scope
\begin{scope}[rotate=\thetau]
% Rotating Frame
\draw[fill=black!20!white] (-2.6, -2.6) rectangle (2.6, 2.6);
% Label
\node[anchor=north west, rotate=\thetau] at (-2.6, 2.6) {\small X-Y Stage};
% Mass
\draw[fill=white] (-1, -1) rectangle (1, 1);
% Label
\node[anchor=south west, rotate=\thetau] at (-1, -1) {\small Payload};
% Attached Points
\node[] at (-1, 0){$\bullet$};
\draw[] (-1, 0) -- ++(-0.2, 0) coordinate(cu);
\draw[] ($(cu) + (0, -0.8)$) coordinate(actu) -- ($(cu) + (0, 0.8)$) coordinate(ku);
\node[] at (0, -1){$\bullet$};
\draw[] (0, -1) -- ++(0, -0.2) coordinate(cv);
\draw[] ($(cv) + (-0.8, 0)$)coordinate(kv) -- ($(cv) + (0.8, 0)$) coordinate(actv);
% Spring and Actuator for U
\draw[actuator={0.6}{0.2}] (actu) -- node[above=0.1, rotate=\thetau]{$F_u$} (actu-|-2.6,0);
\draw[spring=0.2] (ku) -- node[above=0.1, rotate=\thetau]{$k$} (ku-|-2.6,0);
\draw[damper={8}{8}] (cu) -- node[above left=0.2 and -0.1, rotate=\thetau]{$c$} (cu-|-2.6,0);
\draw[actuator={0.6}{0.2}] (actv) -- node[left, rotate=\thetau]{$F_v$} (actv|-0,-2.6);
\draw[spring=0.2] (kv) -- node[left, rotate=\thetau]{$k$} (kv|-0,-2.6);
\draw[damper={8}{8}] (cv) -- node[left=0.1, rotate=\thetau]{$c$} (cv|-0,-2.6);
% % Displacement measurement
% \draw[&lt;-&gt;, dashed] (-2.6, -0.8) --node[midway, below, rotate=\thetau]{$d_u$} (-1 , -0.8);
% \draw[&lt;-&gt;, dashed] ( 0.8, -2.6) --node[midway, right, rotate=\thetau]{$d_v$} ( 0.8, -1);
\end{scope}
% Inertial Frame
\draw[-&gt;] (-4, -4) -- ++(2, 0) node[below]{$\vec{i}_x$};
\draw[-&gt;] (-4, -4) -- ++(0, 2) node[left]{$\vec{i}_y$};
\draw[fill, color=black] (-4, -4) circle (0.06);
\node[draw, circle, inner sep=0pt, minimum size=0.3cm, label=left:$\vec{i}_z$] at (-4, -4){};
\draw[-&gt;] (0, 0) -- ++(\thetau:2) node[above, rotate=\thetau]{$\vec{i}_u$};
\draw[-&gt;] (0, 0) -- ++(\thetau+90:2) node[left, rotate=\thetau]{$\vec{i}_v$};
\draw[dashed] (0, 0) -- ++(2, 0);
\draw[] (1.5, 0) arc (0:\thetau:1.5) node[midway, right]{$\theta$};
\node[] at (0,0) {$\bullet$};
\node[left] at (0,0) {$(x, y)$};
\draw[-&gt;] (3.5, 0) arc (0:40:3.5) node[midway, left]{$\Omega$};
\end{tikzpicture}
</pre>
</div>
<div class="figure">
<p><img src="figs/system.png" alt="system.png" />
</p>
</div>
</div>
</div>
<div id="outline-container-org221a454" class="outline-2">
<h2 id="org221a454"><span class="section-number-2">2</span> X-Y Rotating Positioning Platform with Force Sensors</h2>
<div class="outline-text-2" id="text-2">
<div class="org-src-container">
<pre class="src src-latex">\begin{tikzpicture}
% Angle
\def\thetau{25}
% Rotational Stage
\draw[fill=black!60!white] (0, 0) circle (4.3);
\draw[fill=black!40!white] (0, 0) circle (3.8);
% Label
\node[anchor=north west, rotate=\thetau] at (-2.5, 2.5) {\small Rotating Stage};
% Rotating Scope
\begin{scope}[rotate=\thetau]
% Rotating Frame
\draw[fill=black!20!white] (-2.6, -2.6) rectangle (2.6, 2.6);
% Label
\node[anchor=north west, rotate=\thetau] at (-2.6, 2.6) {\small X-Y Stage};
% Mass
\draw[fill=white] (-1, -1) rectangle (1, 1);
% Label
\node[anchor=south west, rotate=\thetau] at (-1, -1) {\small Payload};
% Attached Points
\node[] at (-1, 0){$\bullet$};
\draw[] (-1, 0) -- ++(-0.2, 0) coordinate(au);
\node[] at (0, -1){$\bullet$};
\draw[] (0, -1) -- ++(0, -0.2) coordinate(av);
% Force Sensors
\draw[fill=white] ($(au) + (-0.2, -0.5)$) rectangle ($(au) + (0, 0.5)$);
\draw[] ($(au) + (-0.2, -0.5)$)coordinate(actu) -- ($(au) + (0, 0.5)$);
\draw[] ($(au) + (-0.2, 0.5)$)coordinate(ku) node[above=0.1, rotate=\thetau]{$f_{u}$} -- ($(au) + (0, -0.5)$);
\draw[fill=white] ($(av) + (-0.5, -0.2)$) rectangle ($(av) + (0.5, 0)$);
\draw[] ($(av) + ( 0.5, -0.2)$)coordinate(actv) -- ($(av) + (-0.5, 0)$);
\draw[] ($(av) + (-0.5, -0.2)$)coordinate(kv) node[left=0.1, rotate=\thetau]{$f_{v}$} -- ($(av) + ( 0.5, 0)$);
% Spring and Actuator for U
\draw[actuator={0.6}{0.2}] (actu) -- node[above=0.1, rotate=\thetau]{$F_u$} (actu-|-2.6,0);
\draw[spring=0.2] (ku) -- node[above=0.1, rotate=\thetau]{$k$} (ku-|-2.6,0);
\draw[actuator={0.6}{0.2}] (actv) -- node[left, rotate=\thetau]{$F_v$} (actv|-0,-2.6);
\draw[spring=0.2] (kv) -- node[left, rotate=\thetau]{$k$} (kv|-0,-2.6);
\end{scope}
% Inertial Frame
\draw[-&gt;] (-4, -4) -- ++(2, 0) node[below]{$\vec{i}_x$};
\draw[-&gt;] (-4, -4) -- ++(0, 2) node[left]{$\vec{i}_y$};
\draw[fill, color=black] (-4, -4) circle (0.06);
\node[draw, circle, inner sep=0pt, minimum size=0.3cm, label=left:$\vec{i}_z$] at (-4, -4){};
\draw[-&gt;] (0, 0) -- ++(\thetau:2) node[above, rotate=\thetau]{$\vec{i}_u$};
\draw[-&gt;] (0, 0) -- ++(\thetau+90:2) node[left, rotate=\thetau]{$\vec{i}_v$};
\draw[dashed] (0, 0) -- ++(2, 0);
\draw[] (1.5, 0) arc (0:\thetau:1.5) node[midway, right]{$\theta$};
\node[] at (0,0) {$\bullet$};
\node[left] at (0,0) {$(x, y)$};
\draw[-&gt;] (3.5, 0) arc (0:40:3.5) node[midway, left]{$\Omega$};
\end{tikzpicture}
</pre>
</div>
<div class="figure">
<p><img src="figs/system_force_sensors.png" alt="system_force_sensors.png" />
</p>
</div>
</div>
</div>
<div id="outline-container-org7cc7ccb" class="outline-2">
<h2 id="org7cc7ccb"><span class="section-number-2">3</span> Decentralized Integral Force Feedback</h2>
<div class="outline-text-2" id="text-3">
<div class="org-src-container">
<pre class="src src-latex">\begin{tikzpicture}
% Angle
\def\thetau{25}
% Rotational Stage
\draw[fill=black!60!white] (0, 0) circle (4.3);
\draw[fill=black!40!white] (0, 0) circle (3.8);
% Label
\node[anchor=north west, rotate=\thetau] at (-2.5, 2.5) {\small Rotating Stage};
% Rotating Scope
\begin{scope}[rotate=\thetau]
% Rotating Frame
\draw[fill=black!20!white] (-2.6, -2.6) rectangle (2.6, 2.6);
% Label
\node[anchor=north west, rotate=\thetau] at (-2.6, 2.6) {\small X-Y Stage};
% Mass
\draw[fill=white] (-1, -1) rectangle (1, 1);
% Label
\node[anchor=south west, rotate=\thetau] at (-1, -1) {\small Payload};
% Attached Points
\node[] at (-1, 0){$\bullet$};
\draw[] (-1, 0) -- ++(-0.2, 0) coordinate(au);
\node[] at (0, -1){$\bullet$};
\draw[] (0, -1) -- ++(0, -0.2) coordinate(av);
% Force Sensors
\draw[fill=white] ($(au) + (-0.2, -0.5)$) rectangle ($(au) + (0, 0.5)$);
\draw[] ($(au) + (-0.2, -0.5)$)coordinate(actu) -- ($(au) + (0, 0.5)$);
\draw[] ($(au) + (-0.2, 0.5)$)coordinate(ku) node[above=0.1, rotate=\thetau]{$f_{u}$} -- ($(au) + (0, -0.5)$);
\node[above, rotate=\thetau] at ($(av) + (-0.1, 0.5)$) {$f_{u}$};
\draw[fill=white] ($(av) + (-0.5, -0.2)$) rectangle ($(av) + (0.5, 0)$);
\draw[] ($(av) + ( 0.5, -0.2)$)coordinate(actv) -- ($(av) + (-0.5, 0)$);
\draw[] ($(av) + (-0.5, -0.2)$)coordinate(kv) -- ($(av) + ( 0.5, 0)$);
\node[left, rotate=\thetau] at ($(av) + (-0.5, -0.1)$) {$f_{v}$};
% Spring and Actuator for U
\draw[actuator={0.6}{0.2}] (actu) -- coordinate[midway](actumid) (actu-|-2.6,0);
\draw[spring=0.2] (ku) -- node[above=0.1, rotate=\thetau]{$k$} (ku-|-2.6,0);
% \draw[actuator={0.6}{0.2}] (actv) -- node[right, rotate=\thetau]{$F_v$} (actv|-0,-2.6);
\draw[actuator={0.6}{0.2}] (actv) -- coordinate[midway](actvmid) (actv|-0,-2.6);
\draw[spring=0.2] (kv) -- node[left, rotate=\thetau]{$k$} (kv|-0,-2.6);
\node[block={0.8cm}{0.6cm}, rotate=\thetau] (Ku) at ($(actumid) + (0, -1.2)$) {$K_{F}$};
\draw[-&gt;] ($(au) + (-0.1, -0.5)$) |- (Ku.east);
\draw[-&gt;] (Ku.north) -- ($(actumid) + (0, -0.1)$) node[below left, rotate=\thetau]{$F_u$};
\node[block={0.8cm}{0.6cm}, rotate=\thetau] (Kv) at ($(actvmid) + (1.2, 0)$) {$K_{F}$};
\draw[-&gt;] ($(av) + (0.5, -0.1)$) -| (Kv.north);
\draw[-&gt;] (Kv.west) -- ($(actvmid) + (0.1, 0)$) node[below right, rotate=\thetau]{$F_v$};
\end{scope}
% Inertial Frame
\draw[-&gt;] (-4, -4) -- ++(2, 0) node[below]{$\vec{i}_x$};
\draw[-&gt;] (-4, -4) -- ++(0, 2) node[left]{$\vec{i}_y$};
\draw[fill, color=black] (-4, -4) circle (0.06);
\node[draw, circle, inner sep=0pt, minimum size=0.3cm, label=left:$\vec{i}_z$] at (-4, -4){};
\draw[-&gt;] (0, 0) -- ++(\thetau:2) node[above, rotate=\thetau]{$\vec{i}_u$};
\draw[-&gt;] (0, 0) -- ++(\thetau+90:2) node[left, rotate=\thetau]{$\vec{i}_v$};
\draw[dashed] (0, 0) -- ++(2, 0);
\draw[] (1.5, 0) arc (0:\thetau:1.5) node[midway, right]{$\theta$};
\node[] at (0,0) {$\bullet$};
\node[left] at (0,0) {$(x, y)$};
\draw[-&gt;] (3.5, 0) arc (0:40:3.5) node[midway, left]{$\Omega$};
\end{tikzpicture}
</pre>
</div>
<div class="figure">
<p><img src="figs/system_iff.png" alt="system_iff.png" />
</p>
</div>
</div>
</div>
<div id="outline-container-orgbd891cf" class="outline-2">
<h2 id="orgbd891cf"><span class="section-number-2">4</span> Decentralized Direct Velocity Feedback</h2>
<div class="outline-text-2" id="text-4">
<div class="org-src-container">
<pre class="src src-latex">\begin{tikzpicture}
% Angle
\def\thetau{25}
% Rotational Stage
\draw[fill=black!60!white] (0, 0) circle (4.3);
\draw[fill=black!40!white] (0, 0) circle (3.8);
% Label
\node[anchor=north west, rotate=\thetau] at (-2.5, 2.5) {\small Rotating Stage};
% Rotating Scope
\begin{scope}[rotate=\thetau]
% Rotating Frame
\draw[fill=black!20!white] (-2.6, -2.6) rectangle (2.6, 2.6);
% Label
\node[anchor=north west, rotate=\thetau] at (-2.6, 2.6) {\small X-Y Stage};
% Mass
\draw[fill=white] (-1, -1) rectangle (1, 1);
% Label
\node[anchor=south west, rotate=\thetau] at (-1, -1) {\small Payload};
% Attached Points
\node[] at (-1, 0){$\bullet$};
\draw[] (-1, 0) -- ++(-0.2, 0) coordinate(au);
\node[] at (0, -1){$\bullet$};
\draw[] (0, -1) -- ++(0, -0.2) coordinate(av);
% Attached Points
\node[] at (-1, 0){$\bullet$};
\draw[] (-1, 0) -- ++(-0.2, 0) coordinate(cu);
\draw[] ($(cu) + (0, -0.5)$) coordinate(actu) -- ($(cu) + (0, 0.5)$) coordinate(ku);
\node[] at (0, -1){$\bullet$};
\draw[] (0, -1) -- ++(0, -0.2) coordinate(cv);
\draw[] ($(cv) + (-0.5, 0)$)coordinate(kv) -- ($(cv) + (0.5, 0)$) coordinate(actv);
% Spring and Actuator for U
\draw[actuator={0.6}{0.2}] (actu) -- coordinate[midway](actumid) (actu-|-2.6,0);
\draw[spring=0.2] (ku) -- node[above=0.1, rotate=\thetau]{$k$} (ku-|-2.6,0);
\draw[actuator={0.6}{0.2}] (actv) -- coordinate[midway](actvmid) (actv|-0,-2.6);
\draw[spring=0.2] (kv) -- node[left, rotate=\thetau]{$k$} (kv|-0,-2.6);
% Displacement measurement
\draw[&lt;-&gt;, dashed] (-2.6, -0.8) -- (-1 , -0.8) coordinate(dutop);
\draw[&lt;-&gt;, dashed] ( 0.8, -2.6) -- ( 0.8, -1) coordinate(dvtop);
% Controllers
\node[block={0.6cm}{0.6cm}, rotate=\thetau] (Ku) at ($(actumid) + (0, -1.2)$) {$K_{V}$};
\draw[-&gt;] ($(dutop) + (-0.1, 0)$) node[below left, rotate=\thetau]{$v_u$} |- (Ku.east);
\draw[-&gt;] (Ku.north) -- ($(actumid) + (0, -0.1)$);
\node[block={0.6cm}{0.6cm}, rotate=\thetau] (Kv) at ($(actvmid) + (1.2, 0)$) {$K_{V}$};
\draw[-&gt;] ($(dvtop) + (0, -0.1)$) node[below right, rotate=\thetau]{$v_v$} -| (Kv.north);
\draw[-&gt;] (Kv.west) -- ($(actvmid) + (0.1, 0)$);
\node[above=0.1, rotate=\thetau] at (actumid) {$F_u$};
\node[left=0.1, rotate=\thetau] at (actvmid) {$F_v$};
\end{scope}
% Inertial Frame
\draw[-&gt;] (-4, -4) -- ++(2, 0) node[below]{$\vec{i}_x$};
\draw[-&gt;] (-4, -4) -- ++(0, 2) node[left]{$\vec{i}_y$};
\draw[fill, color=black] (-4, -4) circle (0.06);
\node[draw, circle, inner sep=0pt, minimum size=0.3cm, label=left:$\vec{i}_z$] at (-4, -4){};
\draw[-&gt;] (0, 0) -- ++(\thetau:2) node[above, rotate=\thetau]{$\vec{i}_u$};
\draw[-&gt;] (0, 0) -- ++(\thetau+90:2) node[left, rotate=\thetau]{$\vec{i}_v$};
\draw[dashed] (0, 0) -- ++(2, 0);
\draw[] (1.5, 0) arc (0:\thetau:1.5) node[midway, right]{$\theta$};
\node[] at (0,0) {$\bullet$};
\node[left] at (0,0) {$(x, y)$};
\draw[-&gt;] (3.5, 0) arc (0:40:3.5) node[midway, left]{$\Omega$};
\end{tikzpicture}
</pre>
</div>
<div class="figure">
<p><img src="figs/system_dvf.png" alt="system_dvf.png" />
</p>
</div>
</div>
</div>
<div id="outline-container-orgedc1f23" class="outline-2">
<h2 id="orgedc1f23"><span class="section-number-2">5</span> Springs in parallel</h2>
<div class="outline-text-2" id="text-5">
<div class="org-src-container">
<pre class="src src-latex">\begin{tikzpicture}
% Angle
\def\thetau{25}
% Rotational Stage
\draw[fill=black!60!white] (0, 0) circle (4.3);
\draw[fill=black!40!white] (0, 0) circle (3.8);
% Label
\node[anchor=north west, rotate=\thetau] at (-2.5, 2.5) {\small Rotating Stage};
% Rotating Scope
\begin{scope}[rotate=\thetau]
% Rotating Frame
\draw[fill=black!20!white] (-2.6, -2.6) rectangle (2.6, 2.6);
% Label
\node[anchor=north west, rotate=\thetau] at (-2.6, 2.6) {\small X-Y Stage};
% Mass
\draw[fill=white] (-1, -1) rectangle (1, 1);
% Label
\node[anchor=south west, rotate=\thetau] at (-1, -1) {\small Payload};
% Attached Points
\draw[] (-1, 0) -- ++(-0.2, 0) coordinate(au);
\draw[] (0, -1) -- ++(0, -0.2) coordinate(av);
% Force Sensors
\draw[fill=white] ($(au) + (-0.2, -0.5)$) rectangle ($(au) + (0, 0.5)$);
\draw[] ($(au) + (-0.2, -0.5)$)coordinate(actu) -- ($(au) + (0, 0.5)$);
\draw[] ($(au) + (-0.2, 0.5)$)coordinate(ku) -- ($(au) + (0, -0.5)$);
\node[below=0.1, rotate=\thetau] at ($(au) + (-0.1, -0.5)$) {$f_{u}$}
\draw[fill=white] ($(av) + (-0.5, -0.2)$) rectangle ($(av) + (0.5, 0)$);
\draw[] ($(av) + ( 0.5, -0.2)$)coordinate(actv) -- ($(av) + (-0.5, 0)$);
\draw[] ($(av) + (-0.5, -0.2)$)coordinate(kv) -- ($(av) + ( 0.5, 0)$) ;
\node[right=0.1, rotate=\thetau] at ($(av) + (0.5, -0.1)$) {$f_{v}$}
% Spring and Actuator for U
\draw[actuator={0.6}{0.2}] (actu) -- node[below=0.1, rotate=\thetau]{$F_u$} (actu-|-2.6,0);
\draw[spring=0.2] (ku) -- node[below=0.1, rotate=\thetau]{$k$} (ku-|-2.6,0);
\draw[spring=0.2] (-1, 0.8) -- node[above=0.1, rotate=\thetau]{$k_{p}$} (-1, 0.8-|-2.6,0);
\draw[actuator={0.6}{0.2}] (actv) -- node[right=0.1, rotate=\thetau]{$F_v$} (actv|-0,-2.6);
\draw[spring=0.2] (kv) -- node[right=0.1, rotate=\thetau]{$k$} (kv|-0,-2.6);
\draw[spring=0.2] (-0.8, -1) -- node[left=0.1, rotate=\thetau]{$k_{p}$} (-0.8, -1|-0,-2.6);
\end{scope}
% Inertial Frame
\draw[-&gt;] (-4, -4) -- ++(2, 0) node[below]{$\vec{i}_x$};
\draw[-&gt;] (-4, -4) -- ++(0, 2) node[left]{$\vec{i}_y$};
\draw[fill, color=black] (-4, -4) circle (0.06);
\node[draw, circle, inner sep=0pt, minimum size=0.3cm, label=left:$\vec{i}_z$] at (-4, -4){};
\draw[-&gt;] (0, 0) -- ++(\thetau:2) node[above, rotate=\thetau]{$\vec{i}_u$};
\draw[-&gt;] (0, 0) -- ++(\thetau+90:2) node[left, rotate=\thetau]{$\vec{i}_v$};
\draw[dashed] (0, 0) -- ++(2, 0);
\draw[] (1.5, 0) arc (0:\thetau:1.5) node[midway, right]{$\theta$};
\node[] at (0,0) {$\bullet$};
\node[left] at (0,0) {$(x, y)$};
\draw[-&gt;] (3.5, 0) arc (0:40:3.5) node[midway, left]{$\Omega$};
\end{tikzpicture}
</pre>
</div>
<div class="figure">
<p><img src="figs/system_parallel_springs.png" alt="system_parallel_springs.png" />
</p>
</div>
</div>
</div>
</div>
<div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2020-03-16 lun. 10:52</p>
<p class="author">Author: Thomas Dehaeze</p>
<p class="date">Created: 2020-06-22 lun. 14:45</p>
</div>
</body>
</html>

243
tikz/index.org
View File

@ -26,7 +26,74 @@
Configuration file is accessible [[file:config.org][here]].
* X-Y Rotating Positioning Platform
#+begin_src latex :file rotating_xy_platform.pdf
#+begin_src latex :file system.pdf
\begin{tikzpicture}
% Angle
\def\thetau{25}
% Rotational Stage
\draw[fill=black!60!white] (0, 0) circle (4.3);
\draw[fill=black!40!white] (0, 0) circle (3.8);
% Label
\node[anchor=north west, rotate=\thetau] at (-2.5, 2.5) {\small Rotating Stage};
% Rotating Scope
\begin{scope}[rotate=\thetau]
% Rotating Frame
\draw[fill=black!20!white] (-2.6, -2.6) rectangle (2.6, 2.6);
% Label
\node[anchor=north west, rotate=\thetau] at (-2.6, 2.6) {\small X-Y Stage};
% Mass
\draw[fill=white] (-1, -1) rectangle (1, 1);
% Label
\node[anchor=south west, rotate=\thetau] at (-1, -1) {\small Payload};
% Attached Points
\node[] at (-1, 0){$\bullet$};
\draw[] (-1, 0) -- ++(-0.2, 0) coordinate(cu);
\draw[] ($(cu) + (0, -0.8)$) coordinate(actu) -- ($(cu) + (0, 0.8)$) coordinate(ku);
\node[] at (0, -1){$\bullet$};
\draw[] (0, -1) -- ++(0, -0.2) coordinate(cv);
\draw[] ($(cv) + (-0.8, 0)$)coordinate(kv) -- ($(cv) + (0.8, 0)$) coordinate(actv);
% Spring and Actuator for U
\draw[actuator={0.6}{0.2}] (actu) -- node[above=0.1, rotate=\thetau]{$F_u$} (actu-|-2.6,0);
\draw[spring=0.2] (ku) -- node[above=0.1, rotate=\thetau]{$k$} (ku-|-2.6,0);
\draw[damper={8}{8}] (cu) -- node[above left=0.2 and -0.1, rotate=\thetau]{$c$} (cu-|-2.6,0);
\draw[actuator={0.6}{0.2}] (actv) -- node[left, rotate=\thetau]{$F_v$} (actv|-0,-2.6);
\draw[spring=0.2] (kv) -- node[left, rotate=\thetau]{$k$} (kv|-0,-2.6);
\draw[damper={8}{8}] (cv) -- node[left=0.1, rotate=\thetau]{$c$} (cv|-0,-2.6);
% % Displacement measurement
% \draw[<->, dashed] (-2.6, -0.8) --node[midway, below, rotate=\thetau]{$d_u$} (-1 , -0.8);
% \draw[<->, dashed] ( 0.8, -2.6) --node[midway, right, rotate=\thetau]{$d_v$} ( 0.8, -1);
\end{scope}
% Inertial Frame
\draw[->] (-4, -4) -- ++(2, 0) node[below]{$\vec{i}_x$};
\draw[->] (-4, -4) -- ++(0, 2) node[left]{$\vec{i}_y$};
\draw[fill, color=black] (-4, -4) circle (0.06);
\node[draw, circle, inner sep=0pt, minimum size=0.3cm, label=left:$\vec{i}_z$] at (-4, -4){};
\draw[->] (0, 0) -- ++(\thetau:2) node[above, rotate=\thetau]{$\vec{i}_u$};
\draw[->] (0, 0) -- ++(\thetau+90:2) node[left, rotate=\thetau]{$\vec{i}_v$};
\draw[dashed] (0, 0) -- ++(2, 0);
\draw[] (1.5, 0) arc (0:\thetau:1.5) node[midway, right]{$\theta$};
\node[] at (0,0) {$\bullet$};
\node[left] at (0,0) {$(x, y)$};
\draw[->] (3.5, 0) arc (0:40:3.5) node[midway, left]{$\Omega$};
\end{tikzpicture}
#+end_src
#+RESULTS:
[[file:figs/system.png]]
* X-Y Rotating Positioning Platform with Force Sensors
#+begin_src latex :file system_force_sensors.pdf
\begin{tikzpicture}
% Angle
\def\thetau{25}
@ -71,10 +138,6 @@ Configuration file is accessible [[file:config.org][here]].
\draw[actuator={0.6}{0.2}] (actv) -- node[left, rotate=\thetau]{$F_v$} (actv|-0,-2.6);
\draw[spring=0.2] (kv) -- node[left, rotate=\thetau]{$k$} (kv|-0,-2.6);
% Displacement measurement
\draw[<->, dashed] (-2.6, -0.8) --node[midway, below, rotate=\thetau]{$d_u$} (-1 , -0.8);
\draw[<->, dashed] ( 0.8, -2.6) --node[midway, right, rotate=\thetau]{$d_v$} ( 0.8, -1);
\end{scope}
% Inertial Frame
@ -95,10 +158,172 @@ Configuration file is accessible [[file:config.org][here]].
#+end_src
#+RESULTS:
[[file:figs/rotating_xy_platform.png]]
[[file:figs/system_force_sensors.png]]
* X-Y Rotating Positioning Platform with Springs in parallel
#+begin_src latex :file rotating_xy_platform_springs.pdf
* Decentralized Integral Force Feedback
#+begin_src latex :file system_iff.pdf
\begin{tikzpicture}
% Angle
\def\thetau{25}
% Rotational Stage
\draw[fill=black!60!white] (0, 0) circle (4.3);
\draw[fill=black!40!white] (0, 0) circle (3.8);
% Label
\node[anchor=north west, rotate=\thetau] at (-2.5, 2.5) {\small Rotating Stage};
% Rotating Scope
\begin{scope}[rotate=\thetau]
% Rotating Frame
\draw[fill=black!20!white] (-2.6, -2.6) rectangle (2.6, 2.6);
% Label
\node[anchor=north west, rotate=\thetau] at (-2.6, 2.6) {\small X-Y Stage};
% Mass
\draw[fill=white] (-1, -1) rectangle (1, 1);
% Label
\node[anchor=south west, rotate=\thetau] at (-1, -1) {\small Payload};
% Attached Points
\node[] at (-1, 0){$\bullet$};
\draw[] (-1, 0) -- ++(-0.2, 0) coordinate(au);
\node[] at (0, -1){$\bullet$};
\draw[] (0, -1) -- ++(0, -0.2) coordinate(av);
% Force Sensors
\draw[fill=white] ($(au) + (-0.2, -0.5)$) rectangle ($(au) + (0, 0.5)$);
\draw[] ($(au) + (-0.2, -0.5)$)coordinate(actu) -- ($(au) + (0, 0.5)$);
\draw[] ($(au) + (-0.2, 0.5)$)coordinate(ku) node[above=0.1, rotate=\thetau]{$f_{u}$} -- ($(au) + (0, -0.5)$);
\node[above, rotate=\thetau] at ($(av) + (-0.1, 0.5)$) {$f_{u}$};
\draw[fill=white] ($(av) + (-0.5, -0.2)$) rectangle ($(av) + (0.5, 0)$);
\draw[] ($(av) + ( 0.5, -0.2)$)coordinate(actv) -- ($(av) + (-0.5, 0)$);
\draw[] ($(av) + (-0.5, -0.2)$)coordinate(kv) -- ($(av) + ( 0.5, 0)$);
\node[left, rotate=\thetau] at ($(av) + (-0.5, -0.1)$) {$f_{v}$};
% Spring and Actuator for U
\draw[actuator={0.6}{0.2}] (actu) -- coordinate[midway](actumid) (actu-|-2.6,0);
\draw[spring=0.2] (ku) -- node[above=0.1, rotate=\thetau]{$k$} (ku-|-2.6,0);
% \draw[actuator={0.6}{0.2}] (actv) -- node[right, rotate=\thetau]{$F_v$} (actv|-0,-2.6);
\draw[actuator={0.6}{0.2}] (actv) -- coordinate[midway](actvmid) (actv|-0,-2.6);
\draw[spring=0.2] (kv) -- node[left, rotate=\thetau]{$k$} (kv|-0,-2.6);
\node[block={0.8cm}{0.6cm}, rotate=\thetau] (Ku) at ($(actumid) + (0, -1.2)$) {$K_{F}$};
\draw[->] ($(au) + (-0.1, -0.5)$) |- (Ku.east);
\draw[->] (Ku.north) -- ($(actumid) + (0, -0.1)$) node[below left, rotate=\thetau]{$F_u$};
\node[block={0.8cm}{0.6cm}, rotate=\thetau] (Kv) at ($(actvmid) + (1.2, 0)$) {$K_{F}$};
\draw[->] ($(av) + (0.5, -0.1)$) -| (Kv.north);
\draw[->] (Kv.west) -- ($(actvmid) + (0.1, 0)$) node[below right, rotate=\thetau]{$F_v$};
\end{scope}
% Inertial Frame
\draw[->] (-4, -4) -- ++(2, 0) node[below]{$\vec{i}_x$};
\draw[->] (-4, -4) -- ++(0, 2) node[left]{$\vec{i}_y$};
\draw[fill, color=black] (-4, -4) circle (0.06);
\node[draw, circle, inner sep=0pt, minimum size=0.3cm, label=left:$\vec{i}_z$] at (-4, -4){};
\draw[->] (0, 0) -- ++(\thetau:2) node[above, rotate=\thetau]{$\vec{i}_u$};
\draw[->] (0, 0) -- ++(\thetau+90:2) node[left, rotate=\thetau]{$\vec{i}_v$};
\draw[dashed] (0, 0) -- ++(2, 0);
\draw[] (1.5, 0) arc (0:\thetau:1.5) node[midway, right]{$\theta$};
\node[] at (0,0) {$\bullet$};
\node[left] at (0,0) {$(x, y)$};
\draw[->] (3.5, 0) arc (0:40:3.5) node[midway, left]{$\Omega$};
\end{tikzpicture}
#+end_src
#+RESULTS:
[[file:figs/system_iff.png]]
* Decentralized Direct Velocity Feedback
#+begin_src latex :file system_dvf.pdf
\begin{tikzpicture}
% Angle
\def\thetau{25}
% Rotational Stage
\draw[fill=black!60!white] (0, 0) circle (4.3);
\draw[fill=black!40!white] (0, 0) circle (3.8);
% Label
\node[anchor=north west, rotate=\thetau] at (-2.5, 2.5) {\small Rotating Stage};
% Rotating Scope
\begin{scope}[rotate=\thetau]
% Rotating Frame
\draw[fill=black!20!white] (-2.6, -2.6) rectangle (2.6, 2.6);
% Label
\node[anchor=north west, rotate=\thetau] at (-2.6, 2.6) {\small X-Y Stage};
% Mass
\draw[fill=white] (-1, -1) rectangle (1, 1);
% Label
\node[anchor=south west, rotate=\thetau] at (-1, -1) {\small Payload};
% Attached Points
\node[] at (-1, 0){$\bullet$};
\draw[] (-1, 0) -- ++(-0.2, 0) coordinate(au);
\node[] at (0, -1){$\bullet$};
\draw[] (0, -1) -- ++(0, -0.2) coordinate(av);
% Attached Points
\node[] at (-1, 0){$\bullet$};
\draw[] (-1, 0) -- ++(-0.2, 0) coordinate(cu);
\draw[] ($(cu) + (0, -0.5)$) coordinate(actu) -- ($(cu) + (0, 0.5)$) coordinate(ku);
\node[] at (0, -1){$\bullet$};
\draw[] (0, -1) -- ++(0, -0.2) coordinate(cv);
\draw[] ($(cv) + (-0.5, 0)$)coordinate(kv) -- ($(cv) + (0.5, 0)$) coordinate(actv);
% Spring and Actuator for U
\draw[actuator={0.6}{0.2}] (actu) -- coordinate[midway](actumid) (actu-|-2.6,0);
\draw[spring=0.2] (ku) -- node[above=0.1, rotate=\thetau]{$k$} (ku-|-2.6,0);
\draw[actuator={0.6}{0.2}] (actv) -- coordinate[midway](actvmid) (actv|-0,-2.6);
\draw[spring=0.2] (kv) -- node[left, rotate=\thetau]{$k$} (kv|-0,-2.6);
% Displacement measurement
\draw[<->, dashed] (-2.6, -0.8) -- (-1 , -0.8) coordinate(dutop);
\draw[<->, dashed] ( 0.8, -2.6) -- ( 0.8, -1) coordinate(dvtop);
% Controllers
\node[block={0.6cm}{0.6cm}, rotate=\thetau] (Ku) at ($(actumid) + (0, -1.2)$) {$K_{V}$};
\draw[->] ($(dutop) + (-0.1, 0)$) node[below left, rotate=\thetau]{$v_u$} |- (Ku.east);
\draw[->] (Ku.north) -- ($(actumid) + (0, -0.1)$);
\node[block={0.6cm}{0.6cm}, rotate=\thetau] (Kv) at ($(actvmid) + (1.2, 0)$) {$K_{V}$};
\draw[->] ($(dvtop) + (0, -0.1)$) node[below right, rotate=\thetau]{$v_v$} -| (Kv.north);
\draw[->] (Kv.west) -- ($(actvmid) + (0.1, 0)$);
\node[above=0.1, rotate=\thetau] at (actumid) {$F_u$};
\node[left=0.1, rotate=\thetau] at (actvmid) {$F_v$};
\end{scope}
% Inertial Frame
\draw[->] (-4, -4) -- ++(2, 0) node[below]{$\vec{i}_x$};
\draw[->] (-4, -4) -- ++(0, 2) node[left]{$\vec{i}_y$};
\draw[fill, color=black] (-4, -4) circle (0.06);
\node[draw, circle, inner sep=0pt, minimum size=0.3cm, label=left:$\vec{i}_z$] at (-4, -4){};
\draw[->] (0, 0) -- ++(\thetau:2) node[above, rotate=\thetau]{$\vec{i}_u$};
\draw[->] (0, 0) -- ++(\thetau+90:2) node[left, rotate=\thetau]{$\vec{i}_v$};
\draw[dashed] (0, 0) -- ++(2, 0);
\draw[] (1.5, 0) arc (0:\thetau:1.5) node[midway, right]{$\theta$};
\node[] at (0,0) {$\bullet$};
\node[left] at (0,0) {$(x, y)$};
\draw[->] (3.5, 0) arc (0:40:3.5) node[midway, left]{$\Omega$};
\end{tikzpicture}
#+end_src
#+RESULTS:
[[file:figs/system_dvf.png]]
* Springs in parallel
#+begin_src latex :file system_parallel_springs.pdf
\begin{tikzpicture}
% Angle
\def\thetau{25}
@ -165,4 +390,4 @@ Configuration file is accessible [[file:config.org][here]].
#+end_src
#+RESULTS:
[[file:figs/rotating_xy_platform_springs.png]]
[[file:figs/system_parallel_springs.png]]