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Thomas Dehaeze 2021-02-16 21:24:22 +01:00
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@ -3,7 +3,7 @@
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en"> <html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
<head> <head>
<!-- 2021-02-16 mar. 19:15 --> <!-- 2021-02-16 mar. 21:23 -->
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" /> <meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
<title>Flexible Joint - Test Bench</title> <title>Flexible Joint - Test Bench</title>
<meta name="generator" content="Org mode" /> <meta name="generator" content="Org mode" />
@ -39,27 +39,28 @@
<h2>Table of Contents</h2> <h2>Table of Contents</h2>
<div id="text-table-of-contents"> <div id="text-table-of-contents">
<ul> <ul>
<li><a href="#org108197d">1. Flexible Joints - Requirements</a></li> <li><a href="#org7706130">1. Flexible Joints - Requirements</a></li>
<li><a href="#org0e51a3c">2. Test Bench Description</a> <li><a href="#org2925cfa">2. Test Bench Description</a>
<ul> <ul>
<li><a href="#orgd387cac">2.1. Flexible joint Geometry</a></li> <li><a href="#org1121b59">2.1. Flexible joint Geometry</a></li>
<li><a href="#org8da94ef">2.2. Required external applied force</a></li> <li><a href="#org8e5eddc">2.2. Required external applied force</a></li>
<li><a href="#orgdda06ee">2.3. Required actuator stroke and sensors range</a></li> <li><a href="#org5baf14d">2.3. Required actuator stroke and sensors range</a></li>
<li><a href="#orgb6763c2">2.4. First try with the APA95ML</a></li> <li><a href="#orge82143e">2.4. First try with the APA95ML</a></li>
<li><a href="#orge3df316">2.5. Test Bench</a></li> <li><a href="#orgfd806d9">2.5. Test Bench</a></li>
</ul> </ul>
</li> </li>
<li><a href="#orgb94416f">3. Agreement between the probe and the encoder</a> <li><a href="#org169b47f">3. Agreement between the probe and the encoder</a>
<ul> <ul>
<li><a href="#org57bb37e">3.1. Results</a></li> <li><a href="#org5ed49b7">3.1. Setup</a></li>
<li><a href="#orga83f29f">3.2. Results</a></li>
</ul> </ul>
</li> </li>
<li><a href="#orgaca8c01">4. Measurement of the Millimar 1318 probe stiffness</a> <li><a href="#org0fbb329">4. Measurement of the Millimar 1318 probe stiffness</a>
<ul> <ul>
<li><a href="#org837827a">4.1. Results</a></li> <li><a href="#orgc7d7173">4.1. Results</a></li>
</ul> </ul>
</li> </li>
<li><a href="#orgac55925">5. Experimental measurement</a></li> <li><a href="#orgda9e689">5. Experimental measurement</a></li>
</ul> </ul>
</div> </div>
</div> </div>
@ -67,8 +68,8 @@
<p>This report is also available as a <a href="./test-bench-flexible-joints.pdf">pdf</a>.</p> <p>This report is also available as a <a href="./test-bench-flexible-joints.pdf">pdf</a>.</p>
<hr> <hr>
<div id="outline-container-org108197d" class="outline-2"> <div id="outline-container-org7706130" class="outline-2">
<h2 id="org108197d"><span class="section-number-2">1</span> Flexible Joints - Requirements</h2> <h2 id="org7706130"><span class="section-number-2">1</span> Flexible Joints - Requirements</h2>
<div class="outline-text-2" id="text-1"> <div class="outline-text-2" id="text-1">
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides"> <table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
@ -119,8 +120,8 @@
</div> </div>
</div> </div>
<div id="outline-container-org0e51a3c" class="outline-2"> <div id="outline-container-org2925cfa" class="outline-2">
<h2 id="org0e51a3c"><span class="section-number-2">2</span> Test Bench Description</h2> <h2 id="org2925cfa"><span class="section-number-2">2</span> Test Bench Description</h2>
<div class="outline-text-2" id="text-2"> <div class="outline-text-2" id="text-2">
<p> <p>
The main characteristic of the flexible joint that we want to measure is its bending stiffness \(k_{R_x} \approx k_{R_y}\). The main characteristic of the flexible joint that we want to measure is its bending stiffness \(k_{R_x} \approx k_{R_y}\).
@ -136,23 +137,23 @@ The basic idea is to measured the angular deflection of the flexible joint as a
</p> </p>
<div id="org43c60ee" class="figure"> <div id="org5c42ee1" class="figure">
<p><img src="figs/test-bench-schematic.png" alt="test-bench-schematic.png" /> <p><img src="figs/test-bench-schematic.png" alt="test-bench-schematic.png" />
</p> </p>
<p><span class="figure-number">Figure 1: </span>Schematic of the test bench to measure the bending stiffness of the flexible joints</p> <p><span class="figure-number">Figure 1: </span>Schematic of the test bench to measure the bending stiffness of the flexible joints</p>
</div> </div>
</div> </div>
<div id="outline-container-orgd387cac" class="outline-3"> <div id="outline-container-org1121b59" class="outline-3">
<h3 id="orgd387cac"><span class="section-number-3">2.1</span> Flexible joint Geometry</h3> <h3 id="org1121b59"><span class="section-number-3">2.1</span> Flexible joint Geometry</h3>
<div class="outline-text-3" id="text-2-1"> <div class="outline-text-3" id="text-2-1">
<p> <p>
The flexible joint used for the Nano-Hexapod is shown in Figure <a href="#org6500c8a">2</a>. The flexible joint used for the Nano-Hexapod is shown in Figure <a href="#org4639f1b">2</a>.
Its bending stiffness is foreseen to be \(k_{R_y}\approx 20\,\frac{Nm}{rad}\) and its stroke \(\theta_{y,\text{max}}\approx 20\,mrad\). Its bending stiffness is foreseen to be \(k_{R_y}\approx 20\,\frac{Nm}{rad}\) and its stroke \(\theta_{y,\text{max}}\approx 20\,mrad\).
</p> </p>
<div id="org6500c8a" class="figure"> <div id="org4639f1b" class="figure">
<p><img src="figs/flexible_joint_geometry.png" alt="flexible_joint_geometry.png" /> <p><img src="figs/flexible_joint_geometry.png" alt="flexible_joint_geometry.png" />
</p> </p>
<p><span class="figure-number">Figure 2: </span>Geometry of the flexible joint</p> <p><span class="figure-number">Figure 2: </span>Geometry of the flexible joint</p>
@ -174,8 +175,8 @@ Let&rsquo;s define the parameters on Matlab.
</div> </div>
</div> </div>
<div id="outline-container-org8da94ef" class="outline-3"> <div id="outline-container-org8e5eddc" class="outline-3">
<h3 id="org8da94ef"><span class="section-number-3">2.2</span> Required external applied force</h3> <h3 id="org8e5eddc"><span class="section-number-3">2.2</span> Required external applied force</h3>
<div class="outline-text-3" id="text-2-2"> <div class="outline-text-3" id="text-2-2">
<p> <p>
The bending \(\theta_y\) of the flexible joint due to the force \(F_x\) is: The bending \(\theta_y\) of the flexible joint due to the force \(F_x\) is:
@ -207,8 +208,8 @@ The measurement range of the force sensor should then be higher than \(20\,N\).
</div> </div>
</div> </div>
<div id="outline-container-orgdda06ee" class="outline-3"> <div id="outline-container-org5baf14d" class="outline-3">
<h3 id="orgdda06ee"><span class="section-number-3">2.3</span> Required actuator stroke and sensors range</h3> <h3 id="org5baf14d"><span class="section-number-3">2.3</span> Required actuator stroke and sensors range</h3>
<div class="outline-text-3" id="text-2-3"> <div class="outline-text-3" id="text-2-3">
<p> <p>
The flexible joint is designed to allow a bending motion of \(\pm 20\,mrad\). The flexible joint is designed to allow a bending motion of \(\pm 20\,mrad\).
@ -233,8 +234,8 @@ The measurement range of the displacement sensor should also be higher than \(0.
</div> </div>
</div> </div>
<div id="outline-container-orgb6763c2" class="outline-3"> <div id="outline-container-orge82143e" class="outline-3">
<h3 id="orgb6763c2"><span class="section-number-3">2.4</span> First try with the APA95ML</h3> <h3 id="orge82143e"><span class="section-number-3">2.4</span> First try with the APA95ML</h3>
<div class="outline-text-3" id="text-2-4"> <div class="outline-text-3" id="text-2-4">
<p> <p>
The APA95ML as a stroke of \(100\,\mu m\) and the encoder in parallel can easily measure the required stroke. The APA95ML as a stroke of \(100\,\mu m\) and the encoder in parallel can easily measure the required stroke.
@ -262,17 +263,25 @@ And the tested angular range is:
</div> </div>
</div> </div>
<div id="outline-container-orge3df316" class="outline-3"> <div id="outline-container-orgfd806d9" class="outline-3">
<h3 id="orge3df316"><span class="section-number-3">2.5</span> Test Bench</h3> <h3 id="orgfd806d9"><span class="section-number-3">2.5</span> Test Bench</h3>
<div class="outline-text-3" id="text-2-5"> <div class="outline-text-3" id="text-2-5">
<div id="org2a1f8c7" class="figure"> <div id="org0957ecc" class="figure">
<p><img src="figs/test-bench-schematic.png" alt="test-bench-schematic.png" /> <p><img src="figs/test_bench_flex_overview.png" alt="test_bench_flex_overview.png" />
</p> </p>
<p><span class="figure-number">Figure 3: </span>Schematic of the test bench to measure the bending stiffness of the flexible joints</p> <p><span class="figure-number">Figure 3: </span>Schematic of the test bench to measure the bending stiffness of the flexible joints</p>
</div> </div>
<div class="note" id="orgf1de4cf">
<div id="org5b8e491" class="figure">
<p><img src="figs/test_bench_flex_side.png" alt="test_bench_flex_side.png" />
</p>
<p><span class="figure-number">Figure 4: </span>Schematic of the test bench to measure the bending stiffness of the flexible joints</p>
</div>
<div class="note" id="org96d3620">
<ul class="org-ul"> <ul class="org-ul">
<li><b>Translation Stage</b>: <a href="doc/V-408-Datasheet.pdf">V-408</a></li> <li><b>Translation Stage</b>: <a href="doc/V-408-Datasheet.pdf">V-408</a></li>
<li><b>Load Cells</b>: <a href="doc/A700000007147087.pdf">FC2231-0000-0010-L</a> and <a href="doc/FRE_DS_XFL212R_FR_A3.pdf">XFL212R</a></li> <li><b>Load Cells</b>: <a href="doc/A700000007147087.pdf">FC2231-0000-0010-L</a> and <a href="doc/FRE_DS_XFL212R_FR_A3.pdf">XFL212R</a></li>
@ -285,73 +294,101 @@ And the tested angular range is:
</div> </div>
</div> </div>
<div id="outline-container-orgb94416f" class="outline-2"> <div id="outline-container-org169b47f" class="outline-2">
<h2 id="orgb94416f"><span class="section-number-2">3</span> Agreement between the probe and the encoder</h2> <h2 id="org169b47f"><span class="section-number-2">3</span> Agreement between the probe and the encoder</h2>
<div class="outline-text-2" id="text-3"> <div class="outline-text-2" id="text-3">
</div> </div>
<div id="outline-container-org57bb37e" class="outline-3"> <div id="outline-container-org5ed49b7" class="outline-3">
<h3 id="org57bb37e"><span class="section-number-3">3.1</span> Results</h3> <h3 id="org5ed49b7"><span class="section-number-3">3.1</span> Setup</h3>
<div class="outline-text-3" id="text-3-1"> <div class="outline-text-3" id="text-3-1">
<p>
The measurement setup is made such that the probe measured the translation table displacement.
It should then measure the same displacement as the encoder.
Using this setup, we should be able to compare the probe and the encoder.
</p>
</div>
</div>
<div id="outline-container-orga83f29f" class="outline-3">
<h3 id="orga83f29f"><span class="section-number-3">3.2</span> Results</h3>
<div class="outline-text-3" id="text-3-2">
<p>
Let&rsquo;s load the measurements.
</p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">load(<span class="org-string">'meas_probe_against_encoder.mat'</span>, <span class="org-string">'t'</span>, <span class="org-string">'d'</span>, <span class="org-string">'dp'</span>, <span class="org-string">'F'</span>) <pre class="src src-matlab">load(<span class="org-string">'meas_probe_against_encoder.mat'</span>, <span class="org-string">'t'</span>, <span class="org-string">'d'</span>, <span class="org-string">'dp'</span>, <span class="org-string">'F'</span>)
</pre> </pre>
</div> </div>
<p>
The time domain measured displacement by the probe and by the encoder is shown in Figure <a href="#orgfed4851">5</a>.
</p>
<div id="org090f800" class="figure">
<div id="orgfed4851" class="figure">
<p><img src="figs/comp_encoder_probe_time.png" alt="comp_encoder_probe_time.png" /> <p><img src="figs/comp_encoder_probe_time.png" alt="comp_encoder_probe_time.png" />
</p> </p>
<p><span class="figure-number">Figure 4: </span>Time domain measurement</p> <p><span class="figure-number">Figure 5: </span>Time domain measurement</p>
</div> </div>
<p>
If we zoom, we see that there is some delay between the encoder and the probe (Figure <a href="#org8b829e0">6</a>).
</p>
<div id="orgeedac3e" class="figure">
<div id="org8b829e0" class="figure">
<p><img src="figs/comp_encoder_probe_time_zoom.png" alt="comp_encoder_probe_time_zoom.png" /> <p><img src="figs/comp_encoder_probe_time_zoom.png" alt="comp_encoder_probe_time_zoom.png" />
</p> </p>
<p><span class="figure-number">Figure 5: </span>Time domain measurement (Zoom)</p> <p><span class="figure-number">Figure 6: </span>Time domain measurement (Zoom)</p>
</div> </div>
<div class="org-src-container"> <p>
<pre class="src src-matlab">finddelay(d, dp) This delay is estimated using the <code>finddelay</code> command.
</pre> </p>
</div>
<pre class="example"> <pre class="example">
316 The time delay is approximately 15.8 [ms]
</pre> </pre>
<div class="org-src-container"> <p>
<pre class="src src-matlab">Ts<span class="org-type">*</span>finddelay(d, dp) The measured mismatch between the encoder and the probe with and without compensating for the time delay are shown in Figure <a href="#org325c41d">7</a>.
</pre> </p>
</div>
<pre class="example">
0.0158
</pre>
<div id="org325c41d" class="figure">
<div id="org196ee5e" class="figure">
<p><img src="figs/comp_encoder_probe_mismatch.png" alt="comp_encoder_probe_mismatch.png" /> <p><img src="figs/comp_encoder_probe_mismatch.png" alt="comp_encoder_probe_mismatch.png" />
</p> </p>
<p><span class="figure-number">Figure 6: </span>Measurement mismatch, with and without delay compensation</p> <p><span class="figure-number">Figure 7: </span>Measurement mismatch, with and without delay compensation</p>
</div> </div>
<p>
Finally, the displacement of the probe is shown as a function of the displacement of the encoder and a linear fit is made (Figure <a href="#org6b2fa2a">8</a>).
</p>
<div id="org4c16552" class="figure">
<div id="org6b2fa2a" class="figure">
<p><img src="figs/comp_encoder_probe_linear_fit.png" alt="comp_encoder_probe_linear_fit.png" /> <p><img src="figs/comp_encoder_probe_linear_fit.png" alt="comp_encoder_probe_linear_fit.png" />
</p> </p>
<p><span class="figure-number">Figure 7: </span>Measured displacement by the probe as a function of the measured displacement by the encoder</p> <p><span class="figure-number">Figure 8: </span>Measured displacement by the probe as a function of the measured displacement by the encoder</p>
</div>
<div class="important" id="orgd63f29c">
<p>
From the measurement, it is shown that the probe is well calibrated.
However, there is some time delay of tens of milliseconds that could induce some measurement errors.
</p>
</div> </div>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-orgaca8c01" class="outline-2"> <div id="outline-container-org0fbb329" class="outline-2">
<h2 id="orgaca8c01"><span class="section-number-2">4</span> Measurement of the Millimar 1318 probe stiffness</h2> <h2 id="org0fbb329"><span class="section-number-2">4</span> Measurement of the Millimar 1318 probe stiffness</h2>
<div class="outline-text-2" id="text-4"> <div class="outline-text-2" id="text-4">
<div class="note" id="org2b211f7"> <div class="note" id="org8fed4a1">
<ul class="org-ul"> <ul class="org-ul">
<li><b>Translation Stage</b>: <a href="doc/V-408-Datasheet.pdf">V-408</a></li> <li><b>Translation Stage</b>: <a href="doc/V-408-Datasheet.pdf">V-408</a></li>
<li><b>Load Cell</b>: <a href="doc/A700000007147087.pdf">FC2231-0000-0010-L</a></li> <li><b>Load Cell</b>: <a href="doc/A700000007147087.pdf">FC2231-0000-0010-L</a></li>
@ -362,37 +399,40 @@ And the tested angular range is:
</div> </div>
<div id="org68dec3a" class="figure"> <div id="org2cc75ab" class="figure">
<p><img src="figs/setup_mahr_stiff_meas_side.jpg" alt="setup_mahr_stiff_meas_side.jpg" /> <p><img src="figs/setup_mahr_stiff_meas_side.jpg" alt="setup_mahr_stiff_meas_side.jpg" />
</p> </p>
<p><span class="figure-number">Figure 8: </span>Setup - Side View</p> <p><span class="figure-number">Figure 9: </span>Setup - Side View</p>
</div> </div>
<div id="org28e5fd0" class="figure"> <div id="org91485ce" class="figure">
<p><img src="figs/setup_mahr_stiff_meas_top.jpg" alt="setup_mahr_stiff_meas_top.jpg" /> <p><img src="figs/setup_mahr_stiff_meas_top.jpg" alt="setup_mahr_stiff_meas_top.jpg" />
</p> </p>
<p><span class="figure-number">Figure 9: </span>Setup - Top View</p> <p><span class="figure-number">Figure 10: </span>Setup - Top View</p>
</div> </div>
</div> </div>
<div id="outline-container-org837827a" class="outline-3"> <div id="outline-container-orgc7d7173" class="outline-3">
<h3 id="org837827a"><span class="section-number-3">4.1</span> Results</h3> <h3 id="orgc7d7173"><span class="section-number-3">4.1</span> Results</h3>
<div class="outline-text-3" id="text-4-1"> <div class="outline-text-3" id="text-4-1">
<p>
Let&rsquo;s load the measurement results.
</p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">load(<span class="org-string">'meas_stiff_probe.mat'</span>, <span class="org-string">'t'</span>, <span class="org-string">'d'</span>, <span class="org-string">'dp'</span>, <span class="org-string">'F'</span>) <pre class="src src-matlab">load(<span class="org-string">'meas_stiff_probe.mat'</span>, <span class="org-string">'t'</span>, <span class="org-string">'d'</span>, <span class="org-string">'dp'</span>, <span class="org-string">'F'</span>)
</pre> </pre>
</div> </div>
<p> <p>
The time domain measured force and displacement are shown in Figure <a href="#orged81df2">10</a>. The time domain measured force and displacement are shown in Figure <a href="#orgd45dfc2">11</a>.
</p> </p>
<div id="orged81df2" class="figure"> <div id="orgd45dfc2" class="figure">
<p><img src="figs/mahr_time_domain.png" alt="mahr_time_domain.png" /> <p><img src="figs/mahr_time_domain.png" alt="mahr_time_domain.png" />
</p> </p>
<p><span class="figure-number">Figure 10: </span>Time domain measurements</p> <p><span class="figure-number">Figure 11: </span>Time domain measurements</p>
</div> </div>
@ -410,25 +450,33 @@ This is very close to the 0.04 [N/mm] written in the <a href="doc/tmp3m0cvmue_78
</p> </p>
<p> <p>
And compare the linear fit with the raw measurement data (Figure <a href="#orgba688b9">11</a>). And compare the linear fit with the raw measurement data (Figure <a href="#org4939523">12</a>).
</p> </p>
<div id="orgba688b9" class="figure"> <div id="org4939523" class="figure">
<p><img src="figs/mahr_stiffness_f_d_plot.png" alt="mahr_stiffness_f_d_plot.png" /> <p><img src="figs/mahr_stiffness_f_d_plot.png" alt="mahr_stiffness_f_d_plot.png" />
</p> </p>
<p><span class="figure-number">Figure 12: </span>Measured displacement as a function of the measured force. Raw data and linear fit</p>
</div>
<div class="summary" id="org18e09dc">
<p>
The Millimar 1318 probe has a stiffness of \(\approx 0.04\,[N/mm]\).
</p>
</div> </div>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-orgac55925" class="outline-2"> <div id="outline-container-orgda9e689" class="outline-2">
<h2 id="orgac55925"><span class="section-number-2">5</span> Experimental measurement</h2> <h2 id="orgda9e689"><span class="section-number-2">5</span> Experimental measurement</h2>
</div> </div>
</div> </div>
<div id="postamble" class="status"> <div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p> <p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2021-02-16 mar. 19:15</p> <p class="date">Created: 2021-02-16 mar. 21:23</p>
</div> </div>
</body> </body>
</html> </html>

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test-bench-flexible-joints.org
View File

@ -174,9 +174,16 @@ And the tested angular range is:
** Test Bench ** Test Bench
#+name: fig:test-bench-schematic #+name: fig:test_bench_flex_overview
#+caption: Schematic of the test bench to measure the bending stiffness of the flexible joints #+caption: Schematic of the test bench to measure the bending stiffness of the flexible joints
[[file:figs/test-bench-schematic.png]] #+attr_latex: :width 0.8\linewidth
[[file:figs/test_bench_flex_overview.png]]
#+name: fig:test_bench_flex_side
#+caption: Schematic of the test bench to measure the bending stiffness of the flexible joints
#+attr_latex: :width 0.25\linewidth
[[file:figs/test_bench_flex_side.png]]
#+begin_note #+begin_note
- *Translation Stage*: [[file:doc/V-408-Datasheet.pdf][V-408]] - *Translation Stage*: [[file:doc/V-408-Datasheet.pdf][V-408]]

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test-bench-flexible-joints.pdf
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