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