200 lines
6.7 KiB
HTML
200 lines
6.7 KiB
HTML
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<title>Flexible Joint - Test Bench</title>
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<a accesskey="h" href="../index.html"> UP </a>
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<a accesskey="H" href="../index.html"> HOME </a>
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</div><div id="content">
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<h1 class="title">Flexible Joint - Test Bench</h1>
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<div id="table-of-contents">
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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="#org3ec0fb6">1. Test Bench Description</a>
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<ul>
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<li><a href="#org1c35c31">1.1. Flexible joint Geometry</a></li>
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<li><a href="#org943ed6d">1.2. Required external applied force</a></li>
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<li><a href="#org866642a">1.3. Required actuator stroke and sensors range</a></li>
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<li><a href="#org4789077">1.4. First try with the APA95ML</a></li>
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</ul>
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</li>
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<li><a href="#org75cb5e5">2. Experimental measurement</a></li>
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</ul>
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</div>
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</div>
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<div id="outline-container-org3ec0fb6" class="outline-2">
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<h2 id="org3ec0fb6"><span class="section-number-2">1</span> Test Bench Description</h2>
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<div class="outline-text-2" id="text-1">
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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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</p>
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<p>
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To do so, a test bench is used.
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Specifications of the test bench to precisely measure the bending stiffness are described in this section.
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</p>
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<p>
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The basic idea is to measured the angular deflection of the flexible joint as a function of the applied torque.
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</p>
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<div id="org12e0ba4" 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-org1c35c31" class="outline-3">
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<h3 id="org1c35c31"><span class="section-number-3">1.1</span> Flexible joint Geometry</h3>
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<div class="outline-text-3" id="text-1-1">
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<p>
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The flexible joint used for the Nano-Hexapod is shown in Figure <a href="#org907b319">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="org907b319" 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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</div>
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<p>
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The height between the flexible point (center of the joint) and the point where external forces are applied is \(h = 20\,mm\).
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</p>
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<p>
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Let’s define the parameters on Matlab.
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">kRx = 20; <span class="org-comment">% Bending Stiffness [Nm/rad]</span>
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Rxmax = 20e<span class="org-type">-</span>3; <span class="org-comment">% Bending Stroke [rad]</span>
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h = 20e<span class="org-type">-</span>3; <span class="org-comment">% Height [m]</span>
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</pre>
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</div>
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</div>
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</div>
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<div id="outline-container-org943ed6d" class="outline-3">
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<h3 id="org943ed6d"><span class="section-number-3">1.2</span> Required external applied force</h3>
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<div class="outline-text-3" id="text-1-2">
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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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</p>
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\begin{equation}
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\theta_y = \frac{M_y}{k_{R_y}} = \frac{F_x h}{k_{R_y}}
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\end{equation}
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<p>
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Therefore, the applied force to test the full range of the flexible joint is:
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</p>
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\begin{equation}
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F_{x,\text{max}} = \frac{k_{R_y} \theta_{y,\text{max}}}{h}
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\end{equation}
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<div class="org-src-container">
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<pre class="src src-matlab">Fxmax = kRx<span class="org-type">*</span>Rxmax<span class="org-type">/</span>h; <span class="org-comment">% Force to induce maximum stroke [N]</span>
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</pre>
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</div>
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<p>
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And we obtain:
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</p>
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\begin{equation} F_{max} = 20.0\, [N] \end{equation}
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<p>
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The measurement range of the force sensor should then be higher than \(20\,N\).
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</p>
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</div>
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</div>
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<div id="outline-container-org866642a" class="outline-3">
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<h3 id="org866642a"><span class="section-number-3">1.3</span> Required actuator stroke and sensors range</h3>
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<div class="outline-text-3" id="text-1-3">
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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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The corresponding actuator stroke to impose such motion is:
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</p>
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<p>
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\[ d_{x,\text{max}} = h \tan(R_{x,\text{max}}) \]
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">dxmax = h<span class="org-type">*</span>tan(Rxmax);
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</pre>
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</div>
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\begin{equation} d_{max} = 0.4\, [mm] \end{equation}
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<p>
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In order to test the full range of the flexible joint, the stroke of the actuator should be higher than \(0.4\,mm\).
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The measurement range of the displacement sensor should also be higher than \(0.4\,mm\).
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</p>
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</div>
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</div>
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<div id="outline-container-org4789077" class="outline-3">
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<h3 id="org4789077"><span class="section-number-3">1.4</span> First try with the APA95ML</h3>
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<div class="outline-text-3" id="text-1-4">
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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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</p>
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<p>
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Suppose the full stroke of the APA can be used to bend the flexible joint (ideal case), the measured force will be:
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">Fxmax = kRx<span class="org-type">*</span>100e<span class="org-type">-</span>6<span class="org-type">/</span>h<span class="org-type">^</span>2; <span class="org-comment">% Force at maximum stroke [N]</span>
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</pre>
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</div>
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\begin{equation} F_{max} = 5.0\, [N] \end{equation}
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<p>
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And the tested angular range is:
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">Rmax = tan(100e<span class="org-type">-</span>6<span class="org-type">/</span>h);
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</pre>
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</div>
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\begin{equation} \theta_{max} = 5.0\, [mrad] \end{equation}
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</div>
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</div>
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</div>
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<div id="outline-container-org75cb5e5" class="outline-2">
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<h2 id="org75cb5e5"><span class="section-number-2">2</span> Experimental measurement</h2>
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</div>
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</div>
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<div id="postamble" class="status">
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<p class="author">Author: Dehaeze Thomas</p>
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<p class="date">Created: 2020-12-15 mar. 22:32</p>
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</div>
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</body>
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