diff --git a/index.html b/index.html deleted file mode 100644 index 7fea54f..0000000 --- a/index.html +++ /dev/null @@ -1,221 +0,0 @@ - - - - - - -Flexible Joint - Test Bench - - - - - - - - -
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Flexible Joint - Test Bench

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Table of Contents

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1 Test Bench Description

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-

-The main characteristic of the flexible joint that we want to measure is its bending stiffness \(k_{R_x} \approx k_{R_y}\). -

- -

-To do so, a test bench is used. -Specifications of the test bench to precisely measure the bending stiffness are described in this section. -

- -

-The basic idea is to measured the angular deflection of the flexible joint as a function of the applied torque. -

- - -
-

test-bench-schematic.png -

-

Figure 1: Schematic of the test bench to measure the bending stiffness of the flexible joints

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- -
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1.1 Flexible joint Geometry

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-The flexible joint used for the Nano-Hexapod is shown in Figure 2. -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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flexible_joint_geometry.png -

-

Figure 2: Geometry of the flexible joint

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- -

-The height between the flexible point (center of the joint) and the point where external forces are applied is \(h = 20\,mm\). -

- -

-Let’s define the parameters on Matlab. -

-
-
kRx = 20; % Bending Stiffness [Nm/rad]
-Rxmax = 20e-3; % Bending Stroke [rad]
-h = 20e-3; % Height [m]
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- -
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1.2 Required external applied force

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-

-The bending \(\theta_y\) of the flexible joint due to the force \(F_x\) is: -

-\begin{equation} - \theta_y = \frac{M_y}{k_{R_y}} = \frac{F_x h}{k_{R_y}} -\end{equation} - -

-Therefore, the applied force to test the full range of the flexible joint is: -

-\begin{equation} - F_{x,\text{max}} = \frac{k_{R_y} \theta_{y,\text{max}}}{h} -\end{equation} - -
-
Fxmax = kRx*Rxmax/h; % Force to induce maximum stroke [N]
-
-
- -

-And we obtain: -

-\begin{equation} F_{max} = 20.0\, [N] \end{equation} - -

-The measurement range of the force sensor should then be higher than \(20\,N\). -

-
-
- -
-

1.3 Required actuator stroke and sensors range

-
-

-The flexible joint is designed to allow a bending motion of \(\pm 20\,mrad\). -The corresponding actuator stroke to impose such motion is: -

- -

-\[ d_{x,\text{max}} = h \tan(R_{x,\text{max}}) \] -

- -
-
dxmax = h*tan(Rxmax);
-
-
- -\begin{equation} d_{max} = 0.4\, [mm] \end{equation} - -

-In order to test the full range of the flexible joint, the stroke of the actuator should be higher than \(0.4\,mm\). -The measurement range of the displacement sensor should also be higher than \(0.4\,mm\). -

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-
- -
-

1.4 First try with the APA95ML

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-

-The APA95ML as a stroke of \(100\,\mu m\) and the encoder in parallel can easily measure the required stroke. -

- -

-Suppose the full stroke of the APA can be used to bend the flexible joint (ideal case), the measured force will be: -

-
-
Fxmax = kRx*100e-6/h^2; % Force at maximum stroke [N]
-
-
- -\begin{equation} F_{max} = 5.0\, [N] \end{equation} - -

-And the tested angular range is: -

-
-
Rmax = tan(100e-6/h);
-
-
- -\begin{equation} \theta_{max} = 5.0\, [mrad] \end{equation} -
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- -
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1.5 Test Bench

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test-bench-schematic.png -

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Figure 3: Schematic of the test bench to measure the bending stiffness of the flexible joints

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2 Experimental measurement

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Author: Dehaeze Thomas

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Created: 2020-12-17 jeu. 14:47

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- - diff --git a/index.html b/index.html new file mode 120000 index 0000000..88fb25a --- /dev/null +++ b/index.html @@ -0,0 +1 @@ +test-bench-flexible-joints.html \ No newline at end of file diff --git a/test-bench-flexible-joints.html b/test-bench-flexible-joints.html new file mode 100644 index 0000000..5df7758 --- /dev/null +++ b/test-bench-flexible-joints.html @@ -0,0 +1,286 @@ + + + + + + +Flexible Joint - Test Bench + + + + + + + + +
+ UP + | + HOME +
+

Flexible Joint - Test Bench

+
+

Table of Contents

+
+ +
+
+
+

This report is also available as a pdf.

+
+ +
+

1 Flexible Joints - Requirements

+
+ + + +++ ++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
 Specification
Axial Stiffness> 200 [N/um]
Shear Stiffness> 1 [N/um]
Bending Stiffness< 100 [Nm/rad]
Torsion Stiffness< 500 [Nm/rad]
Bending Stroke> 1 [mrad]
Torsion Stroke> 5 [urad]
+
+
+ +
+

2 Test Bench Description

+
+

+The main characteristic of the flexible joint that we want to measure is its bending stiffness \(k_{R_x} \approx k_{R_y}\). +

+ +

+To do so, a test bench is used. +Specifications of the test bench to precisely measure the bending stiffness are described in this section. +

+ +

+The basic idea is to measured the angular deflection of the flexible joint as a function of the applied torque. +

+ + +
+

test-bench-schematic.png +

+

Figure 1: Schematic of the test bench to measure the bending stiffness of the flexible joints

+
+
+ +
+

2.1 Flexible joint Geometry

+
+

+The flexible joint used for the Nano-Hexapod is shown in Figure 2. +Its bending stiffness is foreseen to be \(k_{R_y}\approx 20\,\frac{Nm}{rad}\) and its stroke \(\theta_{y,\text{max}}\approx 20\,mrad\). +

+ + +
+

flexible_joint_geometry.png +

+

Figure 2: Geometry of the flexible joint

+
+ +

+The height between the flexible point (center of the joint) and the point where external forces are applied is \(h = 20\,mm\). +

+ +

+Let’s define the parameters on Matlab. +

+
+
  kRx = 20; % Bending Stiffness [Nm/rad]
+  Rxmax = 20e-3; % Bending Stroke [rad]
+  h = 20e-3; % Height [m]
+
+
+
+
+ +
+

2.2 Required external applied force

+
+

+The bending \(\theta_y\) of the flexible joint due to the force \(F_x\) is: +

+\begin{equation} + \theta_y = \frac{M_y}{k_{R_y}} = \frac{F_x h}{k_{R_y}} +\end{equation} + +

+Therefore, the applied force to test the full range of the flexible joint is: +

+\begin{equation} + F_{x,\text{max}} = \frac{k_{R_y} \theta_{y,\text{max}}}{h} +\end{equation} + +
+
  Fxmax = kRx*Rxmax/h; % Force to induce maximum stroke [N]
+
+
+ +

+And we obtain: +

+\begin{equation} F_{max} = 20.0\, [N] \end{equation} + +

+The measurement range of the force sensor should then be higher than \(20\,N\). +

+
+
+ +
+

2.3 Required actuator stroke and sensors range

+
+

+The flexible joint is designed to allow a bending motion of \(\pm 20\,mrad\). +The corresponding actuator stroke to impose such motion is: +

+ +

+\[ d_{x,\text{max}} = h \tan(R_{x,\text{max}}) \] +

+ +
+
  dxmax = h*tan(Rxmax);
+
+
+ +\begin{equation} d_{max} = 0.4\, [mm] \end{equation} + +

+In order to test the full range of the flexible joint, the stroke of the actuator should be higher than \(0.4\,mm\). +The measurement range of the displacement sensor should also be higher than \(0.4\,mm\). +

+
+
+ +
+

2.4 First try with the APA95ML

+
+

+The APA95ML as a stroke of \(100\,\mu m\) and the encoder in parallel can easily measure the required stroke. +

+ +

+Suppose the full stroke of the APA can be used to bend the flexible joint (ideal case), the measured force will be: +

+
+
  Fxmax = kRx*100e-6/h^2; % Force at maximum stroke [N]
+
+
+ +\begin{equation} F_{max} = 5.0\, [N] \end{equation} + +

+And the tested angular range is: +

+
+
  Rmax = tan(100e-6/h);
+
+
+ +\begin{equation} \theta_{max} = 5.0\, [mrad] \end{equation} +
+
+ +
+

2.5 Test Bench

+
+ +
+

test-bench-schematic.png +

+

Figure 3: Schematic of the test bench to measure the bending stiffness of the flexible joints

+
+ +
+ + +
+
+
+
+ +
+

3 Experimental measurement

+
+
+
+

Author: Dehaeze Thomas

+

Created: 2021-02-02 mar. 19:12

+
+ + diff --git a/index.org b/test-bench-flexible-joints.org similarity index 92% rename from index.org rename to test-bench-flexible-joints.org index a942aa9..a32ce7a 100644 --- a/index.org +++ b/test-bench-flexible-joints.org @@ -40,6 +40,23 @@ #+PROPERTY: header-args:latex+ :post pdf2svg(file=*this*, ext="png") :END: +#+begin_export html +
+

This report is also available as a pdf.

+
+#+end_export + +* Flexible Joints - Requirements + +| | *Specification* | +|-------------------+-----------------| +| Axial Stiffness | > 200 [N/um] | +| Shear Stiffness | > 1 [N/um] | +| Bending Stiffness | < 100 [Nm/rad] | +| Torsion Stiffness | < 500 [Nm/rad] | +| Bending Stroke | > 1 [mrad] | +| Torsion Stroke | > 5 [urad] | + * Test Bench Description ** Introduction :ignore: diff --git a/test-bench-flexible-joints.pdf b/test-bench-flexible-joints.pdf new file mode 100644 index 0000000..d02327a Binary files /dev/null and b/test-bench-flexible-joints.pdf differ