diff --git a/docs/cubic-configuration.html b/docs/cubic-configuration.html index 075f003..e289382 100644 --- a/docs/cubic-configuration.html +++ b/docs/cubic-configuration.html @@ -4,7 +4,7 @@ "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> - + Cubic configuration for the Stewart Platform @@ -274,26 +274,26 @@ for the JavaScript code in this tag.
  • 1.2. Cubic Stewart platform centered with the cube center - Jacobian not estimated at the cube center
  • 1.3. Cubic Stewart platform not centered with the cube center - Jacobian estimated at the cube center
  • 1.4. Cubic Stewart platform not centered with the cube center - Jacobian estimated at the Stewart platform center
    • -
  • 1.5. Conclusion
    • +
  • 1.5. Conclusion
  • 2. Configuration with the Cube’s center above the mobile platform
  • 3. Cubic size analysis
  • 4. Dynamic Coupling
  • 5. Functions @@ -388,7 +388,7 @@ We here study what makes the Stiffness matrix diagonal when using a cubic config

    1.1 Cubic Stewart platform centered with the cube center - Jacobian estimated at the cube center

    -We create a cubic Stewart platform (figure 1) in such a way that the center of the cube (black dot) is located at the center of the Stewart platform (blue dot). +We create a cubic Stewart platform (figure 1) in such a way that the center of the cube (black star) is located at the center of the Stewart platform (blue dot). The Jacobian matrix is estimated at the location of the center of the cube.

    @@ -412,21 +412,14 @@ stewart = initializeCylindricalPlatforms(stewart, 'Fpr'
    -
    -

    3d-cubic-stewart-aligned.png -

    -

    Figure 1: Centered cubic configuration

    -
    - -

    cubic_conf_centered_J_center.png

    -

    Figure 2: Cubic Stewart platform centered with the cube center - Jacobian estimated at the cube center (png, pdf)

    +

    Figure 1: Cubic Stewart platform centered with the cube center - Jacobian estimated at the cube center (png, pdf)

    - - +
    +@@ -504,7 +497,7 @@ stewart = initializeCylindricalPlatforms(stewart, 'Fpr'

    1.2 Cubic Stewart platform centered with the cube center - Jacobian not estimated at the cube center

    -We create a cubic Stewart platform with center of the cube located at the center of the Stewart platform (figure 1). +We create a cubic Stewart platform with center of the cube located at the center of the Stewart platform (figure 2). The Jacobian matrix is not estimated at the location of the center of the cube.

    @@ -531,11 +524,11 @@ stewart = initializeCylindricalPlatforms(stewart, 'Fpr'

    cubic_conf_centered_J_not_center.png

    -

    Figure 3: Cubic Stewart platform centered with the cube center - Jacobian not estimated at the cube center (png, pdf)

    +

    Figure 2: Cubic Stewart platform centered with the cube center - Jacobian not estimated at the cube center (png, pdf)

    -
    Table 1: Stiffness Matrix
    - +
    +@@ -613,7 +606,7 @@ stewart = initializeCylindricalPlatforms(stewart, 'Fpr'

    1.3 Cubic Stewart platform not centered with the cube center - Jacobian estimated at the cube center

    -Here, the “center” of the Stewart platform is not at the cube center (figure 4). +Here, the “center” of the Stewart platform is not at the cube center (figure 3). The Jacobian is estimated at the cube center.

    @@ -640,11 +633,11 @@ stewart = initializeCylindricalPlatforms(stewart, 'Fpr'

    cubic_conf_not_centered_J_center.png

    -

    Figure 4: Cubic Stewart platform not centered with the cube center - Jacobian estimated at the cube center (png, pdf)

    +

    Figure 3: Cubic Stewart platform not centered with the cube center - Jacobian estimated at the cube center (png, pdf)

    -
    Table 2: Stiffness Matrix
    - +
    +@@ -760,11 +753,11 @@ stewart = initializeCylindricalPlatforms(stewart, 'Fpr'

    cubic_conf_not_centered_J_stewart_center.png

    -

    Figure 5: Cubic Stewart platform not centered with the cube center - Jacobian estimated at the Stewart platform center (png, pdf)

    +

    Figure 4: Cubic Stewart platform not centered with the cube center - Jacobian estimated at the Stewart platform center (png, pdf)

    -
    Table 3: Stiffness Matrix
    - +
    +@@ -838,8 +831,8 @@ stewart = initializeCylindricalPlatforms(stewart, 'Fpr' -
    -

    1.5 Conclusion

    +
    +

    1.5 Conclusion

    @@ -892,9 +885,9 @@ We find the several Cubic configuration for the Stewart platform where the cente The differences between the configuration are the cube’s size:

      -
    • Small Cube Size in Figure 6
      • -
    • Medium Cube Size in Figure 7
      • -
    • Large Cube Size in Figure 8
      • +
    • Small Cube Size in Figure 5
      • +
    • Medium Cube Size in Figure 6
      • +
    • Large Cube Size in Figure 7

    @@ -912,11 +905,11 @@ FOc = H + MO_B; % Cente

    stewart_cubic_conf_type_1.png

    -

    Figure 6: Cubic Configuration for the Stewart Platform - Small Cube Size (png, pdf)

    +

    Figure 5: Cubic Configuration for the Stewart Platform - Small Cube Size (png, pdf)

    -
    Table 4: Stiffness Matrix
    - +
    +@@ -998,12 +991,12 @@ FOc = H + MO_B; % Cente

    stewart_cubic_conf_type_2.png

    -

    Figure 7: Cubic Configuration for the Stewart Platform - Medium Cube Size (png, pdf)

    +

    Figure 6: Cubic Configuration for the Stewart Platform - Medium Cube Size (png, pdf)

    -
    Table 5: Stiffness Matrix
    - +
    +@@ -1085,12 +1078,12 @@ FOc = H + MO_B; % Cente

    stewart_cubic_conf_type_3.png

    -

    Figure 8: Cubic Configuration for the Stewart Platform - Large Cube Size (png, pdf)

    +

    Figure 7: Cubic Configuration for the Stewart Platform - Large Cube Size (png, pdf)

    -
    Table 6: Stiffness Matrix
    - +
    +@@ -1164,8 +1157,8 @@ FOc = H + MO_B; % Cente -
    -

    2.2 Conclusion

    +
    +

    2.2 Conclusion

    @@ -1227,20 +1220,20 @@ FOc = H + MO_B; % Cente

    We find that for all the cube’s size, \(k_x = k_y = k_z = k\) where \(k\) is the strut stiffness. -We also find that \(k_{\theta_x} = k_{\theta_y}\) and \(k_{\theta_z}\) are varying with the cube’s size (figure 9). +We also find that \(k_{\theta_x} = k_{\theta_y}\) and \(k_{\theta_z}\) are varying with the cube’s size (figure 8).

    stiffness_cube_size.png

    -

    Figure 9: \(k_{\theta_x} = k_{\theta_y}\) and \(k_{\theta_z}\) function of the size of the cube

    +

    Figure 8: \(k_{\theta_x} = k_{\theta_y}\) and \(k_{\theta_z}\) function of the size of the cube

    -
    -

    3.2 Conclusion

    +
    +

    3.2 Conclusion

    We observe that \(k_{\theta_x} = k_{\theta_y}\) and \(k_{\theta_z}\) increase linearly with the cube size. @@ -1271,8 +1264,8 @@ In order to maximize the rotational stiffness of the Stewart platform, the size

    4.2 Dynamic decoupling between the actuators and sensors

    -
    -

    4.3 Conclusion

    +
    +

    4.3 Conclusion

    @@ -1330,7 +1323,7 @@ This Matlab function is accessible

    cubic-configuration-definition.png

    -

    Figure 10: Cubic Configuration

    +

    Figure 9: Cubic Configuration

    @@ -1435,7 +1428,7 @@ stewart.platform_M.Mb = Mb;

    Author: Dehaeze Thomas

    -

    Created: 2020-02-12 mer. 11:18

    +

    Created: 2020-02-12 mer. 11:23

    diff --git a/org/cubic-configuration.org b/org/cubic-configuration.org index 1ca357f..ba97a22 100644 --- a/org/cubic-configuration.org +++ b/org/cubic-configuration.org @@ -91,7 +91,7 @@ We here study what makes the Stiffness matrix diagonal when using a cubic config #+end_src ** Cubic Stewart platform centered with the cube center - Jacobian estimated at the cube center -We create a cubic Stewart platform (figure [[fig:3d-cubic-stewart-aligned]]) in such a way that the center of the cube (black dot) is located at the center of the Stewart platform (blue dot). +We create a cubic Stewart platform (figure [[fig:cubic_conf_centered_J_center]]) in such a way that the center of the cube (black star) is located at the center of the Stewart platform (blue dot). The Jacobian matrix is estimated at the location of the center of the cube. #+begin_src matlab @@ -111,10 +111,6 @@ The Jacobian matrix is estimated at the location of the center of the cube. stewart = initializeCylindricalPlatforms(stewart, 'Fpr', 175e-3, 'Mpr', 150e-3); #+end_src -#+name: fig:3d-cubic-stewart-aligned -#+caption: Centered cubic configuration -[[file:figs/3d-cubic-stewart-aligned.png]] - #+begin_src matlab :exports none displayArchitecture(stewart, 'labels', false); scatter3(0, 0, FOc, 200, 'kh'); @@ -133,6 +129,8 @@ The Jacobian matrix is estimated at the location of the center of the cube. data2orgtable(stewart.kinematics.K, {}, {}, ' %.2g '); #+end_src +#+name: tab:cubic_conf_centered_J_center +#+caption: Stiffness Matrix #+RESULTS: | 2 | 0 | -2.5e-16 | 0 | 2.1e-17 | 0 | | 0 | 2 | 0 | -7.8e-19 | 0 | 0 | @@ -142,7 +140,7 @@ The Jacobian matrix is estimated at the location of the center of the cube. | 6.6e-18 | -3.3e-18 | 0 | 1.7e-18 | 0 | 0.06 | ** Cubic Stewart platform centered with the cube center - Jacobian not estimated at the cube center -We create a cubic Stewart platform with center of the cube located at the center of the Stewart platform (figure [[fig:3d-cubic-stewart-aligned]]). +We create a cubic Stewart platform with center of the cube located at the center of the Stewart platform (figure [[fig:cubic_conf_centered_J_not_center]]). The Jacobian matrix is not estimated at the location of the center of the cube. #+begin_src matlab @@ -180,6 +178,8 @@ The Jacobian matrix is not estimated at the location of the center of the cube. data2orgtable(stewart.kinematics.K, {}, {}, ' %.2g '); #+end_src +#+name: tab:cubic_conf_centered_J_not_center +#+caption: Stiffness Matrix #+RESULTS: | 2 | 0 | -2.5e-16 | 0 | -0.14 | 0 | | 0 | 2 | 0 | 0.14 | 0 | 0 | @@ -227,6 +227,8 @@ The Jacobian is estimated at the cube center. data2orgtable(stewart.kinematics.K, {}, {}, ' %.2g '); #+end_src +#+name: tab:cubic_conf_not_centered_J_center +#+caption: Stiffness Matrix #+RESULTS: | 2 | 0 | -1.7e-16 | 0 | 4.9e-17 | 0 | | 0 | 2 | 0 | -2.2e-17 | 0 | 2.8e-17 | @@ -281,6 +283,8 @@ The center of the cube from the top platform is at $z = 110 - 175 = -65$. data2orgtable(stewart.kinematics.K, {}, {}, ' %.2g '); #+end_src +#+name: tab:cubic_conf_not_centered_J_stewart_center +#+caption: Stiffness Matrix #+RESULTS: | 2 | 0 | 1.5e-16 | 0 | 0.02 | 0 | | 0 | 2 | 0 | -0.02 | 0 | 0 | @@ -366,6 +370,8 @@ However, the rotational stiffnesses are increasing with the cube's size but the data2orgtable(stewart.kinematics.K, {}, {}, ' %.2g '); #+end_src +#+name: tab:stewart_cubic_conf_type_1 +#+caption: Stiffness Matrix #+RESULTS: | 2 | 0 | -2.8e-16 | 0 | 2.4e-17 | 0 | | 0 | 2 | 0 | -2.3e-17 | 0 | 0 | @@ -405,6 +411,8 @@ However, the rotational stiffnesses are increasing with the cube's size but the data2orgtable(stewart.kinematics.K, {}, {}, ' %.2g '); #+end_src +#+name: tab:stewart_cubic_conf_type_2 +#+caption: Stiffness Matrix #+RESULTS: | 2 | 0 | -1.9e-16 | 0 | 5.6e-17 | 0 | | 0 | 2 | 0 | -7.6e-17 | 0 | 0 | @@ -444,6 +452,8 @@ However, the rotational stiffnesses are increasing with the cube's size but the data2orgtable(stewart.kinematics.K, {}, {}, ' %.2g '); #+end_src +#+name: tab:stewart_cubic_conf_type_3 +#+caption: Stiffness Matrix #+RESULTS: | 2 | 0 | -3e-16 | 0 | -8.3e-17 | 0 | | 0 | 2 | 0 | -2.2e-17 | 0 | 5.6e-17 |
    Table 7: Stiffness Matrix