Reworked Flexor parts
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215
index.org
@ -41,9 +41,9 @@ In this document, Finite Element Models (FEM) of parts of the Nano-Hexapod are d
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- Section [[sec:APA300ML]]:
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A super-element of the Amplified Piezoelectric Actuator APA300ML used for the NASS is exported using Ansys and imported in Simscape.
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The static and dynamical properties of the APA300ML are then estimated using the Simscape model.
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- Section [[sec:first_flexible_joint]]:
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- Section [[sec:flexor_ID16]]:
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A first geometry of a Flexible joint is modelled and its characteristics are identified from the Stiffness matrix as well as from the Simscape model.
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||||
- Section [[sec:optimized_flexible_joint]]:
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- Section [[sec:flexor_025]]:
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An optimized flexible joint is developed for the Nano-Hexapod and is then imported in a Simscape model.
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- Section [[sec:integral_force_feedback]]:
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- Section [[sec:strut_fem]]:
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@ -805,7 +805,10 @@ The dynamics of the Simscape simplified model is identified and compared with th
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[[file:figs/apa300ml_comp_simpler_simscape.png]]
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* First Flexible Joint Geometry
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<<sec:first_flexible_joint>>
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:PROPERTIES:
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||||
:header-args:matlab+: :tangle matlab/flexor_ID16.m
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:END:
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<<sec:flexor_ID16>>
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** Introduction :ignore:
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||||
The studied flexor is shown in Figure [[fig:flexor_id16_screenshot]].
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@ -827,11 +830,16 @@ A simplified model of the flexor is then developped.
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<<matlab-init>>
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#+end_src
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#+begin_src matlab
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addpath('./data/flexor_ID16/');
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#+begin_src matlab :tangle no
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addpath('matlab/');
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addpath('matlab/flexor_ID16/');
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#+end_src
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||||
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#+begin_src matlab :exports none
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#+begin_src matlab :eval no
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addpath('flexor_ID16/');
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#+end_src
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||||
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#+begin_src matlab
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open('flexor_ID16.slx');
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#+end_src
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@ -842,41 +850,6 @@ We first extract the stiffness and mass matrices.
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||||
M = extractMatrix('mat_M_6modes_2MDoF.matrix');
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||||
#+end_src
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Then, we extract the coordinates of the interface nodes.
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#+begin_src matlab
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[int_xyz, int_i, n_xyz, n_i, nodes] = extractNodes('out_nodes_3D.txt');
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#+end_src
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#+begin_src matlab
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save('./mat/flexor_ID16.mat', 'int_xyz', 'int_i', 'n_xyz', 'n_i', 'nodes', 'M', 'K');
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#+end_src
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** Output parameters
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||||
#+begin_src matlab
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||||
load('./mat/flexor_ID16.mat', 'int_xyz', 'int_i', 'n_xyz', 'n_i', 'nodes', 'M', 'K');
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#+end_src
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#+begin_src matlab :exports results :results value table replace :tangle no
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data2orgtable([length(n_i); length(int_i); size(M,1) - 6*length(int_i); size(M,1)], {'Total number of Nodes', 'Number of interface Nodes', 'Number of Modes', 'Size of M and K matrices'}, {}, ' %.0f ');
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#+end_src
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#+RESULTS:
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||||
| Total number of Nodes | 2 |
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||||
| Number of interface Nodes | 2 |
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||||
| Number of Modes | 6 |
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| Size of M and K matrices | 18 |
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#+begin_src matlab :exports results :results value table replace :tangle no :post addhdr(*this*)
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data2orgtable([[1:length(int_i)]', int_i, int_xyz], {}, {'Node i', 'Node Number', 'x [m]', 'y [m]', 'z [m]'}, ' %f ');
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#+end_src
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#+caption: Coordinates of the interface nodes
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#+RESULTS:
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| Node i | Node Number | x [m] | y [m] | z [m] |
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|--------+-------------+-------+-------+-------|
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| 1.0 | 181278.0 | 0.0 | 0.0 | 0.0 |
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| 2.0 | 181279.0 | 0.0 | 0.0 | -0.0 |
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#+begin_src matlab :exports results :results value table replace :tangle no
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data2orgtable(K(1:10, 1:10), {}, {}, ' %.2e ');
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#+end_src
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@ -894,7 +867,6 @@ Then, we extract the coordinates of the interface nodes.
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| -2220.0 | -1290.0 | -119000000.0 | -1.31 | -1.49 | -1.79 | 1640.0 | 1290.0 | 119000000.0 | 1.32 |
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| 0.147 | 148.0 | -1.31 | -33.0 | 0.00026 | 0.000379 | 120.0 | -72.0 | 1.32 | 34.7 |
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#+begin_src matlab :exports results :results value table replace :tangle no
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data2orgtable(M(1:10, 1:10), {}, {}, ' %.1g ');
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#+end_src
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@ -912,25 +884,35 @@ Then, we extract the coordinates of the interface nodes.
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| 7e-08 | 3e-07 | 0.003 | -8e-10 | 2e-09 | -1e-09 | -3e-07 | -4e-08 | 0.02 | -1e-09 |
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| 1e-10 | 1e-05 | 1e-09 | -1e-09 | -3e-13 | 2e-12 | -2e-10 | 0.0002 | -1e-09 | 2e-06 |
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Using =K=, =M= and =int_xyz=, we can use the =Reduced Order Flexible Solid= simscape block.
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** Flexible Joint Characteristics
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The most important parameters of the flexible joint can be directly estimated from the stiffness matrix.
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Then, we extract the coordinates of the interface nodes.
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#+begin_src matlab
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[int_xyz, int_i, n_xyz, n_i, nodes] = extractNodes('out_nodes_3D.txt');
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#+end_src
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#+begin_src matlab :exports results :results value table replace :tangle no :post addhdr(*this*)
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data2orgtable([1e-6*K(3,3), 1e-6*K(2,2), K(4,4), K(5,5), K(6,6); 60, 0, 15, 15, 20]', {'Axial Stiffness [N/um]', 'Shear Stiffness [N/um]', 'Bending Stiffness [Nm/rad]', 'Bending Stiffness [Nm/rad]', 'Torsion Stiffness [Nm/rad]'}, {'*Caracteristic*', '*Value*', '*Estimation by Francois*'}, ' %0.f ');
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data2orgtable([[1:length(int_i)]', int_i, int_xyz], {}, {'Node i', 'Node Number', 'x [m]', 'y [m]', 'z [m]'}, ' %f ');
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#+end_src
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#+caption: Coordinates of the interface nodes
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#+RESULTS:
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| Node i | Node Number | x [m] | y [m] | z [m] |
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|--------+-------------+-------+-------+-------|
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| 1.0 | 181278.0 | 0.0 | 0.0 | 0.0 |
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| 2.0 | 181279.0 | 0.0 | 0.0 | -0.0 |
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#+begin_src matlab :exports results :results value table replace :tangle no
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data2orgtable([length(n_i); length(int_i); size(M,1) - 6*length(int_i); size(M,1)], {'Total number of Nodes', 'Number of interface Nodes', 'Number of Modes', 'Size of M and K matrices'}, {}, ' %.0f ');
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#+end_src
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#+RESULTS:
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| *Caracteristic* | *Value* | *Estimation by Francois* |
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|----------------------------+---------+--------------------------|
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| Axial Stiffness [N/um] | 119 | 60 |
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| Shear Stiffness [N/um] | 11 | 0 |
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| Bending Stiffness [Nm/rad] | 33 | 15 |
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| Bending Stiffness [Nm/rad] | 33 | 15 |
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| Torsion Stiffness [Nm/rad] | 236 | 20 |
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| Total number of Nodes | 2 |
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| Number of interface Nodes | 2 |
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| Number of Modes | 6 |
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| Size of M and K matrices | 18 |
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|
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** Identification of the parameters using Simscape
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Using =K=, =M= and =int_xyz=, we can use the =Reduced Order Flexible Solid= simscape block.
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|
||||
** Identification of the parameters using Simscape and looking at the Stiffness Matrix
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The flexor is now imported into Simscape and its parameters are estimated using an identification.
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#+begin_src matlab :exports none
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@ -960,9 +942,9 @@ And we find the same parameters as the one estimated from the Stiffness matrix.
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| *Caracteristic* | *Value* | *Identification* |
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|-------------------------------+---------+------------------|
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| Axial Stiffness Dz [N/um] | 119 | 119 |
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| Bending Stiffness Rx [Nm/rad] | 33 | 34 |
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| Bending Stiffness Ry [Nm/rad] | 33 | 126 |
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| Torsion Stiffness Rz [Nm/rad] | 236 | 238 |
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| Bending Stiffness Rx [Nm/rad] | 33 | 33 |
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| Bending Stiffness Ry [Nm/rad] | 33 | 33 |
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| Torsion Stiffness Rz [Nm/rad] | 236 | 236 |
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** Simpler Model
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Let's now model the flexible joint with a "perfect" Bushing joint as shown in Figure [[fig:flexible_joint_simscape]].
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@ -1000,8 +982,9 @@ The two obtained dynamics are compared in Figure
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freqs = logspace(0, 5, 1000);
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figure;
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tiledlayout(1, 2, 'TileSpacing', 'None', 'Padding', 'None');
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ax1 = subplot(1,2,1);
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ax1 = nexttile;
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hold on;
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set(gca,'ColorOrderIndex',1)
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plot(freqs, abs(squeeze(freqresp(G(1,1), freqs, 'Hz'))), '-', 'DisplayName', '$D_x/F_x$');
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@ -1019,9 +1002,9 @@ The two obtained dynamics are compared in Figure
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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xlabel('Frequency [Hz]'); ylabel('Amplitude [m/N]');
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hold off;
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legend('location', 'northeast');
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legend('location', 'southwest');
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ax2 = subplot(1,2,2);
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ax2 = nexttile;
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hold on;
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set(gca,'ColorOrderIndex',1)
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plot(freqs, abs(squeeze(freqresp(G(4,4), freqs, 'Hz'))), '-', 'DisplayName', '$R_x/M_x$');
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@ -1039,11 +1022,11 @@ The two obtained dynamics are compared in Figure
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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xlabel('Frequency [Hz]'); ylabel('Amplitude [rad/Nm]');
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hold off;
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legend('location', 'northeast');
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legend('location', 'southwest');
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#+end_src
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||||
#+begin_src matlab :tangle no :exports results :results file replace
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||||
exportFig('figs/flexor_ID16_compare_bushing_joint.pdf', 'width', 'full', 'height', 'tall');
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exportFig('figs/flexor_ID16_compare_bushing_joint.pdf', 'width', 'wide', 'height', 'normal');
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#+end_src
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#+name: fig:flexor_ID16_compare_bushing_joint
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@ -1052,14 +1035,21 @@ The two obtained dynamics are compared in Figure
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[[file:figs/flexor_ID16_compare_bushing_joint.png]]
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||||
* Optimized Flexible Joint
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||||
<<sec:optimized_flexible_joint>>
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||||
:PROPERTIES:
|
||||
:header-args:matlab+: :tangle matlab/flexor_025.m
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||||
:END:
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||||
<<sec:flexor_025>>
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** Introduction :ignore:
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||||
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||||
The joint geometry has been optimized using Ansys to have lower bending stiffness while keeping a large axial stiffness.
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||||
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||||
The obtained geometry is shown in Figure [[fig:optimal_flexor]].
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#+name: fig:optimal_flexor
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#+caption: Flexor studied
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[[file:data/flexor_circ_025/CS.jpg]]
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[[file:figs/flexor_025_MDoF.jpg]]
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** Matlab Init :noexport:ignore:
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** Matlab Init :noexport:ignore:
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#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
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<<matlab-dir>>
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#+end_src
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@ -1068,11 +1058,16 @@ The two obtained dynamics are compared in Figure
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<<matlab-init>>
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#+end_src
|
||||
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#+begin_src matlab
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addpath('./data/flexor_circ_025/');
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#+begin_src matlab :tangle no
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addpath('matlab/');
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addpath('matlab/flexor_025/');
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#+end_src
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#+begin_src matlab :exports none
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#+begin_src matlab :eval no
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addpath('flexor_025/');
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#+end_src
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#+begin_src matlab
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open('flexor_025.slx');
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#+end_src
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@ -1083,41 +1078,6 @@ We first extract the stiffness and mass matrices.
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M = readmatrix('mat_M.CSV');
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#+end_src
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Then, we extract the coordinates of the interface nodes.
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#+begin_src matlab
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[int_xyz, int_i, n_xyz, n_i, nodes] = extractNodes('out_nodes_3D.txt');
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#+end_src
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||||
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#+begin_src matlab
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save('./mat/flexor_025.mat', 'int_xyz', 'int_i', 'n_xyz', 'n_i', 'nodes', 'M', 'K');
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#+end_src
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** Output parameters
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#+begin_src matlab
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load('./mat/flexor_025.mat', 'int_xyz', 'int_i', 'n_xyz', 'n_i', 'nodes', 'M', 'K');
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#+end_src
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#+begin_src matlab :exports results :results value table replace :tangle no
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data2orgtable([length(n_i); length(int_i); size(M,1) - 6*length(int_i); size(M,1)], {'Total number of Nodes', 'Number of interface Nodes', 'Number of Modes', 'Size of M and K matrices'}, {}, ' %.0f ');
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#+end_src
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#+RESULTS:
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| Total number of Nodes | 2 |
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| Number of interface Nodes | 2 |
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||||
| Number of Modes | 6 |
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| Size of M and K matrices | 18 |
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|
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#+begin_src matlab :exports results :results value table replace :tangle no :post addhdr(*this*)
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data2orgtable([[1:length(int_i)]', int_i, int_xyz], {}, {'Node i', 'Node Number', 'x [m]', 'y [m]', 'z [m]'}, ' %f ');
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#+end_src
|
||||
|
||||
#+caption: Coordinates of the interface nodes
|
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#+RESULTS:
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| Node i | Node Number | x [m] | y [m] | z [m] |
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|--------+-------------+-------+-------+-------|
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||||
| 1.0 | 528875.0 | 0.0 | 0.0 | 0.0 |
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| 2.0 | 528876.0 | 0.0 | 0.0 | -0.0 |
|
||||
|
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#+begin_src matlab :exports results :results value table replace :tangle no
|
||||
data2orgtable(K(1:10, 1:10), {}, {}, ' %.2e ');
|
||||
#+end_src
|
||||
@ -1153,23 +1113,34 @@ Then, we extract the coordinates of the interface nodes.
|
||||
| 9e-09 | -5e-08 | 0.003 | -1e-08 | 6e-11 | -1e-11 | 1e-07 | -8e-08 | 0.01 | -6e-08 |
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||||
| 2e-12 | 3e-09 | -1e-08 | 3e-10 | -6e-16 | 1e-13 | -4e-12 | 3e-05 | -6e-08 | 2e-07 |
|
||||
|
||||
Using =K=, =M= and =int_xyz=, we can use the =Reduced Order Flexible Solid= simscape block.
|
||||
|
||||
** Flexible Joint Characteristics
|
||||
The most important parameters of the flexible joint can be directly estimated from the stiffness matrix.
|
||||
Then, we extract the coordinates of the interface nodes.
|
||||
#+begin_src matlab
|
||||
[int_xyz, int_i, n_xyz, n_i, nodes] = extractNodes('out_nodes_3D.txt');
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :exports results :results value table replace :tangle no :post addhdr(*this*)
|
||||
data2orgtable([1e-6*K(3,3), 1e-6*K(2,2), K(4,4), K(5,5), K(6,6)]', {'Axial Stiffness [N/um]', 'Shear Stiffness [N/um]', 'Bending Stiffness [Nm/rad]', 'Bending Stiffness [Nm/rad]', 'Torsion Stiffness [Nm/rad]'}, {'*Caracteristic*', '*Value*'}, ' %.1f ');
|
||||
#+begin_src matlab :exports results :results value table replace :tangle no
|
||||
data2orgtable([length(n_i); length(int_i); size(M,1) - 6*length(int_i); size(M,1)], {'Total number of Nodes', 'Number of interface Nodes', 'Number of Modes', 'Size of M and K matrices'}, {}, ' %.0f ');
|
||||
#+end_src
|
||||
|
||||
#+RESULTS:
|
||||
| *Caracteristic* | *Value* |
|
||||
|----------------------------+---------|
|
||||
| Axial Stiffness [N/um] | 94.0 |
|
||||
| Shear Stiffness [N/um] | 12.7 |
|
||||
| Bending Stiffness [Nm/rad] | 4.8 |
|
||||
| Bending Stiffness [Nm/rad] | 4.8 |
|
||||
| Torsion Stiffness [Nm/rad] | 260.2 |
|
||||
| Total number of Nodes | 2 |
|
||||
| Number of interface Nodes | 2 |
|
||||
| Number of Modes | 6 |
|
||||
| Size of M and K matrices | 18 |
|
||||
|
||||
#+begin_src matlab :exports results :results value table replace :tangle no :post addhdr(*this*)
|
||||
data2orgtable([[1:length(int_i)]', int_i, int_xyz], {}, {'Node i', 'Node Number', 'x [m]', 'y [m]', 'z [m]'}, ' %f ');
|
||||
#+end_src
|
||||
|
||||
#+caption: Coordinates of the interface nodes
|
||||
#+RESULTS:
|
||||
| Node i | Node Number | x [m] | y [m] | z [m] |
|
||||
|--------+-------------+-------+-------+-------|
|
||||
| 1.0 | 528875.0 | 0.0 | 0.0 | 0.0 |
|
||||
| 2.0 | 528876.0 | 0.0 | 0.0 | -0.0 |
|
||||
|
||||
Using =K=, =M= and =int_xyz=, we can use the =Reduced Order Flexible Solid= simscape block.
|
||||
|
||||
** Identification of the parameters using Simscape
|
||||
The flexor is now imported into Simscape and its parameters are estimated using an identification.
|
||||
@ -1206,7 +1177,6 @@ And we find the same parameters as the one estimated from the Stiffness matrix.
|
||||
| Torsion Stiffness Rz [Nm/rad] | 260.2 | 260.2 |
|
||||
|
||||
** Simpler Model
|
||||
|
||||
Let's now model the flexible joint with a "perfect" Bushing joint as shown in Figure [[fig:flexible_joint_simscape]].
|
||||
|
||||
#+name: fig:flexible_joint_simscape
|
||||
@ -1242,8 +1212,9 @@ The two obtained dynamics are compared in Figure
|
||||
freqs = logspace(0, 5, 1000);
|
||||
|
||||
figure;
|
||||
tiledlayout(1, 2, 'TileSpacing', 'None', 'Padding', 'None');
|
||||
|
||||
ax1 = subplot(1,2,1);
|
||||
ax1 = nexttile;
|
||||
hold on;
|
||||
set(gca,'ColorOrderIndex',1)
|
||||
plot(freqs, abs(squeeze(freqresp(G(1,1), freqs, 'Hz'))), '-', 'DisplayName', '$D_x/F_x$');
|
||||
@ -1261,9 +1232,9 @@ The two obtained dynamics are compared in Figure
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
xlabel('Frequency [Hz]'); ylabel('Amplitude [m/N]');
|
||||
hold off;
|
||||
legend('location', 'northeast');
|
||||
legend('location', 'southwest');
|
||||
|
||||
ax2 = subplot(1,2,2);
|
||||
ax2 = nexttile;
|
||||
hold on;
|
||||
set(gca,'ColorOrderIndex',1)
|
||||
plot(freqs, abs(squeeze(freqresp(G(4,4), freqs, 'Hz'))), '-', 'DisplayName', '$R_x/M_x$');
|
||||
@ -1281,11 +1252,11 @@ The two obtained dynamics are compared in Figure
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
xlabel('Frequency [Hz]'); ylabel('Amplitude [rad/Nm]');
|
||||
hold off;
|
||||
legend('location', 'northeast');
|
||||
legend('location', 'southwest');
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :tangle no :exports results :results file replace
|
||||
exportFig('figs/flexor_ID16_compare_bushing_joint.pdf', 'width', 'full', 'height', 'tall');
|
||||
exportFig('figs/flexor_ID16_compare_bushing_joint.pdf', 'width', 'wide', 'height', 'normal');
|
||||
#+end_src
|
||||
|
||||
#+name: fig:flexor_ID16_compare_bushing_joint
|
||||
|
135
matlab/flexor_025.m
Normal file
@ -0,0 +1,135 @@
|
||||
%% Clear Workspace and Close figures
|
||||
clear; close all; clc;
|
||||
|
||||
%% Intialize Laplace variable
|
||||
s = zpk('s');
|
||||
|
||||
addpath('flexor_025/');
|
||||
|
||||
open('flexor_025.slx');
|
||||
|
||||
% Import Mass Matrix, Stiffness Matrix, and Interface Nodes Coordinates
|
||||
% We first extract the stiffness and mass matrices.
|
||||
|
||||
K = readmatrix('mat_K.CSV');
|
||||
M = readmatrix('mat_M.CSV');
|
||||
|
||||
|
||||
|
||||
% #+caption: First 10x10 elements of the Mass matrix
|
||||
% #+RESULTS:
|
||||
% | 0.006 | 8e-09 | -2e-08 | -1e-10 | 3e-05 | 3e-08 | 0.003 | -3e-09 | 9e-09 | 2e-12 |
|
||||
% | 8e-09 | 0.02 | 1e-07 | -3e-05 | 1e-11 | 6e-10 | 1e-08 | 0.003 | -5e-08 | 3e-09 |
|
||||
% | -2e-08 | 1e-07 | 0.01 | -6e-08 | -6e-11 | -8e-12 | -1e-07 | 1e-08 | 0.003 | -1e-08 |
|
||||
% | -1e-10 | -3e-05 | -6e-08 | 1e-06 | 7e-14 | 6e-13 | 1e-10 | 1e-06 | -1e-08 | 3e-10 |
|
||||
% | 3e-05 | 1e-11 | -6e-11 | 7e-14 | 2e-07 | 1e-10 | 3e-08 | -7e-12 | 6e-11 | -6e-16 |
|
||||
% | 3e-08 | 6e-10 | -8e-12 | 6e-13 | 1e-10 | 5e-07 | 1e-08 | -5e-10 | -1e-11 | 1e-13 |
|
||||
% | 0.003 | 1e-08 | -1e-07 | 1e-10 | 3e-08 | 1e-08 | 0.02 | -2e-08 | 1e-07 | -4e-12 |
|
||||
% | -3e-09 | 0.003 | 1e-08 | 1e-06 | -7e-12 | -5e-10 | -2e-08 | 0.006 | -8e-08 | 3e-05 |
|
||||
% | 9e-09 | -5e-08 | 0.003 | -1e-08 | 6e-11 | -1e-11 | 1e-07 | -8e-08 | 0.01 | -6e-08 |
|
||||
% | 2e-12 | 3e-09 | -1e-08 | 3e-10 | -6e-16 | 1e-13 | -4e-12 | 3e-05 | -6e-08 | 2e-07 |
|
||||
|
||||
|
||||
% Then, we extract the coordinates of the interface nodes.
|
||||
|
||||
[int_xyz, int_i, n_xyz, n_i, nodes] = extractNodes('out_nodes_3D.txt');
|
||||
|
||||
% Identification of the parameters using Simscape
|
||||
% The flexor is now imported into Simscape and its parameters are estimated using an identification.
|
||||
|
||||
|
||||
m = 1;
|
||||
|
||||
|
||||
|
||||
% The dynamics is identified from the applied force/torque to the measured displacement/rotation of the flexor.
|
||||
|
||||
%% Name of the Simulink File
|
||||
mdl = 'flexor_025';
|
||||
|
||||
%% Input/Output definition
|
||||
clear io; io_i = 1;
|
||||
io(io_i) = linio([mdl, '/T'], 1, 'openinput'); io_i = io_i + 1;
|
||||
io(io_i) = linio([mdl, '/D'], 1, 'openoutput'); io_i = io_i + 1;
|
||||
|
||||
G = linearize(mdl, io);
|
||||
|
||||
% Simpler Model
|
||||
% Let's now model the flexible joint with a "perfect" Bushing joint as shown in Figure [[fig:flexible_joint_simscape]].
|
||||
|
||||
% #+name: fig:flexible_joint_simscape
|
||||
% #+caption: Bushing Joint used to model the flexible joint
|
||||
% [[file:figs/flexible_joint_simscape.png]]
|
||||
|
||||
% The parameters of the Bushing joint (stiffnesses) are estimated from the Stiffness matrix that was computed from the FEM.
|
||||
|
||||
Kx = K(1,1); % [N/m]
|
||||
Ky = K(2,2); % [N/m]
|
||||
Kz = K(3,3); % [N/m]
|
||||
Krx = K(4,4); % [Nm/rad]
|
||||
Kry = K(5,5); % [Nm/rad]
|
||||
Krz = K(6,6); % [Nm/rad]
|
||||
|
||||
|
||||
|
||||
% The dynamics from the applied force/torque to the measured displacement/rotation of the flexor is identified again for this simpler model.
|
||||
|
||||
%% Name of the Simulink File
|
||||
mdl = 'flexor_025_simplified';
|
||||
|
||||
%% Input/Output definition
|
||||
clear io; io_i = 1;
|
||||
io(io_i) = linio([mdl, '/T'], 1, 'openinput'); io_i = io_i + 1;
|
||||
io(io_i) = linio([mdl, '/D'], 1, 'openoutput'); io_i = io_i + 1;
|
||||
|
||||
Gs = linearize(mdl, io);
|
||||
|
||||
|
||||
|
||||
% The two obtained dynamics are compared in Figure
|
||||
|
||||
|
||||
freqs = logspace(0, 5, 1000);
|
||||
|
||||
figure;
|
||||
tiledlayout(1, 2, 'TileSpacing', 'None', 'Padding', 'None');
|
||||
|
||||
ax1 = nexttile;
|
||||
hold on;
|
||||
set(gca,'ColorOrderIndex',1)
|
||||
plot(freqs, abs(squeeze(freqresp(G(1,1), freqs, 'Hz'))), '-', 'DisplayName', '$D_x/F_x$');
|
||||
set(gca,'ColorOrderIndex',1)
|
||||
plot(freqs, abs(squeeze(freqresp(Gs(1,1), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||
set(gca,'ColorOrderIndex',2)
|
||||
plot(freqs, abs(squeeze(freqresp(G(2,2), freqs, 'Hz'))), '-', 'DisplayName', '$D_y/F_y$');
|
||||
set(gca,'ColorOrderIndex',2)
|
||||
plot(freqs, abs(squeeze(freqresp(Gs(2,2), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||
set(gca,'ColorOrderIndex',3)
|
||||
plot(freqs, abs(squeeze(freqresp(G(3,3), freqs, 'Hz'))), '-', 'DisplayName', '$D_z/F_z$');
|
||||
set(gca,'ColorOrderIndex',3)
|
||||
plot(freqs, abs(squeeze(freqresp(Gs(3,3), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
xlabel('Frequency [Hz]'); ylabel('Amplitude [m/N]');
|
||||
hold off;
|
||||
legend('location', 'southwest');
|
||||
|
||||
ax2 = nexttile;
|
||||
hold on;
|
||||
set(gca,'ColorOrderIndex',1)
|
||||
plot(freqs, abs(squeeze(freqresp(G(4,4), freqs, 'Hz'))), '-', 'DisplayName', '$R_x/M_x$');
|
||||
set(gca,'ColorOrderIndex',1)
|
||||
plot(freqs, abs(squeeze(freqresp(Gs(4,4), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||
set(gca,'ColorOrderIndex',2)
|
||||
plot(freqs, abs(squeeze(freqresp(G(5,5), freqs, 'Hz'))), '-', 'DisplayName', '$R_y/M_y$');
|
||||
set(gca,'ColorOrderIndex',2)
|
||||
plot(freqs, abs(squeeze(freqresp(Gs(5,5), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||
set(gca,'ColorOrderIndex',3)
|
||||
plot(freqs, abs(squeeze(freqresp(G(6,6), freqs, 'Hz'))), '-', 'DisplayName', '$R_z/M_z$');
|
||||
set(gca,'ColorOrderIndex',3)
|
||||
plot(freqs, abs(squeeze(freqresp(Gs(6,6), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
xlabel('Frequency [Hz]'); ylabel('Amplitude [rad/Nm]');
|
||||
hold off;
|
||||
legend('location', 'southwest');
|
BIN
matlab/flexor_025.slx
Normal file
134
matlab/flexor_ID16.m
Normal file
@ -0,0 +1,134 @@
|
||||
%% Clear Workspace and Close figures
|
||||
clear; close all; clc;
|
||||
|
||||
%% Intialize Laplace variable
|
||||
s = zpk('s');
|
||||
|
||||
addpath('flexor_ID16/');
|
||||
|
||||
open('flexor_ID16.slx');
|
||||
|
||||
% Import Mass Matrix, Stiffness Matrix, and Interface Nodes Coordinates
|
||||
% We first extract the stiffness and mass matrices.
|
||||
|
||||
K = extractMatrix('mat_K_6modes_2MDoF.matrix');
|
||||
M = extractMatrix('mat_M_6modes_2MDoF.matrix');
|
||||
|
||||
|
||||
|
||||
% #+caption: First 10x10 elements of the Mass matrix
|
||||
% #+RESULTS:
|
||||
% | 0.02 | 1e-09 | -4e-08 | -1e-10 | 0.0002 | -3e-11 | 0.004 | 5e-08 | 7e-08 | 1e-10 |
|
||||
% | 1e-09 | 0.02 | -3e-07 | -0.0002 | -1e-10 | -2e-09 | 2e-08 | 0.004 | 3e-07 | 1e-05 |
|
||||
% | -4e-08 | -3e-07 | 0.02 | 7e-10 | -2e-09 | 1e-09 | 3e-07 | 7e-08 | 0.003 | 1e-09 |
|
||||
% | -1e-10 | -0.0002 | 7e-10 | 4e-06 | -1e-12 | -6e-13 | 2e-10 | -7e-06 | -8e-10 | -1e-09 |
|
||||
% | 0.0002 | -1e-10 | -2e-09 | -1e-12 | 3e-06 | 2e-13 | 9e-06 | 4e-11 | 2e-09 | -3e-13 |
|
||||
% | -3e-11 | -2e-09 | 1e-09 | -6e-13 | 2e-13 | 4e-07 | 8e-11 | 9e-10 | -1e-09 | 2e-12 |
|
||||
% | 0.004 | 2e-08 | 3e-07 | 2e-10 | 9e-06 | 8e-11 | 0.02 | -7e-08 | -3e-07 | -2e-10 |
|
||||
% | 5e-08 | 0.004 | 7e-08 | -7e-06 | 4e-11 | 9e-10 | -7e-08 | 0.01 | -4e-08 | 0.0002 |
|
||||
% | 7e-08 | 3e-07 | 0.003 | -8e-10 | 2e-09 | -1e-09 | -3e-07 | -4e-08 | 0.02 | -1e-09 |
|
||||
% | 1e-10 | 1e-05 | 1e-09 | -1e-09 | -3e-13 | 2e-12 | -2e-10 | 0.0002 | -1e-09 | 2e-06 |
|
||||
|
||||
% Then, we extract the coordinates of the interface nodes.
|
||||
|
||||
[int_xyz, int_i, n_xyz, n_i, nodes] = extractNodes('out_nodes_3D.txt');
|
||||
|
||||
% Identification of the parameters using Simscape and looking at the Stiffness Matrix
|
||||
% The flexor is now imported into Simscape and its parameters are estimated using an identification.
|
||||
|
||||
|
||||
m = 1;
|
||||
|
||||
|
||||
|
||||
% The dynamics is identified from the applied force/torque to the measured displacement/rotation of the flexor.
|
||||
|
||||
%% Name of the Simulink File
|
||||
mdl = 'flexor_ID16';
|
||||
|
||||
%% Input/Output definition
|
||||
clear io; io_i = 1;
|
||||
io(io_i) = linio([mdl, '/T'], 1, 'openinput'); io_i = io_i + 1;
|
||||
io(io_i) = linio([mdl, '/D'], 1, 'openoutput'); io_i = io_i + 1;
|
||||
|
||||
G = linearize(mdl, io);
|
||||
|
||||
% Simpler Model
|
||||
% Let's now model the flexible joint with a "perfect" Bushing joint as shown in Figure [[fig:flexible_joint_simscape]].
|
||||
|
||||
% #+name: fig:flexible_joint_simscape
|
||||
% #+caption: Bushing Joint used to model the flexible joint
|
||||
% [[file:figs/flexible_joint_simscape.png]]
|
||||
|
||||
% The parameters of the Bushing joint (stiffnesses) are estimated from the Stiffness matrix that was computed from the FEM.
|
||||
|
||||
Kx = K(1,1); % [N/m]
|
||||
Ky = K(2,2); % [N/m]
|
||||
Kz = K(3,3); % [N/m]
|
||||
Krx = K(4,4); % [Nm/rad]
|
||||
Kry = K(5,5); % [Nm/rad]
|
||||
Krz = K(6,6); % [Nm/rad]
|
||||
|
||||
|
||||
|
||||
% The dynamics from the applied force/torque to the measured displacement/rotation of the flexor is identified again for this simpler model.
|
||||
|
||||
%% Name of the Simulink File
|
||||
mdl = 'flexor_ID16_simplified';
|
||||
|
||||
%% Input/Output definition
|
||||
clear io; io_i = 1;
|
||||
io(io_i) = linio([mdl, '/T'], 1, 'openinput'); io_i = io_i + 1;
|
||||
io(io_i) = linio([mdl, '/D'], 1, 'openoutput'); io_i = io_i + 1;
|
||||
|
||||
Gs = linearize(mdl, io);
|
||||
|
||||
|
||||
|
||||
% The two obtained dynamics are compared in Figure
|
||||
|
||||
|
||||
freqs = logspace(0, 5, 1000);
|
||||
|
||||
figure;
|
||||
tiledlayout(1, 2, 'TileSpacing', 'None', 'Padding', 'None');
|
||||
|
||||
ax1 = nexttile;
|
||||
hold on;
|
||||
set(gca,'ColorOrderIndex',1)
|
||||
plot(freqs, abs(squeeze(freqresp(G(1,1), freqs, 'Hz'))), '-', 'DisplayName', '$D_x/F_x$');
|
||||
set(gca,'ColorOrderIndex',1)
|
||||
plot(freqs, abs(squeeze(freqresp(Gs(1,1), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||
set(gca,'ColorOrderIndex',2)
|
||||
plot(freqs, abs(squeeze(freqresp(G(2,2), freqs, 'Hz'))), '-', 'DisplayName', '$D_y/F_y$');
|
||||
set(gca,'ColorOrderIndex',2)
|
||||
plot(freqs, abs(squeeze(freqresp(Gs(2,2), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||
set(gca,'ColorOrderIndex',3)
|
||||
plot(freqs, abs(squeeze(freqresp(G(3,3), freqs, 'Hz'))), '-', 'DisplayName', '$D_z/F_z$');
|
||||
set(gca,'ColorOrderIndex',3)
|
||||
plot(freqs, abs(squeeze(freqresp(Gs(3,3), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
xlabel('Frequency [Hz]'); ylabel('Amplitude [m/N]');
|
||||
hold off;
|
||||
legend('location', 'southwest');
|
||||
|
||||
ax2 = nexttile;
|
||||
hold on;
|
||||
set(gca,'ColorOrderIndex',1)
|
||||
plot(freqs, abs(squeeze(freqresp(G(4,4), freqs, 'Hz'))), '-', 'DisplayName', '$R_x/M_x$');
|
||||
set(gca,'ColorOrderIndex',1)
|
||||
plot(freqs, abs(squeeze(freqresp(Gs(4,4), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||
set(gca,'ColorOrderIndex',2)
|
||||
plot(freqs, abs(squeeze(freqresp(G(5,5), freqs, 'Hz'))), '-', 'DisplayName', '$R_y/M_y$');
|
||||
set(gca,'ColorOrderIndex',2)
|
||||
plot(freqs, abs(squeeze(freqresp(Gs(5,5), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||
set(gca,'ColorOrderIndex',3)
|
||||
plot(freqs, abs(squeeze(freqresp(G(6,6), freqs, 'Hz'))), '-', 'DisplayName', '$R_z/M_z$');
|
||||
set(gca,'ColorOrderIndex',3)
|
||||
plot(freqs, abs(squeeze(freqresp(Gs(6,6), freqs, 'Hz'))), '--', 'HandleVisibility', 'off');
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
xlabel('Frequency [Hz]'); ylabel('Amplitude [rad/Nm]');
|
||||
hold off;
|
||||
legend('location', 'southwest');
|