From 1d2ff3b48327522941ea9219103a8d7de9608452 Mon Sep 17 00:00:00 2001 From: Thomas Dehaeze Date: Thu, 12 Nov 2020 17:46:28 +0100 Subject: [PATCH] Reworked Flexor parts --- .../figs/CS.jpg => figs/flexor_025_CS.jpg | Bin .../flexor_025_Geometry.jpg | Bin .../figs/MDoF.jpg => figs/flexor_025_MDoF.jpg | Bin figs/flexor_ID16_compare_bushing_joint.pdf | Bin 142296 -> 127285 bytes figs/flexor_ID16_compare_bushing_joint.png | Bin 164189 -> 88678 bytes index.org | 215 ++++++++---------- matlab/flexor_025.m | 135 +++++++++++ matlab/flexor_025.slx | Bin 0 -> 38483 bytes .../flexor_ID16.slx => flexor_025.slx.r2020a} | Bin .../flexor_025.STEP} | 0 .../data => flexor_025}/mat_K.CSV | 0 .../data => flexor_025}/mat_K.matrix | 0 .../data => flexor_025}/mat_M.CSV | 0 .../data => flexor_025}/mat_M.matrix | 0 .../data => flexor_025}/out_nodes_3D.txt | 0 .../flexor_025_simplified.slx | Bin matlab/flexor_ID16.m | 134 +++++++++++ matlab/flexor_ID16.slx | Bin 0 -> 38423 bytes .../flexor_025.slx => flexor_ID16.slx.r2020a} | Bin .../cp91_2MDoF_6modes.sub | Bin .../flexor_ID16/flexor_ID16.STEP | 0 .../mat_K_6modes_2MDoF.matrix | 0 .../mat_M_6modes_2MDoF.matrix | 0 .../data => flexor_ID16}/out_nodes_3D.txt | 0 .../flexor_ID16_simplified.slx | Bin 25 files changed, 362 insertions(+), 122 deletions(-) rename matlab/to-order/flexor_circ_025/figs/CS.jpg => figs/flexor_025_CS.jpg (100%) rename matlab/to-order/flexor_circ_025/figs/Geometry.jpg => figs/flexor_025_Geometry.jpg (100%) rename matlab/to-order/flexor_circ_025/figs/MDoF.jpg => figs/flexor_025_MDoF.jpg (100%) create mode 100644 matlab/flexor_025.m create mode 100644 matlab/flexor_025.slx rename matlab/{to-order/flexor_ID16/flexor_ID16.slx => flexor_025.slx.r2020a} (100%) rename matlab/{to-order/flexor_circ_025/Flex-DC-0.25.step => flexor_025/flexor_025.STEP} (100%) rename matlab/{to-order/flexor_circ_025/data => flexor_025}/mat_K.CSV (100%) rename matlab/{to-order/flexor_circ_025/data => flexor_025}/mat_K.matrix (100%) rename matlab/{to-order/flexor_circ_025/data => flexor_025}/mat_M.CSV (100%) rename matlab/{to-order/flexor_circ_025/data => flexor_025}/mat_M.matrix (100%) rename matlab/{to-order/flexor_circ_025/data => flexor_025}/out_nodes_3D.txt (100%) rename matlab/{to-order/flexor_circ_025 => }/flexor_025_simplified.slx (100%) create mode 100644 matlab/flexor_ID16.m create mode 100644 matlab/flexor_ID16.slx rename matlab/{to-order/flexor_circ_025/flexor_025.slx => flexor_ID16.slx.r2020a} (100%) rename matlab/{to-order/flexor_ID16/data => flexor_ID16}/cp91_2MDoF_6modes.sub (100%) rename matlab/{to-order => }/flexor_ID16/flexor_ID16.STEP (100%) rename matlab/{to-order/flexor_ID16/data => flexor_ID16}/mat_K_6modes_2MDoF.matrix (100%) rename matlab/{to-order/flexor_ID16/data => flexor_ID16}/mat_M_6modes_2MDoF.matrix (100%) rename matlab/{to-order/flexor_ID16/data => flexor_ID16}/out_nodes_3D.txt (100%) rename matlab/{to-order/flexor_ID16 => }/flexor_ID16_simplified.slx (100%) diff --git 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zaJ1Kojs33ikEnNq{FFSwn)=y9`hrUn@6X);P2gHN?c8a?i7zZV$+Lzf@`SaM5+wFC z+>0L^QzugI=UW`U%d_|U(BJZU@21_kb)L=D>r(hK-Te+041;FR*4H!X+`3S}sUv@? zOHKdqUF%(Z80+7(haKdt_tAZ$T}Ko(hYKu@$Wdw`jbi5g%JLu~ xP%a)mEp?;A7eSEY)Qo`tzVY8bjZ9-I$uEC*C{OO=;it&08yeR?T(x}ie*k3|ITio_ diff --git a/index.org b/index.org index 53e0370..8d7defb 100644 --- a/index.org +++ b/index.org @@ -41,9 +41,9 @@ In this document, Finite Element Models (FEM) of parts of the Nano-Hexapod are d - Section [[sec:APA300ML]]: A super-element of the Amplified Piezoelectric Actuator APA300ML used for the NASS is exported using Ansys and imported in Simscape. The static and dynamical properties of the APA300ML are then estimated using the Simscape model. -- Section [[sec:first_flexible_joint]]: +- Section [[sec:flexor_ID16]]: 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. -- Section [[sec:optimized_flexible_joint]]: +- Section [[sec:flexor_025]]: An optimized flexible joint is developed for the Nano-Hexapod and is then imported in a Simscape model. - Section [[sec:integral_force_feedback]]: - Section [[sec:strut_fem]]: @@ -805,7 +805,10 @@ The dynamics of the Simscape simplified model is identified and compared with th [[file:figs/apa300ml_comp_simpler_simscape.png]] * First Flexible Joint Geometry -<> +:PROPERTIES: +:header-args:matlab+: :tangle matlab/flexor_ID16.m +:END: +<> ** Introduction :ignore: The studied flexor is shown in Figure [[fig:flexor_id16_screenshot]]. @@ -827,11 +830,16 @@ A simplified model of the flexor is then developped. <> #+end_src -#+begin_src matlab - addpath('./data/flexor_ID16/'); +#+begin_src matlab :tangle no + addpath('matlab/'); + addpath('matlab/flexor_ID16/'); #+end_src -#+begin_src matlab :exports none +#+begin_src matlab :eval no + addpath('flexor_ID16/'); +#+end_src + +#+begin_src matlab open('flexor_ID16.slx'); #+end_src @@ -842,41 +850,6 @@ We first extract the stiffness and mass matrices. M = extractMatrix('mat_M_6modes_2MDoF.matrix'); #+end_src -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 - save('./mat/flexor_ID16.mat', 'int_xyz', 'int_i', 'n_xyz', 'n_i', 'nodes', 'M', 'K'); -#+end_src - -** Output parameters -#+begin_src matlab - load('./mat/flexor_ID16.mat', 'int_xyz', 'int_i', 'n_xyz', 'n_i', 'nodes', 'M', 'K'); -#+end_src - -#+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: -| 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 | 181278.0 | 0.0 | 0.0 | 0.0 | -| 2.0 | 181279.0 | 0.0 | 0.0 | -0.0 | - #+begin_src matlab :exports results :results value table replace :tangle no data2orgtable(K(1:10, 1:10), {}, {}, ' %.2e '); #+end_src @@ -894,7 +867,6 @@ Then, we extract the coordinates of the interface nodes. | -2220.0 | -1290.0 | -119000000.0 | -1.31 | -1.49 | -1.79 | 1640.0 | 1290.0 | 119000000.0 | 1.32 | | 0.147 | 148.0 | -1.31 | -33.0 | 0.00026 | 0.000379 | 120.0 | -72.0 | 1.32 | 34.7 | - #+begin_src matlab :exports results :results value table replace :tangle no data2orgtable(M(1:10, 1:10), {}, {}, ' %.1g '); #+end_src @@ -912,25 +884,35 @@ Then, we extract the coordinates of the interface nodes. | 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 | -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); 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 '); + 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 | 181278.0 | 0.0 | 0.0 | 0.0 | +| 2.0 | 181279.0 | 0.0 | 0.0 | -0.0 | + +#+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* | *Estimation by Francois* | -|----------------------------+---------+--------------------------| -| Axial Stiffness [N/um] | 119 | 60 | -| Shear Stiffness [N/um] | 11 | 0 | -| Bending Stiffness [Nm/rad] | 33 | 15 | -| Bending Stiffness [Nm/rad] | 33 | 15 | -| Torsion Stiffness [Nm/rad] | 236 | 20 | +| Total number of Nodes | 2 | +| Number of interface Nodes | 2 | +| Number of Modes | 6 | +| Size of M and K matrices | 18 | -** Identification of the parameters using Simscape +Using =K=, =M= and =int_xyz=, we can use the =Reduced Order Flexible Solid= simscape block. + +** 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. #+begin_src matlab :exports none @@ -960,9 +942,9 @@ And we find the same parameters as the one estimated from the Stiffness matrix. | *Caracteristic* | *Value* | *Identification* | |-------------------------------+---------+------------------| | Axial Stiffness Dz [N/um] | 119 | 119 | -| Bending Stiffness Rx [Nm/rad] | 33 | 34 | -| Bending Stiffness Ry [Nm/rad] | 33 | 126 | -| Torsion Stiffness Rz [Nm/rad] | 236 | 238 | +| Bending Stiffness Rx [Nm/rad] | 33 | 33 | +| Bending Stiffness Ry [Nm/rad] | 33 | 33 | +| Torsion Stiffness Rz [Nm/rad] | 236 | 236 | ** Simpler Model Let's now model the flexible joint with a "perfect" Bushing joint as shown in Figure [[fig:flexible_joint_simscape]]. @@ -1000,8 +982,9 @@ 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', '$D_x/F_x$'); @@ -1019,9 +1002,9 @@ 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', '$R_x/M_x$'); @@ -1039,11 +1022,11 @@ 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 @@ -1052,14 +1035,21 @@ The two obtained dynamics are compared in Figure [[file:figs/flexor_ID16_compare_bushing_joint.png]] * Optimized Flexible Joint -<> +:PROPERTIES: +:header-args:matlab+: :tangle matlab/flexor_025.m +:END: +<> ** Introduction :ignore: +The joint geometry has been optimized using Ansys to have lower bending stiffness while keeping a large axial stiffness. + +The obtained geometry is shown in Figure [[fig:optimal_flexor]]. + #+name: fig:optimal_flexor #+caption: Flexor studied -[[file:data/flexor_circ_025/CS.jpg]] +[[file:figs/flexor_025_MDoF.jpg]] -** Matlab Init :noexport:ignore: +** Matlab Init :noexport:ignore: #+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name) <> #+end_src @@ -1068,11 +1058,16 @@ The two obtained dynamics are compared in Figure <> #+end_src -#+begin_src matlab - addpath('./data/flexor_circ_025/'); +#+begin_src matlab :tangle no + addpath('matlab/'); + addpath('matlab/flexor_025/'); #+end_src -#+begin_src matlab :exports none +#+begin_src matlab :eval no + addpath('flexor_025/'); +#+end_src + +#+begin_src matlab open('flexor_025.slx'); #+end_src @@ -1083,41 +1078,6 @@ We first extract the stiffness and mass matrices. M = readmatrix('mat_M.CSV'); #+end_src -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 - save('./mat/flexor_025.mat', 'int_xyz', 'int_i', 'n_xyz', 'n_i', 'nodes', 'M', 'K'); -#+end_src - -** Output parameters -#+begin_src matlab - load('./mat/flexor_025.mat', 'int_xyz', 'int_i', 'n_xyz', 'n_i', 'nodes', 'M', 'K'); -#+end_src - -#+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: -| 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 | - #+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 | | 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 diff --git a/matlab/flexor_025.m b/matlab/flexor_025.m new file mode 100644 index 0000000..8dd24f3 --- /dev/null +++ b/matlab/flexor_025.m @@ -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'); diff --git a/matlab/flexor_025.slx b/matlab/flexor_025.slx new file mode 100644 index 0000000000000000000000000000000000000000..a1ae8b989e60ffe019db1a7274185c2b0097cfca GIT binary patch literal 38483 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similarity index 100% rename from matlab/to-order/flexor_circ_025/data/mat_K.CSV rename to matlab/flexor_025/mat_K.CSV diff --git a/matlab/to-order/flexor_circ_025/data/mat_K.matrix b/matlab/flexor_025/mat_K.matrix similarity index 100% rename from matlab/to-order/flexor_circ_025/data/mat_K.matrix rename to matlab/flexor_025/mat_K.matrix diff --git a/matlab/to-order/flexor_circ_025/data/mat_M.CSV b/matlab/flexor_025/mat_M.CSV similarity index 100% rename from matlab/to-order/flexor_circ_025/data/mat_M.CSV rename to matlab/flexor_025/mat_M.CSV diff --git a/matlab/to-order/flexor_circ_025/data/mat_M.matrix b/matlab/flexor_025/mat_M.matrix similarity index 100% rename from matlab/to-order/flexor_circ_025/data/mat_M.matrix rename to matlab/flexor_025/mat_M.matrix diff --git a/matlab/to-order/flexor_circ_025/data/out_nodes_3D.txt b/matlab/flexor_025/out_nodes_3D.txt similarity index 100% rename from matlab/to-order/flexor_circ_025/data/out_nodes_3D.txt rename to matlab/flexor_025/out_nodes_3D.txt diff --git a/matlab/to-order/flexor_circ_025/flexor_025_simplified.slx b/matlab/flexor_025_simplified.slx similarity index 100% rename from matlab/to-order/flexor_circ_025/flexor_025_simplified.slx rename to matlab/flexor_025_simplified.slx diff --git a/matlab/flexor_ID16.m b/matlab/flexor_ID16.m new file mode 100644 index 0000000..fccc305 --- /dev/null +++ b/matlab/flexor_ID16.m @@ -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'); diff --git a/matlab/flexor_ID16.slx b/matlab/flexor_ID16.slx new file mode 100644 index 0000000000000000000000000000000000000000..7eaf55cea09e6977b181de309473b91f851060c9 GIT binary patch literal 38423 zcmaI6Q*@_M)8-w!V|8rXwrxB4$F^;|W81cEbZpyp^7S*bzO~+GX017?gZr$m>$mUP zyQ&nVLBUXgfPkQY#-ptj%aWy(FhPKTGGT#$Q2u?@7Phl>2G~05t9aN0oOJ2jZLEh= zb?w#}P(y#Dk~bpKu8r2ogj5BoRV%nyxUP`1xyU0zdQG^CFIR5BDC+8);FOO3K6}kP 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