Rename all files, tangle Matlab code
This commit is contained in:
75
matlab/test_joints_1_dim_meas.m
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75
matlab/test_joints_1_dim_meas.m
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%% Clear Workspace and Close figures
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clear; close all; clc;
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%% Intialize Laplace variable
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s = zpk('s');
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%% Path for functions, data and scripts
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addpath('./mat/'); % Path for data
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%% Colors for the figures
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colors = colororder;
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% Measurement Results
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% # - Strange shape: 5
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% The expected flexible beam thickness is $250\,\mu m$.
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% However, it is more important that the thickness of all beams are close to each other.
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% The dimension of the beams are been measured at each end to be able to estimate the mean of the beam thickness.
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% All the measured dimensions are summarized in Table ref:tab:test_joints_flex_dim.
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meas_flex = [[223, 226, 224, 214];
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[229, 231, 237, 224];
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[234, 230, 239, 231];
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[233, 227, 229, 232];
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[225, 212, 228, 228];
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[220, 221, 224, 220];
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[206, 207, 228, 226];
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[230, 224, 224, 223];
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[223, 231, 228, 233];
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[228, 230, 235, 231];
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[197, 207, 211, 204];
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[227, 226, 225, 226];
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[215, 228, 231, 220];
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[216, 224, 224, 221];
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[209, 214, 220, 221];
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[213, 210, 230, 229]];
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% #+name: tab:test_joints_flex_dim
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% #+caption: Measured Dimensions of the flexible beams in $\mu m$
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% #+attr_latex: :environment tabularx :width 0.4\linewidth :align Xcccc
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% #+attr_latex: :center t :booktabs t :float t
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% #+RESULTS:
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% | | Y1 | Y2 | X1 | X2 |
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% |----+-----+-----+-----+-----|
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% | 1 | 223 | 226 | 224 | 214 |
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% | 2 | 229 | 231 | 237 | 224 |
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% | 3 | 234 | 230 | 239 | 231 |
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% | 4 | 233 | 227 | 229 | 232 |
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% | 5 | 225 | 212 | 228 | 228 |
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% | 6 | 220 | 221 | 224 | 220 |
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% | 7 | 206 | 207 | 228 | 226 |
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% | 8 | 230 | 224 | 224 | 223 |
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% | 9 | 223 | 231 | 228 | 233 |
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% | 10 | 228 | 230 | 235 | 231 |
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% | 11 | 197 | 207 | 211 | 204 |
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% | 12 | 227 | 226 | 225 | 226 |
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% | 13 | 215 | 228 | 231 | 220 |
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% | 14 | 216 | 224 | 224 | 221 |
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% | 15 | 209 | 214 | 220 | 221 |
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% | 16 | 213 | 210 | 230 | 229 |
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% An histogram of these measured dimensions is shown in Figure ref:fig:test_joints_size_hist.
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figure;
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histogram([(meas_flex(:,1)+meas_flex(:,2))/2,(meas_flex(:,3)+meas_flex(:,4))/2], 7)
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xlabel("Beam's Thickness [$\mu m$]");
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%% Save beam sizes
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save('./mat/flex_meas_dim.mat', 'meas_flex');
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59
matlab/test_joints_2_bench_dimensioning.m
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59
matlab/test_joints_2_bench_dimensioning.m
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%% Clear Workspace and Close figures
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clear; close all; clc;
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%% Intialize Laplace variable
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s = zpk('s');
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%% Path for functions, data and scripts
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addpath('./mat/'); % Path for data
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%% Colors for the figures
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colors = colororder;
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% Flexible joint Geometry
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% The flexible joint used for the Nano-Hexapod is shown in Figure ref:fig:test_joints_bend_geometry.
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% Its bending stiffness is foreseen to be $k_{R_y}\approx 5\,\frac{Nm}{rad}$ and its stroke $\theta_{y,\text{max}}\approx 25\,mrad$.
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% #+name: fig:test_joints_bend_geometry
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% #+caption: Geometry of the flexible joint
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% [[file:figs/test_joints_bend_geometry.png]]
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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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% Let's define the parameters on Matlab.
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kRx = 5; % Bending Stiffness [Nm/rad]
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Rxmax = 25e-3; % Bending Stroke [rad]
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h = 20e-3; % Height [m]
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% Required external applied force
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% The bending $\theta_y$ of the flexible joint due to the force $F_x$ is:
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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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% Therefore, the applied force to test the full range of the flexible joint is:
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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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Fxmax = kRx*Rxmax/h; % Force to induce maximum stroke [N]
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% And we obtain:
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sprintf('\\begin{equation} F_{x,max} = %.1f\\, [N] \\end{equation}', Fxmax)
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% Required actuator stroke and sensors range
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% The flexible joint is designed to allow a bending motion of $\pm 25\,mrad$.
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% The corresponding stroke at the location of the force sensor is:
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% \[ d_{x,\text{max}} = h \tan(R_{x,\text{max}}) \]
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dxmax = h*tan(Rxmax);
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sprintf('\\begin{equation} d_{max} = %.1f\\, [mm] \\end{equation}', 1e3*dxmax)
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73
matlab/test_joints_3_error_budget.m
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73
matlab/test_joints_3_error_budget.m
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%% Clear Workspace and Close figures
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clear; close all; clc;
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%% Intialize Laplace variable
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s = zpk('s');
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%% Path for functions, data and scripts
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addpath('./mat/'); % Path for data
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%% Colors for the figures
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colors = colororder;
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% Finite Element Model
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% From the Finite Element Model, the stiffness and stroke of the flexible joint have been computed and summarized in Tables ref:tab:test_joints_axial_shear_prop and ref:tab:test_joints_bending_torsion_prop.
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%% Stiffness
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ka = 94e6; % Axial Stiffness [N/m]
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ks = 13e6; % Shear Stiffness [N/m]
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kb = 5; % Bending Stiffness [Nm/rad]
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kt = 260; % Torsional Stiffness [Nm/rad]
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%% Maximum force
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Fa = 469; % Axial Force before yield [N]
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Fs = 242; % Shear Force before yield [N]
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Fb = 0.118; % Bending Force before yield [Nm]
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Ft = 1.508; % Torsional Force before yield [Nm]
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%% Compute the corresponding stroke
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Xa = Fa/ka; % Axial Stroke before yield [m]
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Xs = Fs/ks; % Shear Stroke before yield [m]
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Xb = Fb/kb; % Bending Stroke before yield [rad]
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Xt = Ft/kt; % Torsional Stroke before yield [rad]
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% Setup
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% The setup is schematically represented in Figure ref:fig:test_joints_bench_side_bis.
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% The force is applied on top of the flexible joint with a distance $h$ with the joint's center.
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% The displacement of the flexible joint is also measured at the same height.
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% The height between the joint's center and the force application point is:
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h = 25e-3; % Height [m]
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% Estimation error due to force sensor compression
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% The measured displacement is not done directly at the joint's location.
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% The force sensor compression will then induce an error on the joint's stiffness.
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% The force sensor stiffness $k_F$ is estimated to be around:
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kF = 50/0.05e-3; % [N/m]
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sprintf('k_F = %.1e [N/m]', kF)
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% Estimation error due to height estimation error
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% Let's consider an error in the estimation of the height from the application of the force to the joint's center:
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% \begin{equation}
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% h_{\text{est}} = h (1 + \epsilon)
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% \end{equation}
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% The computed bending stiffness will be:
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% \begin{equation}
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% k_\text{est} \approx h_{\text{est}}^2 \frac{F_x}{d_x}
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% \end{equation}
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% And the stiffness estimation error is:
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% \begin{equation}
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% \frac{k_{\text{est}}}{k_{R_y}} = (1 + \epsilon)^2
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% \end{equation}
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h_err = 0.2e-3; % Height estimation error [m]
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175
matlab/test_joints_4_first_meas.m
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175
matlab/test_joints_4_first_meas.m
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%% Clear Workspace and Close figures
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clear; close all; clc;
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%% Intialize Laplace variable
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s = zpk('s');
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%% Path for functions, data and scripts
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addpath('./mat/'); % Path for data
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%% Colors for the figures
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colors = colororder;
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% Force Sensor Calibration
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% #+begin_note
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% *Load Cells*:
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% - [[file:doc/A700000007147087.pdf][FC2231-0000-0010-L]]
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% - [[file:doc/FRE_DS_XFL212R_FR_A3.pdf][XFL212R]]
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% #+end_note
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% There are both specified to have $\pm 1 \%$ of non-linearity over the full range.
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% The XFL212R has a spherical interface while the FC2231 has a flat surface.
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% Therefore, we should have a nice point contact when using the two force sensors as shown in Figure ref:fig:test_joints_force_sensor_calib.
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% #+name: fig:test_joints_force_sensor_calib
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% #+caption: Zoom on the two force sensors in contact
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% #+attr_latex: :width 0.8\linewidth
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% [[file:figs/test_joints_force_sensor_calib.jpg]]
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% The two force sensors are therefore measuring the exact same force, and we can compare the two measurements.
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% Let's load the measured force of both sensors.
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%% Load measurement data
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load('calibration_force_sensor.mat', 't', 'F', 'Fc')
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% We remove any offset such that they are both measuring no force when not in contact.
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%% Remove offset
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F = F - mean(F( t > 0.5 & t < 1.0));
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Fc = Fc - mean(Fc(t > 0.5 & t < 1.0));
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figure;
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hold on;
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plot(t, F, 'DisplayName', 'FC2231');
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plot(t, Fc, 'DisplayName', 'XFL212R');
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hold off;
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xlabel('Time [s]'); ylabel('Measured Force [N]');
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xlim([0,15]); ylim([0,55]);
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legend('location', 'southeast');
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% #+name: fig:test_joints_force_sensor_calib_time
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% #+caption: Measured force using both sensors as a function of time
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% #+RESULTS:
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% [[file:figs/test_joints_force_sensor_calib_time.png]]
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% Let's select only the first part from the moment they are in contact until the maximum force is reached.
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%% Only get the first part until maximum force
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F = F( t > 1.55 & t < 4.65);
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Fc = Fc(t > 1.55 & t < 4.65);
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% Then, let's make a linear fit between the two measured forces.
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%% Make a line fit
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fit_F = polyfit(Fc, F, 1);
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% The two forces are plotted against each other as well as the linear fit in Figure ref:fig:test_joints_force_sensor_calib_fit.
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figure;
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hold on;
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plot(Fc, F, '-', 'DisplayName', 'Raw Data');
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plot(Fc([1,end]), Fc([1,end])*fit_F(1) + fit_F(2), '--', 'DisplayName', 'Line Fit');
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hold off;
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xlabel('XFL212R [N]'); ylabel('FC2231 [N]');
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xlim([0,50]); ylim([0,50]);
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legend('location', 'southeast');
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% #+name: fig:test_joints_force_sensor_calib_fit
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% #+caption: Measured two forces and linear fit
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% #+RESULTS:
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% [[file:figs/test_joints_force_sensor_calib_fit.png]]
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% The measurement error between the two sensors is shown in Figure ref:fig:test_joints_force_sensor_calib_error.
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% It is below 0.1N for the full measurement range.
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figure;
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hold on;
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plot(Fc, F - (Fc*fit_F(1) + fit_F(2)), 'k-');
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hold off;
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xlim([0,50]); ylim([-0.12, 0.12]);
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xlabel('Measured Force [N]');
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ylabel('Error [N]')
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% Force Sensor Stiffness
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% The objective of this measurement is to estimate the stiffness of the force sensor [[file:doc/A700000007147087.pdf][FC2231-0000-0010-L]].
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% To do so, a very stiff element is fixed in front of the force sensor as shown in Figure ref:fig:test_joints_meas_force_sensor_stiffness.
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% Then, we apply a force on the stiff element through the force sensor.
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% We measure the deflection of the force sensor using an encoder.
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% Then, having the force and the deflection, we should be able to estimate the stiffness of the force sensor supposing the stiffness of the other elements are much larger.
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% #+name: fig:test_joints_meas_force_sensor_stiffness
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% #+caption: Bench used to measured the stiffness of the force sensor
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% #+attr_latex: :width 0.6\linewidth
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% [[file:figs/test_joints_meas_force_sensor_stiffness.jpg]]
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% From the documentation, the deflection of the sensor at the maximum load (50N) is 0.05mm, the stiffness is therefore foreseen to be around $1\,N/\mu m$.
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% Let's load the measured force as well as the measured displacement.
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%% Load measurement data
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load('force_sensor_stiffness_meas.mat', 't', 'F', 'd')
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% Some pre-processing is applied on the data.
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%% Remove offset
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F = F - mean(F(t > 0.5 & t < 1.0));
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%% Select important part of data
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F = F( t > 4.55 & t < 7.24);
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d = d( t > 4.55 & t < 7.24); d = d - d(1);
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t = t( t > 4.55 & t < 7.24);
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% The linear fit is performed.
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%% Linear fit
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fit_k = polyfit(F, d, 1);
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% The displacement as a function of the force as well as the linear fit are shown in Figure ref:fig:test_joints_force_sensor_stiffness_fit.
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figure;
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hold on;
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plot(F, 1e6*d, '-', 'DisplayName', 'Raw Data');
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plot(F([1,end]), 1e6*(F([1,end])*fit_k(1) + fit_k(2)), '--', 'DisplayName', 'Line Fit');
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hold off;
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xlabel('Force [$N$]'); ylabel('Displacement [$\mu m$]');
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xlim([0,45]); ylim([0,60]);
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legend('location', 'southeast');
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% #+name: fig:test_joints_force_sensor_stiffness_fit
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% #+caption: Displacement as a function of the measured force
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% #+RESULTS:
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% [[file:figs/test_joints_force_sensor_stiffness_fit.png]]
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% And we obtain the following stiffness:
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%% Force Sensor Stiffness
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sprintf('k = %.2f [N/um]', 1e-6*1/fit_k(1));
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285
matlab/test_joints_5_bending_stiff_meas.m
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285
matlab/test_joints_5_bending_stiff_meas.m
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@@ -0,0 +1,285 @@
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%% Clear Workspace and Close figures
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clear; close all; clc;
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%% Intialize Laplace variable
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s = zpk('s');
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%% Path for functions, data and scripts
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addpath('./mat/'); % Path for data
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%% Colors for the figures
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colors = colororder;
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% Analysis of one measurement
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% In this section is shown how the data are analysis in order to measured:
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% - the bending stiffness
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% - the bending stroke
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% - the stiffness once the mechanical stops are in contact
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% The height from the flexible joint's center and the point of application force $h$ is defined below:
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h = 25e-3; % [m]
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%% Load Data
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load('meas_stiff_flex_1_x.mat', 't', 'F', 'd');
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%% Zero the force
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F = F - mean(F(t > 0.1 & t < 0.3));
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%% Start measurement at t = 0.2 s
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d = d(t > 0.2);
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F = F(t > 0.2);
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t = t(t > 0.2); t = t - t(1);
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% The obtained time domain measurements are shown in Figure ref:fig:test_joints_meas_bend_time.
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%% Time Domain plots
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figure;
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tiledlayout(2, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
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ax1 = nexttile;
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plot(t, F);
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ylabel('Force [N]'); set(gca, 'XTickLabel',[]);
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ax2 = nexttile;
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plot(t, 1e3*d);
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hold off;
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xlabel('Time [s]'); ylabel('Displacement [mm]');
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linkaxes([ax1,ax2],'x');
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xlim([0,5]);
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% #+name: fig:test_joints_meas_bend_time
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% #+caption: Typical time domain measurements
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% #+RESULTS:
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% [[file:figs/test_joints_meas_bend_time.png]]
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% The displacement as a function of the force is then shown in Figure ref:fig:test_joints_meas_F_d.
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figure;
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plot(F, 1e3*d);
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xlabel('Force [N]'); ylabel('Displacement [mm]');
|
||||
xlim([0,6]); ylim([0,1]);
|
||||
|
||||
|
||||
|
||||
% #+name: fig:test_joints_meas_F_d
|
||||
% #+caption: Typical measurement of the diplacement as a function of the applied force
|
||||
% #+RESULTS:
|
||||
% [[file:figs/test_joints_meas_F_d.png]]
|
||||
|
||||
% The bending stiffness can be estimated by computing the slope of the curve in Figure ref:fig:test_joints_meas_F_d.
|
||||
% The bending stroke and the stiffness when touching the mechanical stop can also be estimated from the same figure.
|
||||
|
||||
|
||||
%% Determine the linear region and region when touching the mechanical stop
|
||||
% Find when the force sensor touches the flexible joint
|
||||
i_l_start = find(F > 0.3, 1, 'first');
|
||||
% Reset the measured diplacement at that point
|
||||
d = d - d(i_l_start);
|
||||
% Find then the maximum force is applied
|
||||
[~, i_s_stop] = max(F);
|
||||
% Linear region stops ~ when 90% of the stroke is reached
|
||||
i_l_stop = find(d > 0.9*d(i_s_stop), 1, 'first');
|
||||
% "Stop" region start ~1N before maximum force is applied
|
||||
i_s_start = find(F > max(F)-1, 1, 'first');
|
||||
|
||||
%% Define variables for the two regions
|
||||
F_l = F(i_l_start:i_l_stop);
|
||||
d_l = d(i_l_start:i_l_stop);
|
||||
|
||||
F_s = F(i_s_start:i_s_stop);
|
||||
d_s = d(i_s_start:i_s_stop);
|
||||
|
||||
%% Fit the best straight line for the two regions
|
||||
fit_l = polyfit(F_l, d_l, 1);
|
||||
fit_s = polyfit(F_s, d_s, 1);
|
||||
|
||||
%% Reset displacement based on fit
|
||||
d = d - fit_l(2);
|
||||
fit_s(2) = fit_s(2) - fit_l(2);
|
||||
fit_l(2) = 0;
|
||||
|
||||
|
||||
|
||||
% The raw data as well as the fit corresponding to the two stiffnesses are shown in Figure ref:fig:test_joints_meas_F_d_lin_fit.
|
||||
|
||||
|
||||
figure;
|
||||
hold on;
|
||||
plot(F(1:i_s_stop), 1e3*d(1:i_s_stop), '.k')
|
||||
plot(F_l, 1e3*(F_l*fit_l(1) + fit_l(2)))
|
||||
plot(F_s, 1e3*(F_s*fit_s(1) + fit_s(2)))
|
||||
hold off;
|
||||
xlabel('Force [N]'); ylabel('Displacement [mm]');
|
||||
xlim([0,6]);
|
||||
|
||||
|
||||
|
||||
% #+name: fig:test_joints_meas_F_d_lin_fit
|
||||
% #+caption: Typical measurement of the diplacement as a function of the applied force with estimated linear fits
|
||||
% #+RESULTS:
|
||||
% [[file:figs/test_joints_meas_F_d_lin_fit.png]]
|
||||
|
||||
% Then, the bending stroke is estimated as crossing point between the two fitted lines:
|
||||
|
||||
d_max = fit_l(1)*fit_s(2)/(fit_l(1) - fit_s(1));
|
||||
|
||||
% Bending stiffness and bending stroke of all the flexible joints
|
||||
|
||||
% Now, let's estimate the bending stiffness and stroke for all the flexible joints.
|
||||
|
||||
|
||||
%% Initialize variables
|
||||
kRx = zeros(1,16);
|
||||
kSx = zeros(1,16);
|
||||
Rmx = zeros(1,16);
|
||||
|
||||
for i = 1:16
|
||||
%% Load the data
|
||||
load(['meas_stiff_flex_' num2str(i) '_x.mat'], 't', 'F', 'd');
|
||||
|
||||
%% Automatic Zero of the force
|
||||
F = F - mean(F(t > 0.1 & t < 0.3));
|
||||
|
||||
%% Start measurement at t = 0.2 s
|
||||
d = d(t > 0.2);
|
||||
F = F(t > 0.2);
|
||||
t = t(t > 0.2); t = t - t(1);
|
||||
|
||||
%% Estimate linear region and "stop" region
|
||||
i_l_start = find(F > 0.3, 1, 'first');
|
||||
d = d - d(i_l_start);
|
||||
[~, i_s_stop] = max(F);
|
||||
i_l_stop = find(d > 0.9*d(i_s_stop), 1, 'first');
|
||||
i_s_start = find(F > max(F)-1, 1, 'first');
|
||||
|
||||
F_l = F(i_l_start:i_l_stop);
|
||||
d_l = d(i_l_start:i_l_stop);
|
||||
|
||||
F_s = F(i_s_start:i_s_stop);
|
||||
d_s = d(i_s_start:i_s_stop);
|
||||
|
||||
%% Straight line fit
|
||||
fit_l = polyfit(F_l, d_l, 1);
|
||||
fit_s = polyfit(F_s, d_s, 1);
|
||||
|
||||
%% Reset displacement based on fit
|
||||
d = d - fit_l(2);
|
||||
fit_s(2) = fit_s(2) - fit_l(2);
|
||||
fit_l(2) = 0;
|
||||
|
||||
%% Estimated Stroke
|
||||
d_max = fit_l(1)*fit_s(2)/(fit_l(1) - fit_s(1));
|
||||
|
||||
%% Save stiffnesses and stroke
|
||||
kRx(i) = (h)^2/fit_l(1);
|
||||
kSx(i) = (h)^2/fit_s(1);
|
||||
Rmx(i) = atan2(d_max,h);
|
||||
|
||||
end
|
||||
|
||||
%% Initialize variables
|
||||
kRy = zeros(1,16);
|
||||
kSy = zeros(1,16);
|
||||
Rmy = zeros(1,16);
|
||||
|
||||
for i = 1:16
|
||||
%% Load the data
|
||||
load(['meas_stiff_flex_' num2str(i) '_y.mat'], 't', 'F', 'd');
|
||||
|
||||
%% Automatic Zero of the force
|
||||
F = F - mean(F(t > 0.1 & t < 0.3));
|
||||
|
||||
%% Start measurement at t = 0.2 s
|
||||
d = d(t > 0.2);
|
||||
F = F(t > 0.2);
|
||||
t = t(t > 0.2); t = t - t(1);
|
||||
|
||||
%% Estimate linear region and "stop" region
|
||||
i_l_start = find(F > 0.3, 1, 'first');
|
||||
d = d - d(i_l_start);
|
||||
[~, i_s_stop] = max(F);
|
||||
i_l_stop = find(d > 0.9*d(i_s_stop), 1, 'first');
|
||||
i_s_start = find(F > max(F)-1, 1, 'first');
|
||||
|
||||
F_l = F(i_l_start:i_l_stop);
|
||||
d_l = d(i_l_start:i_l_stop);
|
||||
|
||||
F_s = F(i_s_start:i_s_stop);
|
||||
d_s = d(i_s_start:i_s_stop);
|
||||
|
||||
%% Straight line fit
|
||||
fit_l = polyfit(F_l, d_l, 1);
|
||||
fit_s = polyfit(F_s, d_s, 1);
|
||||
|
||||
%% Reset displacement based on fit
|
||||
d = d - fit_l(2);
|
||||
fit_s(2) = fit_s(2) - fit_l(2);
|
||||
fit_l(2) = 0;
|
||||
|
||||
%% Estimated Stroke
|
||||
d_max = fit_l(1)*fit_s(2)/(fit_l(1) - fit_s(1));
|
||||
|
||||
%% Save stiffnesses and stroke
|
||||
kRy(i) = (h)^2/fit_l(1);
|
||||
kSy(i) = (h)^2/fit_s(1);
|
||||
Rmy(i) = atan2(d_max,h);
|
||||
|
||||
end
|
||||
|
||||
% Analysis
|
||||
% The dispersion of the measured bending stiffness is shown in Figure ref:fig:test_joints_bend_stiff_hist and of the bending stroke in Figure ref:fig:test_joints_bend_stroke_hist.
|
||||
|
||||
|
||||
figure;
|
||||
hold on;
|
||||
histogram(kRx, 'DisplayName', '$k_{R_x}$')
|
||||
histogram(kRy, 'DisplayName', '$k_{R_y}$')
|
||||
hold off;
|
||||
xlabel('Bending Stiffness [Nm/rad]')
|
||||
legend();
|
||||
|
||||
|
||||
|
||||
% #+name: fig:test_joints_bend_stiff_hist
|
||||
% #+caption: Histogram of the measured bending stiffness
|
||||
% #+RESULTS:
|
||||
% [[file:figs/test_joints_bend_stiff_hist.png]]
|
||||
|
||||
|
||||
figure;
|
||||
hold on;
|
||||
histogram(1e3*Rmx, 'DisplayName', '$k_{R_x}$')
|
||||
histogram(1e3*Rmy, 'DisplayName', '$k_{R_y}$')
|
||||
hold off;
|
||||
xlabel('Bending Stroke [mrad]')
|
||||
legend();
|
||||
|
||||
|
||||
|
||||
% #+name: fig:test_joints_bend_stroke_hist
|
||||
% #+caption: Histogram of the measured bending stroke
|
||||
% #+RESULTS:
|
||||
% [[file:figs/test_joints_bend_stroke_hist.png]]
|
||||
|
||||
% The relation between the measured beam thickness and the measured bending stiffness is shown in Figure ref:fig:test_joints_thickness_stiffness.
|
||||
|
||||
|
||||
load('flex_meas_dim.mat', 'meas_flex');
|
||||
figure;
|
||||
hold on;
|
||||
plot((meas_flex(:,1)+meas_flex(:,2))/2, kRx, 'o', 'DisplayName', '$x$')
|
||||
plot((meas_flex(:,3)+meas_flex(:,4))/2, kRy, 'o', 'DisplayName', '$y$')
|
||||
hold off;
|
||||
xlabel('Flexible Beam Thickness [$\mu m$]');
|
||||
ylabel('Bending Stiffness [Nm/rad]');
|
||||
legend('location', 'southeast');
|
||||
Reference in New Issue
Block a user