Rename all files, tangle Matlab code

matlab/test_joints_1_dim_meas.m

@@ -0,0 +1,75 @@
+%% Clear Workspace and Close figures
+clear; close all; clc;
+
+%% Intialize Laplace variable
+s = zpk('s');
+
+%% Path for functions, data and scripts
+addpath('./mat/'); % Path for data
+
+%% Colors for the figures
+colors = colororder;
+
+% Measurement Results
+% # - Strange shape: 5
+
+% The expected flexible beam thickness is $250\,\mu m$.
+% However, it is more important that the thickness of all beams are close to each other.
+
+% The dimension of the beams are been measured at each end to be able to estimate the mean of the beam thickness.
+
+% All the measured dimensions are summarized in Table ref:tab:test_joints_flex_dim.
+
+
+meas_flex = [[223, 226, 224, 214];
+             [229, 231, 237, 224];
+             [234, 230, 239, 231];
+             [233, 227, 229, 232];
+             [225, 212, 228, 228];
+             [220, 221, 224, 220];
+             [206, 207, 228, 226];
+             [230, 224, 224, 223];
+             [223, 231, 228, 233];
+             [228, 230, 235, 231];
+             [197, 207, 211, 204];
+             [227, 226, 225, 226];
+             [215, 228, 231, 220];
+             [216, 224, 224, 221];
+             [209, 214, 220, 221];
+             [213, 210, 230, 229]];
+
+
+
+% #+name: tab:test_joints_flex_dim
+% #+caption: Measured Dimensions of the flexible beams in $\mu m$
+% #+attr_latex: :environment tabularx :width 0.4\linewidth :align Xcccc
+% #+attr_latex: :center t :booktabs t :float t
+% #+RESULTS:
+% |    |  Y1 |  Y2 |  X1 |  X2 |
+% |----+-----+-----+-----+-----|
+% |  1 | 223 | 226 | 224 | 214 |
+% |  2 | 229 | 231 | 237 | 224 |
+% |  3 | 234 | 230 | 239 | 231 |
+% |  4 | 233 | 227 | 229 | 232 |
+% |  5 | 225 | 212 | 228 | 228 |
+% |  6 | 220 | 221 | 224 | 220 |
+% |  7 | 206 | 207 | 228 | 226 |
+% |  8 | 230 | 224 | 224 | 223 |
+% |  9 | 223 | 231 | 228 | 233 |
+% | 10 | 228 | 230 | 235 | 231 |
+% | 11 | 197 | 207 | 211 | 204 |
+% | 12 | 227 | 226 | 225 | 226 |
+% | 13 | 215 | 228 | 231 | 220 |
+% | 14 | 216 | 224 | 224 | 221 |
+% | 15 | 209 | 214 | 220 | 221 |
+% | 16 | 213 | 210 | 230 | 229 |
+
+% An histogram of these measured dimensions is shown in Figure ref:fig:test_joints_size_hist.
+
+
+figure;
+histogram([(meas_flex(:,1)+meas_flex(:,2))/2,(meas_flex(:,3)+meas_flex(:,4))/2], 7)
+xlabel("Beam's Thickness [$\mu m$]");
+
+%% Save beam sizes
+save('./mat/flex_meas_dim.mat', 'meas_flex');

matlab/test_joints_2_bench_dimensioning.m

@@ -0,0 +1,59 @@
+%% Clear Workspace and Close figures
+clear; close all; clc;
+
+%% Intialize Laplace variable
+s = zpk('s');
+
+%% Path for functions, data and scripts
+addpath('./mat/'); % Path for data
+
+%% Colors for the figures
+colors = colororder;
+
+% Flexible joint Geometry
+% The flexible joint used for the Nano-Hexapod is shown in Figure ref:fig:test_joints_bend_geometry.
+% Its bending stiffness is foreseen to be $k_{R_y}\approx 5\,\frac{Nm}{rad}$ and its stroke $\theta_{y,\text{max}}\approx 25\,mrad$.
+
+% #+name: fig:test_joints_bend_geometry
+% #+caption: Geometry of the flexible joint
+% [[file:figs/test_joints_bend_geometry.png]]
+
+% The height between the flexible point (center of the joint) and the point where external forces are applied is $h = 20\,mm$.
+
+% Let's define the parameters on Matlab.
+
+kRx = 5; % Bending Stiffness [Nm/rad]
+Rxmax = 25e-3; % Bending Stroke [rad]
+h = 20e-3; % Height [m]
+
+% Required external applied force
+
+% The bending $\theta_y$ of the flexible joint due to the force $F_x$ is:
+% \begin{equation}
+%   \theta_y = \frac{M_y}{k_{R_y}} = \frac{F_x h}{k_{R_y}}
+% \end{equation}
+
+% Therefore, the applied force to test the full range of the flexible joint is:
+% \begin{equation}
+%   F_{x,\text{max}} = \frac{k_{R_y} \theta_{y,\text{max}}}{h}
+% \end{equation}
+
+
+Fxmax = kRx*Rxmax/h; % Force to induce maximum stroke [N]
+
+
+
+% And we obtain:
+
+sprintf('\\begin{equation} F_{x,max} = %.1f\\, [N] \\end{equation}', Fxmax)
+
+% Required actuator stroke and sensors range
+
+% The flexible joint is designed to allow a bending motion of $\pm 25\,mrad$.
+% The corresponding stroke at the location of the force sensor is:
+% \[ d_{x,\text{max}} = h \tan(R_{x,\text{max}}) \]
+
+
+dxmax = h*tan(Rxmax);
+
+sprintf('\\begin{equation} d_{max} = %.1f\\, [mm] \\end{equation}', 1e3*dxmax)

matlab/test_joints_3_error_budget.m

@@ -0,0 +1,73 @@
+%% Clear Workspace and Close figures
+clear; close all; clc;
+
+%% Intialize Laplace variable
+s = zpk('s');
+
+%% Path for functions, data and scripts
+addpath('./mat/'); % Path for data
+
+%% Colors for the figures
+colors = colororder;
+
+% Finite Element Model
+% 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.
+
+
+%% Stiffness
+ka = 94e6; % Axial Stiffness [N/m]
+ks = 13e6; % Shear Stiffness [N/m]
+kb = 5;    % Bending Stiffness [Nm/rad]
+kt = 260;  % Torsional Stiffness [Nm/rad]
+
+%% Maximum force
+Fa = 469;    % Axial Force before yield [N]
+Fs = 242;    % Shear Force before yield [N]
+Fb = 0.118;  % Bending Force before yield [Nm]
+Ft = 1.508; % Torsional Force before yield [Nm]
+
+%% Compute the corresponding stroke
+Xa = Fa/ka; % Axial Stroke before yield [m]
+Xs = Fs/ks; % Shear Stroke before yield [m]
+Xb = Fb/kb; % Bending Stroke before yield [rad]
+Xt = Ft/kt; % Torsional Stroke before yield [rad]
+
+% Setup
+
+% The setup is schematically represented in Figure ref:fig:test_joints_bench_side_bis.
+
+% The force is applied on top of the flexible joint with a distance $h$ with the joint's center.
+% The displacement of the flexible joint is also measured at the same height.
+
+% The height between the joint's center and the force application point is:
+
+h = 25e-3; % Height [m]
+
+% Estimation error due to force sensor compression
+% The measured displacement is not done directly at the joint's location.
+% The force sensor compression will then induce an error on the joint's stiffness.
+
+% The force sensor stiffness $k_F$ is estimated to be around:
+
+kF = 50/0.05e-3; % [N/m]
+
+sprintf('k_F = %.1e [N/m]', kF)
+
+% Estimation error due to height estimation error
+% Let's consider an error in the estimation of the height from the application of the force to the joint's center:
+% \begin{equation}
+% h_{\text{est}} = h (1 + \epsilon)
+% \end{equation}
+
+% The computed bending stiffness will be:
+% \begin{equation}
+%   k_\text{est} \approx h_{\text{est}}^2 \frac{F_x}{d_x}
+% \end{equation}
+
+% And the stiffness estimation error is:
+% \begin{equation}
+% \frac{k_{\text{est}}}{k_{R_y}} = (1 + \epsilon)^2
+% \end{equation}
+
+
+h_err = 0.2e-3; % Height estimation error [m]