54 lines
1.6 KiB
Mathematica
54 lines
1.6 KiB
Mathematica
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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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% Flexible joint Geometry
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% The flexible joint used for the Nano-Hexapod is shown in Figure [[fig:flexible_joint_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:flexible_joint_geometry
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% #+caption: Geometry of the flexible joint
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% [[file:figs/flexible_joint_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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