52 lines
1.5 KiB
Mathematica
52 lines
1.5 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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simulinkproject('../');
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% Analysis
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% We initialize the wanted cube's size.
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Hcs = 1e-3*[250:20:350]; % Heights for the Cube [m]
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Ks = zeros(6, 6, length(Hcs));
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% The height of the Stewart platform is fixed:
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H = 100e-3; % height of the Stewart platform [m]
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% The frames $\{A\}$ and $\{B\}$ are positioned at the Stewart platform center as well as the cube's center:
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MO_B = -50e-3; % Position {B} with respect to {M} [m]
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FOc = H + MO_B; % Center of the cube with respect to {F}
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stewart = initializeStewartPlatform();
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stewart = initializeFramesPositions(stewart, 'H', H, 'MO_B', MO_B);
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for i = 1:length(Hcs)
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Hc = Hcs(i);
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stewart = generateCubicConfiguration(stewart, 'Hc', Hc, 'FOc', FOc, 'FHa', 0, 'MHb', 0);
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stewart = computeJointsPose(stewart);
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stewart = initializeStrutDynamics(stewart, 'K', ones(6,1));
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stewart = computeJacobian(stewart);
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Ks(:,:,i) = stewart.kinematics.K;
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end
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% We find that for all the cube's size, $k_x = k_y = k_z = k$ where $k$ is the strut stiffness.
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% We also find that $k_{\theta_x} = k_{\theta_y}$ and $k_{\theta_z}$ are varying with the cube's size (figure [[fig:stiffness_cube_size]]).
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figure;
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hold on;
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plot(Hcs, squeeze(Ks(4, 4, :)), 'DisplayName', '$k_{\theta_x} = k_{\theta_y}$');
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plot(Hcs, squeeze(Ks(6, 6, :)), 'DisplayName', '$k_{\theta_z}$');
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hold off;
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legend('location', 'northwest');
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xlabel('Cube Size [m]'); ylabel('Rotational stiffnes [normalized]');
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