stewart-simscape/matlab/cubic_conf_size_analysisl.m

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2020-02-13 16:46:47 +01:00
%% Clear Workspace and Close figures
clear; close all; clc;
%% Intialize Laplace variable
s = zpk('s');
simulinkproject('../');
% Analysis
% We initialize the wanted cube's size.
Hcs = 1e-3*[250:20:350]; % Heights for the Cube [m]
Ks = zeros(6, 6, length(Hcs));
% The height of the Stewart platform is fixed:
H = 100e-3; % height of the Stewart platform [m]
% The frames $\{A\}$ and $\{B\}$ are positioned at the Stewart platform center as well as the cube's center:
MO_B = -50e-3; % Position {B} with respect to {M} [m]
FOc = H + MO_B; % Center of the cube with respect to {F}
stewart = initializeStewartPlatform();
stewart = initializeFramesPositions(stewart, 'H', H, 'MO_B', MO_B);
for i = 1:length(Hcs)
Hc = Hcs(i);
stewart = generateCubicConfiguration(stewart, 'Hc', Hc, 'FOc', FOc, 'FHa', 0, 'MHb', 0);
stewart = computeJointsPose(stewart);
stewart = initializeStrutDynamics(stewart, 'K', ones(6,1));
stewart = computeJacobian(stewart);
Ks(:,:,i) = stewart.kinematics.K;
end
% We find that for all the cube's size, $k_x = k_y = k_z = k$ where $k$ is the strut stiffness.
% 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]]).
figure;
hold on;
plot(Hcs, squeeze(Ks(4, 4, :)), 'DisplayName', '$k_{\theta_x} = k_{\theta_y}$');
plot(Hcs, squeeze(Ks(6, 6, :)), 'DisplayName', '$k_{\theta_z}$');
hold off;
legend('location', 'northwest');
xlabel('Cube Size [m]'); ylabel('Rotational stiffnes [normalized]');