94 lines
4.2 KiB
Mathematica
94 lines
4.2 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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% Having Cube's center above the top platform
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% Let's say we want to have a diagonal stiffness matrix when $\{A\}$ and $\{B\}$ are located above the top platform.
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% Thus, we want the cube's center to be located above the top center.
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% Let's fix the Height of the Stewart platform and the position of frames $\{A\}$ and $\{B\}$:
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H = 100e-3; % height of the Stewart platform [m]
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MO_B = 20e-3; % Position {B} with respect to {M} [m]
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% We find the several Cubic configuration for the Stewart platform where the center of the cube is located at frame $\{A\}$.
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% The differences between the configuration are the cube's size:
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% - Small Cube Size in Figure [[fig:stewart_cubic_conf_type_1]]
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% - Medium Cube Size in Figure [[fig:stewart_cubic_conf_type_2]]
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% - Large Cube Size in Figure [[fig:stewart_cubic_conf_type_3]]
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% For each of the configuration, the Stiffness matrix is diagonal with $k_x = k_y = k_y = 2k$ with $k$ is the stiffness of each strut.
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% However, the rotational stiffnesses are increasing with the cube's size but the required size of the platform is also increasing, so there is a trade-off here.
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Hc = 0.4*H; % Size of the useful part of the cube [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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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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stewart = initializeCylindricalPlatforms(stewart, 'Fpr', 1.2*max(vecnorm(stewart.platform_F.Fa)), 'Mpr', 1.2*max(vecnorm(stewart.platform_M.Mb)));
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displayArchitecture(stewart, 'labels', false);
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scatter3(0, 0, FOc, 200, 'kh');
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% #+name: tab:stewart_cubic_conf_type_1
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% #+caption: Stiffness Matrix
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% #+RESULTS:
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% | 2 | 0 | -2.8e-16 | 0 | 2.4e-17 | 0 |
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% | 0 | 2 | 0 | -2.3e-17 | 0 | 0 |
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% | -2.8e-16 | 0 | 2 | -2.1e-19 | 0 | 0 |
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% | 0 | -2.3e-17 | -2.1e-19 | 0.0024 | -5.4e-20 | 6.5e-19 |
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% | 2.4e-17 | 0 | 4.9e-19 | -2.3e-20 | 0.0024 | 0 |
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% | -1.2e-18 | 1.1e-18 | 0 | 6.2e-19 | 0 | 0.0096 |
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Hc = 1.5*H; % Size of the useful part of the cube [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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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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stewart = initializeCylindricalPlatforms(stewart, 'Fpr', 1.2*max(vecnorm(stewart.platform_F.Fa)), 'Mpr', 1.2*max(vecnorm(stewart.platform_M.Mb)));
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displayArchitecture(stewart, 'labels', false);
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scatter3(0, 0, FOc, 200, 'kh');
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% #+name: tab:stewart_cubic_conf_type_2
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% #+caption: Stiffness Matrix
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% #+RESULTS:
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% | 2 | 0 | -1.9e-16 | 0 | 5.6e-17 | 0 |
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% | 0 | 2 | 0 | -7.6e-17 | 0 | 0 |
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% | -1.9e-16 | 0 | 2 | 2.5e-18 | 2.8e-17 | 0 |
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% | 0 | -7.6e-17 | 2.5e-18 | 0.034 | 8.7e-19 | 8.7e-18 |
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% | 5.7e-17 | 0 | 3.2e-17 | 2.9e-19 | 0.034 | 0 |
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% | -1e-18 | -1.3e-17 | 5.6e-17 | 8.4e-18 | 0 | 0.14 |
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Hc = 2.5*H; % Size of the useful part of the cube [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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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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stewart = initializeCylindricalPlatforms(stewart, 'Fpr', 1.2*max(vecnorm(stewart.platform_F.Fa)), 'Mpr', 1.2*max(vecnorm(stewart.platform_M.Mb)));
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displayArchitecture(stewart, 'labels', false);
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scatter3(0, 0, FOc, 200, 'kh');
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