73 lines
2.4 KiB
Matlab
73 lines
2.4 KiB
Matlab
%% 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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% Stewart architecture definition
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% Let's first define the Stewart platform architecture that we want to study.
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stewart = initializeStewartPlatform();
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stewart = initializeFramesPositions(stewart, 'H', 90e-3, 'MO_B', 45e-3);
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stewart = generateGeneralConfiguration(stewart);
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stewart = computeJointsPose(stewart);
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stewart = initializeStewartPose(stewart);
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stewart = initializeCylindricalPlatforms(stewart);
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stewart = initializeCylindricalStruts(stewart);
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stewart = initializeStrutDynamics(stewart);
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stewart = initializeJointDynamics(stewart);
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stewart = computeJacobian(stewart);
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% Let's now define the actuator stroke.
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L_min = -50e-6; % [m]
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L_max = 50e-6; % [m]
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% Pure translations
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% Let's first estimate the mobility in translation when the orientation of the Stewart platform stays the same.
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% As shown previously, for such small stroke, we can use the approximate Forward Dynamics solution using the Jacobian matrix:
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% \begin{equation*}
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% \delta\bm{\mathcal{L}} = \bm{J} \delta\bm{\mathcal{X}}
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% \end{equation*}
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% To obtain the mobility "volume" attainable by the Stewart platform when it's orientation is set to zero, we use the spherical coordinate $(r, \theta, \phi)$.
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% For each possible value of $(\theta, \phi)$, we compute the maximum radius $r$ attainable with the constraint that the stroke of each actuator should be between =L_min= and =L_max=.
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thetas = linspace(0, pi, 50);
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phis = linspace(0, 2*pi, 50);
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rs = zeros(length(thetas), length(phis));
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for i = 1:length(thetas)
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for j = 1:length(phis)
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Tx = sin(thetas(i))*cos(phis(j));
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Ty = sin(thetas(i))*sin(phis(j));
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Tz = cos(thetas(i));
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dL = stewart.kinematics.J*[Tx; Ty; Tz; 0; 0; 0;]; % dL required for 1m displacement in theta/phi direction
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rs(i, j) = max([dL(dL<0)*L_min; dL(dL>0)*L_max]);
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end
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end
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% #+RESULTS:
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% | =L_min= [$\mu m$] | =L_max= [$\mu m$] | =R= [$\mu m$] |
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% |-------------------+-------------------+---------------|
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% | -50.0 | 50.0 | 31.5 |
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figure;
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plot3(reshape(rs.*(sin(thetas)'*cos(phis)), [1, length(thetas)*length(phis)]), ...
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reshape(rs.*(sin(thetas)'*sin(phis)), [1, length(thetas)*length(phis)]), ...
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reshape(rs.*(cos(thetas)'*ones(1, length(phis))), [1, length(thetas)*length(phis)]))
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xlabel('X Translation [m]');
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ylabel('Y Translation [m]');
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zlabel('Z Translation [m]');
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