Stewart if configure just with one object. Use mask inside simulink.

analyze_jacobian.m

@@ -0,0 +1,46 @@
+figure;
+plot(d_meas.Time, d.Data-d_meas.Data)
+
+%%
+figure;
+plot(error.Time, error.Data)
+legend({'x', 'y', 'z', 'theta_x', 'theta_y', 'theta_z'})
+
+%%
+J = jacobian.Data(:, :, 1);
+
+% Norm of the jacobian with time
+J_change = (jacobian.Data - J)./J;
+
+figure;
+hold on;
+plot(jacobian.Time, squeeze(J_change(1, 1, :)));
+plot(jacobian.Time, squeeze(J_change(2, 2, :)));
+plot(jacobian.Time, squeeze(J_change(3, 3, :)));
+plot(jacobian.Time, squeeze(J_change(4, 4, :)));
+plot(jacobian.Time, squeeze(J_change(5, 5, :)));
+plot(jacobian.Time, squeeze(J_change(6, 6, :)));
+legend({'Jxx', 'Jyy', 'Jzz', 'Jmx', 'Jmy', 'Jmz'})
+hold off;
+
+%% K change
+K_init = J'*J;
+K = zeros(size(jacobian.Data));
+
+for i=1:length(jacobian.Time)
+    K(:, :, i) = jacobian.Data(:, :, i)'*jacobian.Data(:, :, i);
+end
+
+K_change = (permute(K, [2, 1, 3]) - K_init)./K_init;
+
+figure;
+hold on;
+plot(jacobian.Time, squeeze(K_change(1, 1, :)));
+plot(jacobian.Time, squeeze(K_change(2, 2, :)));
+plot(jacobian.Time, squeeze(K_change(3, 3, :)));
+plot(jacobian.Time, squeeze(K_change(4, 4, :)));
+plot(jacobian.Time, squeeze(K_change(5, 5, :)));
+plot(jacobian.Time, squeeze(K_change(6, 6, :)));
+legend({'Kxx', 'Kyy', 'Kzz', 'Kmx', 'Kmy', 'Kmz'})
+hold off;
+

initializeParameters.m

@@ -0,0 +1,80 @@
+function [stewart] = initializeParameters(stewart)
+    %% Connection points on base and top plate w.r.t. World frame at the center of the base plate
+    stewart.pos_base = zeros(6, 3);
+    stewart.pos_top = zeros(6, 3);
+
+    alpha_b = stewart.BP.leg.ang*pi/180; % angle de décalage par rapport à 120 deg (pour positionner les supports bases)
+    alpha_t = stewart.TP.leg.ang*pi/180; % +- offset angle from 120 degree spacing on top
+
+    height = (stewart.h-stewart.BP.thickness-stewart.TP.thickness-stewart.Leg.sphere.bottom-stewart.Leg.sphere.top-stewart.SP.thickness.bottom-stewart.SP.thickness.top)*0.001; % TODO
+
+    radius_b = stewart.BP.leg.rad*0.001; % rayon emplacement support base
+    radius_t = stewart.TP.leg.rad*0.001; % top radius in meters
+
+    for i = 1:3
+      % base points
+      angle_m_b = (2*pi/3)* (i-1) - alpha_b;
+      angle_p_b = (2*pi/3)* (i-1) + alpha_b;
+      stewart.pos_base(2*i-1,:) =  [radius_b*cos(angle_m_b), radius_b*sin(angle_m_b), 0.0];
+      stewart.pos_base(2*i,:) = [radius_b*cos(angle_p_b), radius_b*sin(angle_p_b), 0.0];
+
+      % top points
+      % Top points are 60 degrees offset
+      angle_m_t = (2*pi/3)* (i-1) - alpha_t + 2*pi/6;
+      angle_p_t = (2*pi/3)* (i-1) + alpha_t + 2*pi/6;
+      stewart.pos_top(2*i-1,:) = [radius_t*cos(angle_m_t), radius_t*sin(angle_m_t), height];
+      stewart.pos_top(2*i,:) = [radius_t*cos(angle_p_t), radius_t*sin(angle_p_t), height];
+    end
+
+    % permute pos_top points so that legs are end points of base and top points
+    stewart.pos_top = [stewart.pos_top(6,:); stewart.pos_top(1:5,:)]; %6th point on top connects to 1st on bottom
+    stewart.pos_top_tranform = stewart.pos_top - height*[zeros(6, 2),ones(6, 1)];
+
+    %% leg vectors
+    legs = stewart.pos_top - stewart.pos_base;
+    leg_length = zeros(6, 1);
+    leg_vectors = zeros(6, 3);
+    for i = 1:6
+      leg_length(i) = norm(legs(i,:));
+      leg_vectors(i,:)  = legs(i,:) / leg_length(i);
+    end
+
+    stewart.Leg.lenght = 1000*leg_length(1)/1.5;
+    stewart.Leg.shape.bot = [0 0; ...
+                             stewart.Leg.rad.bottom 0; ...
+                             stewart.Leg.rad.bottom stewart.Leg.lenght; ...
+                             stewart.Leg.rad.top stewart.Leg.lenght; ...
+                             stewart.Leg.rad.top 0.2*stewart.Leg.lenght; ...
+                             0 0.2*stewart.Leg.lenght];
+
+    %% Calculate revolute and cylindrical axes
+    rev1 = zeros(6, 3);
+    rev2 = zeros(6, 3);
+    cyl1 = zeros(6, 3);
+    for i = 1:6
+      rev1(i,:) = cross(leg_vectors(i,:), [0 0 1]);
+      rev1(i,:) = rev1(i,:) / norm(rev1(i,:));
+
+      rev2(i,:) = - cross(rev1(i,:), leg_vectors(i,:));
+      rev2(i,:) = rev2(i,:) / norm(rev2(i,:));
+
+      cyl1(i,:) = leg_vectors(i,:);
+    end
+
+
+    %% Coordinate systems
+    stewart.lower_leg = struct('rotation', eye(3));
+    stewart.upper_leg = struct('rotation', eye(3));
+
+    for i = 1:6
+      stewart.lower_leg(i).rotation = [rev1(i,:)', rev2(i,:)', cyl1(i,:)'];
+      stewart.upper_leg(i).rotation = [rev1(i,:)', rev2(i,:)', cyl1(i,:)'];
+    end
+
+    %% Position Matrix
+    stewart.M_pos_base = stewart.pos_base + (height+(stewart.TP.thickness+stewart.Leg.sphere.top+stewart.SP.thickness.top+stewart.jacobian)*1e-3)*[zeros(6, 2),ones(6, 1)];
+
+    %% Compute Jacobian Matrix
+    aa = stewart.pos_top_tranform + (stewart.jacobian - stewart.TP.thickness - stewart.SP.height.top)*1e-3*[zeros(6, 2),ones(6, 1)];
+    stewart.J  = getJacobianMatrix(leg_vectors', aa');
+end

params_micro_hexapod.m

@@ -0,0 +1,93 @@
+%%
+clear; close all; clc;
+
+%% Stewart Object
+stewart = struct();
+stewart.h        = 350; % Total height of the platform [mm]
+stewart.jacobian = 0;   % Point where the Jacobian is computed => Center of rotation [mm]
+
+%% Bottom Plate
+BP = struct();
+
+BP.rad.int   = 110;   % Internal Radius [mm]
+BP.rad.ext   = 207.5; % External Radius [mm]
+BP.thickness = 26;    % Thickness [mm]
+BP.leg.rad   = 175.5; % Radius where the legs articulations are positionned [mm]
+BP.leg.ang   = 9.5;   % Angle Offset [deg]
+BP.density   = 8000;  % Density of the material [kg/m^3]
+BP.color     = [0.6 0.6 0.6]; % Color [rgb]
+BP.shape     = [BP.rad.int BP.thickness; BP.rad.int 0; BP.rad.ext 0; BP.rad.ext BP.thickness];
+
+%% Top Plate
+TP = struct();
+
+TP.rad.int   = 82;   % Internal Radius [mm]
+TP.rad.ext   = 150;  % Internal Radius [mm]
+TP.thickness = 26;   % Thickness [mm]
+TP.leg.rad   = 118;  % Radius where the legs articulations are positionned [mm]
+TP.leg.ang   = 12.1; % Angle Offset [deg]
+TP.density   = 8000; % Density of the material [kg/m^3]
+TP.color     = [0.6 0.6 0.6]; % Color [rgb]
+TP.shape     = [TP.rad.int TP.thickness; TP.rad.int 0; TP.rad.ext 0; TP.rad.ext TP.thickness];
+
+%% Leg
+Leg = struct(); 
+
+Leg.stroke     = 10e-3; % Maximum Stroke of each leg [m]
+Leg.k.ax       = 5e7; % Stiffness of each leg [N/m]
+Leg.ksi.ax     = 10; % Maximum amplification at resonance []
+Leg.rad.bottom = 25; % Radius of the cylinder of the bottom part [mm]
+Leg.rad.top    = 17; % Radius of the cylinder of the top part [mm]
+Leg.density    = 8000; % Density of the material [kg/m^3]
+Leg.color.bottom  = [0.5 0.5 0.5]; % Color [rgb]
+Leg.color.top     = [0.5 0.5 0.5]; % Color [rgb]
+
+Leg.sphere.bottom = Leg.rad.bottom; % Size of the sphere at the end of the leg [mm]
+Leg.sphere.top    = Leg.rad.top; % Size of the sphere at the end of the leg [mm]
+Leg.m             = TP.density*((pi*(TP.rad.ext/1000)^2)*(TP.thickness/1000)-(pi*(TP.rad.int/1000^2))*(TP.thickness/1000))/6; % TODO [kg]
+Leg = updateDamping(Leg);
+
+
+%% Sphere
+SP = struct();
+
+SP.height.bottom  = 27; % [mm]
+SP.height.top     = 27; % [mm]
+SP.density.bottom = 8000; % [kg/m^3]
+SP.density.top    = 8000; % [kg/m^3]
+SP.color.bottom   = [0.6 0.6 0.6]; % [rgb]
+SP.color.top      = [0.6 0.6 0.6]; % [rgb]
+SP.k.ax           = 0; % [N*m/deg]
+SP.ksi.ax         = 10;
+
+SP.thickness.bottom = SP.height.bottom-Leg.sphere.bottom; % [mm]
+SP.thickness.top    = SP.height.top-Leg.sphere.top; % [mm]
+SP.rad.bottom       = Leg.sphere.bottom; % [mm]
+SP.rad.top          = Leg.sphere.top; % [mm]
+SP.m                = SP.density.bottom*2*pi*((SP.rad.bottom*1e-3)^2)*(SP.height.bottom*1e-3); % TODO [kg]
+
+SP = updateDamping(SP);
+
+%%
+Leg.support.bottom = [0 SP.thickness.bottom; 0 0; SP.rad.bottom 0; SP.rad.bottom SP.height.bottom];
+Leg.support.top    = [0 SP.thickness.top; 0 0; SP.rad.top 0; SP.rad.top SP.height.top];
+
+%%
+stewart.BP = BP;
+stewart.TP = TP;
+stewart.Leg = Leg;
+stewart.SP = SP;
+
+%%
+stewart = initializeParameters(stewart);
+
+%%
+clear BP TP Leg SP;
+
+%%
+function element = updateDamping(element)
+    field = fieldnames(element.k);
+    for i = 1:length(field)
+        element.c.(field{i}) = 1/element.ksi.(field{i})*sqrt(element.k.(field{i})/element.m);
+    end
+end

params_nano_hexapod.m

@@ -0,0 +1,93 @@
+%%
+clear; close all; clc;
+
+%% Stewart Object
+stewart = struct();
+stewart.h        = 90; % Total height of the platform [mm]
+stewart.jacobian = 174.5;   % Point where the Jacobian is computed => Center of rotation [mm]
+
+%% Bottom Plate
+BP = struct();
+
+BP.rad.int   = 0;   % Internal Radius [mm]
+BP.rad.ext   = 150; % External Radius [mm]
+BP.thickness = 10;    % Thickness [mm]
+BP.leg.rad   = 100; % Radius where the legs articulations are positionned [mm]
+BP.leg.ang   = 5;   % Angle Offset [deg]
+BP.density   = 8000;  % Density of the material [kg/m^3]
+BP.color     = [0.7 0.7 0.7]; % Color [rgb]
+BP.shape     = [BP.rad.int BP.thickness; BP.rad.int 0; BP.rad.ext 0; BP.rad.ext BP.thickness];
+
+%% Top Plate
+TP = struct();
+
+TP.rad.int   = 0;   % Internal Radius [mm]
+TP.rad.ext   = 100;  % Internal Radius [mm]
+TP.thickness = 10;   % Thickness [mm]
+TP.leg.rad   = 90;  % Radius where the legs articulations are positionned [mm]
+TP.leg.ang   = 5; % Angle Offset [deg]
+TP.density   = 8000; % Density of the material [kg/m^3]
+TP.color     = [0.7 0.7 0.7]; % Color [rgb]
+TP.shape     = [TP.rad.int TP.thickness; TP.rad.int 0; TP.rad.ext 0; TP.rad.ext TP.thickness];
+
+%% Leg
+Leg = struct(); 
+
+Leg.stroke     = 80e-6; % Maximum Stroke of each leg [m]
+Leg.k.ax       = 5e7; % Stiffness of each leg [N/m]
+Leg.ksi.ax     = 10; % Maximum amplification at resonance []
+Leg.rad.bottom = 12; % Radius of the cylinder of the bottom part [mm]
+Leg.rad.top    = 10; % Radius of the cylinder of the top part [mm]
+Leg.density    = 8000; % Density of the material [kg/m^3]
+Leg.color.bottom  = [0.5 0.5 0.5]; % Color [rgb]
+Leg.color.top     = [0.5 0.5 0.5]; % Color [rgb]
+
+Leg.sphere.bottom = Leg.rad.bottom; % Size of the sphere at the end of the leg [mm]
+Leg.sphere.top    = Leg.rad.top; % Size of the sphere at the end of the leg [mm]
+Leg.m             = TP.density*((pi*(TP.rad.ext/1000)^2)*(TP.thickness/1000)-(pi*(TP.rad.int/1000^2))*(TP.thickness/1000))/6; % TODO [kg]
+Leg = updateDamping(Leg);
+
+
+%% Sphere
+SP = struct();
+
+SP.height.bottom  = 15; % [mm]
+SP.height.top     = 15; % [mm]
+SP.density.bottom = 8000; % [kg/m^3]
+SP.density.top    = 8000; % [kg/m^3]
+SP.color.bottom   = [0.7 0.7 0.7]; % [rgb]
+SP.color.top      = [0.7 0.7 0.7]; % [rgb]
+SP.k.ax           = 0; % [N*m/deg]
+SP.ksi.ax         = 10;
+
+SP.thickness.bottom = SP.height.bottom-Leg.sphere.bottom; % [mm]
+SP.thickness.top    = SP.height.top-Leg.sphere.top; % [mm]
+SP.rad.bottom       = Leg.sphere.bottom; % [mm]
+SP.rad.top          = Leg.sphere.top; % [mm]
+SP.m                = SP.density.bottom*2*pi*((SP.rad.bottom*1e-3)^2)*(SP.height.bottom*1e-3); % TODO [kg]
+
+SP = updateDamping(SP);
+
+%%
+Leg.support.bottom = [0 SP.thickness.bottom; 0 0; SP.rad.bottom 0; SP.rad.bottom SP.height.bottom];
+Leg.support.top    = [0 SP.thickness.top; 0 0; SP.rad.top 0; SP.rad.top SP.height.top];
+
+%%
+stewart.BP = BP;
+stewart.TP = TP;
+stewart.Leg = Leg;
+stewart.SP = SP;
+
+%%
+stewart = initializeParameters(stewart);
+
+%%
+clear BP TP Leg SP;
+
+%%
+function element = updateDamping(element)
+    field = fieldnames(element.k);
+    for i = 1:length(field)
+        element.c.(field{i}) = 1/element.ksi.(field{i})*sqrt(element.k.(field{i})/element.m);
+    end
+end