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Kinematics.m
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%% Motion control for a 3 DoF Stewart platform mechanism
%
% Arash Gobal
%
% This program provides the final length of the hydraulic jacks of a 3
% degree of freedom Stewart platform given the initial and limit length of
% jacks, their base positions and width and length of the platform and the
% platforms final required position (desired elevation and roll and pitch
% angles).
%
% For the sake of simplicity, jacks are assumed to be identical
%
%% Geometry of the mechanism
% Platform dimensions
prompt = {'Length (m):', 'Width (m):'};
dlg_title = 'Platform geometry';
num_lines = 1;
defaultans = {'0.0833', '0.1'};
answer = inputdlg(prompt, dlg_title, num_lines, defaultans);
platform_length = str2double(char(answer(1)));
platform_width = str2double(char(answer(2)));
% Jack properties
prompt = {'Closed length (m):', 'Displacement (m):'};
dlg_title = 'Jack properties';
num_lines = 1;
defaultans = {'0.42', '0.35'};
answer = inputdlg(prompt, dlg_title, num_lines, defaultans);
closed_length = str2double(char(answer(1)));
limit_length = str2double(char(answer(2)))+str2double(char(answer(1)));
% Jack base locations
prompt = {'X-1 (m):', 'Y-1 (m):', 'X-2 (m):', 'Y-2 (m):', 'X-3 (m):', 'Y-3 (m):'};
dlg_title = 'Jack basis';
num_lines = 1;
defaultans = {'0', '-0.01666', '0.1', '-0.1', '-0.1', '-0.1'};
answer = inputdlg(prompt, dlg_title, num_lines, defaultans);
jack1_b = [str2double(char(answer(1))) str2double(char(answer(2))) 0];
jack2_b = [str2double(char(answer(3))) str2double(char(answer(4))) 0];
jack3_b = [str2double(char(answer(5))) str2double(char(answer(6))) 0];
% Jack-to-platform connections
prompt = {'X-1 (m):', 'Y-1 (m):', 'X-2 (m):', 'Y-2 (m):', 'X-3 (m):', 'Y-3 (m):'};
dlg_title = 'Jack-to-platform connections';
num_lines = 1;
defaultans = {'0', '-0.01666', '0.1', '-0.1', '-0.1', '-0.1'};
answer = inputdlg(prompt, dlg_title, num_lines, defaultans);
jack1_p = [str2double(char(answer(1))) str2double(char(answer(2)))];
jack2_p = [str2double(char(answer(3))) str2double(char(answer(4)))];
jack3_p = [str2double(char(answer(5))) str2double(char(answer(6)))];
% Initial platform elevation and angles
z_0 = closed_length; % initial elevation
theta_0 = 0; % initial roll angle
phi_0 = 0; % initial pitch angle
% Desired final platform location (central location and roll and pitch
% angles)
error = 1;
while (error == 1)
prompt = {'Central elevation (m):', 'Roll angle (deg):', 'Pitch angle (deg):'};
dlg_title = 'Final platform location';
num_lines = 1;
defaultans = {'0.6', '40', '40'};
answer = inputdlg(prompt, dlg_title, num_lines, defaultans);
z_final = str2double(char(answer(1)));
theta = str2double(char(answer(2)))*pi/180;
phi = str2double(char(answer(3)))*pi/180;
e1 = z_final+jack1_p(1)*sin(phi)+jack1_p(2)*sin(theta);
e2 = z_final+jack2_p(1)*sin(phi)+jack2_p(2)*sin(theta);
e3 = z_final+jack3_p(1)*sin(phi)+jack3_p(2)*sin(theta);
error = 0;
if (e1 < closed_length) || (e2 < closed_length) || (e3 < closed_length) || (e1 > limit_length) || (e2 > limit_length) || (e3 > limit_length)
error = 1;
else
error = 0;
end
end
%% Final end locations
jack1_initial = [jack1_p z_0];
jack1_final = [jack1_initial(1)*cos(phi) jack1_initial(2)*cos(theta) z_final+jack1_initial(1)*sin(phi)+jack1_initial(2)*sin(theta)];
jack1_length = sqrt((jack1_final(1) - jack1_b(1))^2 + (jack1_final(2) - jack1_b(2))^2 + (jack1_final(3) - jack1_b(3))^2);
jack2_initial = [jack2_p z_0];
jack2_final = [jack2_initial(1)*cos(phi) jack2_initial(2)*cos(theta) z_final+jack2_initial(1)*sin(phi)+jack2_initial(2)*sin(theta)];
jack2_length = sqrt((jack2_final(1) - jack2_b(1))^2 + (jack2_final(2) - jack2_b(2))^2 + (jack2_final(3) - jack2_b(3))^2);
jack3_initial = [jack3_p z_0];
jack3_final = [jack3_initial(1)*cos(phi) jack3_initial(2)*cos(theta) z_final+jack3_initial(1)*sin(phi)+jack3_initial(2)*sin(theta)];
jack3_length = sqrt((jack3_final(1) - jack3_b(1))^2 + (jack3_final(2) - jack3_b(2))^2 + (jack3_final(3) - jack3_b(3))^2);
disp('Final displacements of each jack:');
S=sprintf('Jack 1 displacement: %0.5g meters',(jack1_length - z_0));
% AZ0 = sprintf('Jack 1 initial angle w.r.t z axis: %0.5g degrees',(180/pi)*acos((jack1_initial(3) - jack1_b(3))/closed_length));
% l1 = closed_length*sin(acos((jack1_initial(3) - jack1_b(3))/closed_length));
% AX0 = sprintf('Jack 1 initial angle w.r.t x axis: %0.5g degrees',(180/pi)*acos((jack1_initial(1) - jack1_b(1))/l1));
% AY0 = sprintf('Jack 1 initial angle w.r.t y axis: %0.5g degrees',(180/pi)*acos((jack1_initial(2) - jack1_b(2))/l1));
% AZf = sprintf('Jack 1 final angle w.r.t z axis: %0.5g degrees',(180/pi)*acos((jack1_final(3) - jack1_b(3))/jack1_length));
% l2 = jack1_length*sin(acos((jack1_final(3) - jack1_b(3))/jack1_length));
% AXf = sprintf('Jack 1 final angle w.r.t x axis: %0.5g degrees',(180/pi)*acos((jack1_final(1) - jack1_b(1))/l2));
% AYf = sprintf('Jack 1 final angle w.r.t y axis: %0.5g degrees',(180/pi)*acos((jack1_final(2) - jack1_b(2))/l2));
disp(S);
% disp(AX0);
% disp(AY0);
% disp(AZ0);
% disp(AXf);
% disp(AYf);
% disp(AZf);
S=sprintf('Jack 2 displacement: %0.5g meters',(jack2_length - z_0));
% BZ0 = sprintf('Jack 2 initial angle w.r.t z axis: %0.5g degrees',(180/pi)*acos((jack2_initial(3) - jack2_b(3))/closed_length));
% l1 = closed_length*sin(acos((jack2_initial(3) - jack2_b(3))/closed_length));
% BX0 = sprintf('Jack 2 initial angle w.r.t x axis: %0.5g degrees',(180/pi)*acos((jack2_initial(1) - jack2_b(1))/l1));
% BY0 = sprintf('Jack 2 initial angle w.r.t y axis: %0.5g degrees',(180/pi)*acos((jack2_initial(2) - jack2_b(2))/l1));
% BZf = sprintf('Jack 2 final angle w.r.t z axis: %0.5g degrees',(180/pi)*acos((jack2_final(3) - jack2_b(3))/jack2_length));
% l2 = jack2_length*sin(acos((jack2_final(3) - jack2_b(3))/jack2_length));
% BXf = sprintf('Jack 2 final angle w.r.t x axis: %0.5g degrees',(180/pi)*acos((jack2_final(1) - jack2_b(1))/l2));
% BYf = sprintf('Jack 2 final angle w.r.t y axis: %0.5g degrees',(180/pi)*acos((jack2_final(2) - jack2_b(2))/l2));
disp(S);
% disp(BX0);
% disp(BY0);
% disp(BZ0);
% disp(BXf);
% disp(BYf);
% disp(BZf);
S=sprintf('Jack 3 displacement: %0.5g meters',(jack3_length - z_0));
% CZ0 = sprintf('Jack 3 initial angle w.r.t z axis: %0.5g degrees',(180/pi)*acos((jack3_initial(3) - jack3_b(3))/closed_length));
% l1 = closed_length*sin(acos((jack3_initial(3) - jack3_b(3))/closed_length));
% CX0 = sprintf('Jack 3 initial angle w.r.t x axis: %0.5g degrees',(180/pi)*acos((jack3_initial(1) - jack3_b(1))/l1));
% CY0 = sprintf('Jack 3 initial angle w.r.t y axis: %0.5g degrees',(180/pi)*acos((jack3_initial(2) - jack3_b(2))/l1));
% CZf = sprintf('Jack 3 final angle w.r.t z axis: %0.5g degrees',(180/pi)*acos((jack3_final(3) - jack3_b(3))/jack3_length));
% l2 = jack3_length*sin(acos((jack3_final(3) - jack3_b(3))/jack3_length));
% CXf = sprintf('Jack 3 final angle w.r.t x axis: %0.5g degrees',(180/pi)*acos((jack3_final(1) - jack3_b(1))/l2));
% CYf = sprintf('Jack 3 final angle w.r.t y axis: %0.5g degrees',(180/pi)*acos((jack3_final(2) - jack3_b(2))/l2));
disp(S);
% disp(CX0);
% disp(CY0);
% disp(CZ0);
% disp(CXf);
% disp(CYf);
% disp(CZf);
% Plot the movement and base
xb = [jack1_b(1) jack2_b(1) jack3_b(1)];
yb = [jack1_b(2) jack2_b(2) jack3_b(2)];
zb = [jack1_b(3) jack2_b(3) jack3_b(3)];
x0 = [jack1_initial(1) jack2_initial(1) jack3_initial(1)];
y0 = [jack1_initial(2) jack2_initial(2) jack3_initial(2)];
z0 = [jack1_initial(3) jack2_initial(3) jack3_initial(3)];
plot3(0.1,0.0,0.7,-0.1,-0.1,0)
hold on
plot3([xb(1) x0(1)], [yb(1) y0(1)], [zb(1) z0(1)]);
plot3([xb(2) x0(2)], [yb(2) y0(2)], [zb(2) z0(2)]);
plot3([xb(3) x0(3)], [yb(3) y0(3)], [zb(3) z0(3)]);
fill3(x0,y0,z0,1);
hold off
for i = 1:100
x = [(x0(1) + i*(jack1_final(1) - x0(1))/100) (x0(2) + i*(jack2_final(1) - x0(2))/100) (x0(3) + i*(jack3_final(1) - x0(3))/100)];
y = [(y0(1) + i*(jack1_final(2) - y0(1))/100) (y0(2) + i*(jack2_final(2) - y0(2))/100) (y0(3) + i*(jack3_final(2) - y0(3))/100)];
z = [(z0(1) + i*(jack1_final(3) - z0(1))/100) (z0(2) + i*(jack2_final(3) - z0(2))/100) (z0(3) + i*(jack3_final(3) - z0(3))/100)];
plot3(0.1,0.0,0.7,-0.1,-0.1,0)
hold on
plot3([xb(1) x(1)], [yb(1) y(1)], [zb(1) z(1)]);
plot3([xb(2) x(2)], [yb(2) y(2)], [zb(2) z(2)]);
plot3([xb(3) x(3)], [yb(3) y(3)], [zb(3) z(3)]);
fill3(x,y,z,1)
hold off
pause(0.1);
end