o2 = [0, 0, 0]; % Origin for ain
ain = [26, 0, 0]; % Initial vector for ain
input_axis = [0, 1, 0]; % Axis of rotation for ain (y-axis)
theta1 = deg2rad(10); % Angle of rotation for ain in radians

% Rotation matrix function
rot_matrix = @(axis, theta) cos(theta) * eye(3) + …
sin(theta) * [0, -axis(3), axis(2); axis(3), 0, -axis(1); -axis(2), axis(1), 0] + …
(1 – cos(theta)) * (axis’ * axis);

% Compute the rotated vector for ain
a_rotated = rot_matrix(input_axis, theta1) * (ain’ – o2′) + o2′;
a_final = a_rotated’;
disp(norm(a_final));

cin=[122.95, -20, 0];
c_rotated= rot_matrix(input_axis, theta1) * (cin’ – o2′) + o2′;
naxis=[sin(theta1),0,cos(theta1)];
syms phi;
c_final_rotated=rot_matrix(naxis,phi)*(c_rotated-a_rotated)+a_rotated;

bin = [29.5, 30, 0];
o4 = [13.5, 30, 0]; % Origin for bin
output_axis = [0, 1, 0]; % Axis of rotation for bin (y-axis)
theta2 = deg2rad(10); % Angle of rotation for bin in radians

% Compute the rotated vector for bin
b1_rotated = rot_matrix(output_axis, theta2) * (bin’ – o4′) + o4′;
b1_final = b1_rotated’;
disp(norm(b1_final-o4));

coupler = c_final_rotated’-b1_final;
coupler = subs(coupler, conj(phi), phi);

syms t;
cos_phi = (1 – t^2) / (1 + t^2);
sin_phi = 2 * t / (1 + t^2);

% Substitute parametric forms into coupler components
coupler_parametric = subs(coupler, [cos(phi), sin(phi)], [cos_phi, sin_phi]);

% Display the parametric coupler
disp(‘Parametric form of coupler:’);
disp(coupler_parametric);

syms targetvalue % it might be 3.5 …
normsq = expand(sum(coupler_parametric.^2) – targetvalue^2);

normpoly = simplify(normsq*(t^2+1)^2);
vpa(expand(normpoly),4);
tsolve = solve(normpoly,t,’maxdegree’,4,’returnconditions’,true);
h=vpa(subs(tsolve.t,targetvalue, 106));
%disp(h);
real_solutions = h(imag(h) == 0);
disp(‘Real roots:’);
disp(real_solutions);

angles_rad = 2 * atan(real_solutions);
angles_deg = rad2deg(angles_rad);

% Display angles in degrees
disp(‘Angles in degrees before adjustment:’);
disp(angles_deg);

phi=double(angles_rad(2));

c1_position = double(rot_matrix(naxis,phi) * (c_rotated – a_rotated) + a_rotated);
p=(c1_position’-a_final)’;
%q=(c1_position’-b1_final)’;

angle=acosd(p(2)/norm(p));
disp(angle);

%%I want to run this code for symbolic variables including o2,ain,o4,bin,input_axis,output_axis,naxis,theta1,theta2.
can someone tell how can i do all above calculations in symbolic formo2 = [0, 0, 0]; % Origin for ain
ain = [26, 0, 0]; % Initial vector for ain
input_axis = [0, 1, 0]; % Axis of rotation for ain (y-axis)
theta1 = deg2rad(10); % Angle of rotation for ain in radians

% Rotation matrix function
rot_matrix = @(axis, theta) cos(theta) * eye(3) + …
sin(theta) * [0, -axis(3), axis(2); axis(3), 0, -axis(1); -axis(2), axis(1), 0] + …
(1 – cos(theta)) * (axis’ * axis);

% Compute the rotated vector for ain
a_rotated = rot_matrix(input_axis, theta1) * (ain’ – o2′) + o2′;
a_final = a_rotated’;
disp(norm(a_final));

cin=[122.95, -20, 0];
c_rotated= rot_matrix(input_axis, theta1) * (cin’ – o2′) + o2′;
naxis=[sin(theta1),0,cos(theta1)];
syms phi;
c_final_rotated=rot_matrix(naxis,phi)*(c_rotated-a_rotated)+a_rotated;

bin = [29.5, 30, 0];
o4 = [13.5, 30, 0]; % Origin for bin
output_axis = [0, 1, 0]; % Axis of rotation for bin (y-axis)
theta2 = deg2rad(10); % Angle of rotation for bin in radians

% Compute the rotated vector for bin
b1_rotated = rot_matrix(output_axis, theta2) * (bin’ – o4′) + o4′;
b1_final = b1_rotated’;
disp(norm(b1_final-o4));

coupler = c_final_rotated’-b1_final;
coupler = subs(coupler, conj(phi), phi);

syms t;
cos_phi = (1 – t^2) / (1 + t^2);
sin_phi = 2 * t / (1 + t^2);

% Substitute parametric forms into coupler components
coupler_parametric = subs(coupler, [cos(phi), sin(phi)], [cos_phi, sin_phi]);

% Display the parametric coupler
disp(‘Parametric form of coupler:’);
disp(coupler_parametric);

syms targetvalue % it might be 3.5 …
normsq = expand(sum(coupler_parametric.^2) – targetvalue^2);

normpoly = simplify(normsq*(t^2+1)^2);
vpa(expand(normpoly),4);
tsolve = solve(normpoly,t,’maxdegree’,4,’returnconditions’,true);
h=vpa(subs(tsolve.t,targetvalue, 106));
%disp(h);
real_solutions = h(imag(h) == 0);
disp(‘Real roots:’);
disp(real_solutions);

angles_rad = 2 * atan(real_solutions);
angles_deg = rad2deg(angles_rad);

% Display angles in degrees
disp(‘Angles in degrees before adjustment:’);
disp(angles_deg);

phi=double(angles_rad(2));

c1_position = double(rot_matrix(naxis,phi) * (c_rotated – a_rotated) + a_rotated);
p=(c1_position’-a_final)’;
%q=(c1_position’-b1_final)’;

angle=acosd(p(2)/norm(p));
disp(angle);

%%I want to run this code for symbolic variables including o2,ain,o4,bin,input_axis,output_axis,naxis,theta1,theta2.
can someone tell how can i do all above calculations in symbolic form o2 = [0, 0, 0]; % Origin for ain
ain = [26, 0, 0]; % Initial vector for ain
input_axis = [0, 1, 0]; % Axis of rotation for ain (y-axis)
theta1 = deg2rad(10); % Angle of rotation for ain in radians

% Rotation matrix function
rot_matrix = @(axis, theta) cos(theta) * eye(3) + …
sin(theta) * [0, -axis(3), axis(2); axis(3), 0, -axis(1); -axis(2), axis(1), 0] + …
(1 – cos(theta)) * (axis’ * axis);

% Compute the rotated vector for ain
a_rotated = rot_matrix(input_axis, theta1) * (ain’ – o2′) + o2′;
a_final = a_rotated’;
disp(norm(a_final));

cin=[122.95, -20, 0];
c_rotated= rot_matrix(input_axis, theta1) * (cin’ – o2′) + o2′;
naxis=[sin(theta1),0,cos(theta1)];
syms phi;
c_final_rotated=rot_matrix(naxis,phi)*(c_rotated-a_rotated)+a_rotated;

bin = [29.5, 30, 0];
o4 = [13.5, 30, 0]; % Origin for bin
output_axis = [0, 1, 0]; % Axis of rotation for bin (y-axis)
theta2 = deg2rad(10); % Angle of rotation for bin in radians

% Compute the rotated vector for bin
b1_rotated = rot_matrix(output_axis, theta2) * (bin’ – o4′) + o4′;
b1_final = b1_rotated’;
disp(norm(b1_final-o4));

coupler = c_final_rotated’-b1_final;
coupler = subs(coupler, conj(phi), phi);

syms t;
cos_phi = (1 – t^2) / (1 + t^2);
sin_phi = 2 * t / (1 + t^2);

% Substitute parametric forms into coupler components
coupler_parametric = subs(coupler, [cos(phi), sin(phi)], [cos_phi, sin_phi]);

% Display the parametric coupler
disp(‘Parametric form of coupler:’);
disp(coupler_parametric);

syms targetvalue % it might be 3.5 …
normsq = expand(sum(coupler_parametric.^2) – targetvalue^2);

normpoly = simplify(normsq*(t^2+1)^2);
vpa(expand(normpoly),4);
tsolve = solve(normpoly,t,’maxdegree’,4,’returnconditions’,true);
h=vpa(subs(tsolve.t,targetvalue, 106));
%disp(h);
real_solutions = h(imag(h) == 0);
disp(‘Real roots:’);
disp(real_solutions);

angles_rad = 2 * atan(real_solutions);
angles_deg = rad2deg(angles_rad);

% Display angles in degrees
disp(‘Angles in degrees before adjustment:’);
disp(angles_deg);

phi=double(angles_rad(2));

c1_position = double(rot_matrix(naxis,phi) * (c_rotated – a_rotated) + a_rotated);
p=(c1_position’-a_final)’;
%q=(c1_position’-b1_final)’;

angle=acosd(p(2)/norm(p));
disp(angle);

%%I want to run this code for symbolic variables including o2,ain,o4,bin,input_axis,output_axis,naxis,theta1,theta2.
can someone tell how can i do all above calculations in symbolic form #symbolic, #numerical MATLAB Answers — New Questions

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