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How can I complete this code or reach the result according to this mechanism?

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Furkan
Furkan 2024-1-23
评论： Steven Lord 2024-1-23
% Define physical parameters of the mechanism
AB = 0.09; % m, length of arm 1
BC = 0.4; % m, length of arm 2
CD = 0.7; % m, length of arm 3
La = 0.75; % m
Lb = 0.35; % m
% Define simulation parameters
Nmax = 100; % Maximum number of iterations
x = [20*pi/180, 320*pi/180]; % Adjusted initial guess for th2, th3 (in radians)
xe = 0.0001 * abs(x); % Slightly relaxed error tolerance
dth = 5 * pi / 180; % Step size for thq
thQ = 0:dth:2*pi; % Range of thq (in radians)
w1 = -0.2944 * ones(size(thQ)); % Constant angular velocity w1
acc1 = zeros(size(thQ)); % Constant angular acceleration acc1
% Preallocate arrays for results
th2 = zeros(size(thQ));
th3 = zeros(size(thQ));
w2 = zeros(size(thQ));
w3 = zeros(size(thQ));
acc2 = zeros(size(thQ));
acc3 = zeros(size(thQ));
% Main loop for each th2 value
for k = 1:length(thQ)
x_temp = x; % Temporary variable for the current iteration
kerr = 1; % Flag for convergence
% Iterative solver for position analysis
for n = 1:Nmax
th2_temp = x_temp(1);
th3_temp = x_temp(2);
J = [-BC*sin(th2_temp), -CD*sin(th3_temp); BC*cos(th2_temp), CD*cos(th3_temp)];
% Check for singularity in Jacobian
if cond(J) > 1e10
disp(['Warning: Jacobian is near singular at th2 index: ', num2str(k)]);
break;
end
f = [-(AB*cos(thQ(k)) + BC*cos(th2_temp) + CD*cos(th3_temp) - La); ...
-(AB*sin(thQ(k)) + BC*sin(th2_temp) + CD*sin(th3_temp) + Lb)];
eps = J\f; % More efficient than inv(J)*f
x_temp = x_temp + eps';
if all(abs(eps) < xe)
kerr = 0;
break;
end
end
if kerr == 1
disp(['Error: Solution did not converge at th2 index: ', num2str(k), ' (th2 = ', num2str(thQ(k) * 180/pi), ' degrees)']);
else
th2(k) = x_temp(1);
th3(k) = x_temp(2);
% Velocity analysis
fv = [-AB*sin(thQ(k))*w1(k); AB*cos(thQ(k))*w1(k)];
vel = J\fv;
w2(k) = vel(1);
w3(k) = vel(2);
% Acceleration analysis
fa = [-AB*cos(thQ(k))((w1(k))^2) - BC*cos(th2(k))((w2(k))^2) - CD*cos(th3(k))*((w3(k))^2) - AB*sin(thQ(k))*acc1(k); ...
AB*cos(thQ(k))acc1(k) - BC*sin(th2(k))((w2(k))^2) - CD*sin(th3(k))((w3(k))^2) - AB*sin(thQ(k))((w1(k))^2)];
acc = J\fa;
acc2(k) = acc(1);
acc3(k) = acc(2);
end
end
% Convert angles to degrees for plotting
th2d = th2 * 180/pi;
th3d = th3 * 180/pi;
% Plotting results
figure(1);
subplot(3,3,1), plot(thQ, th2d, 'r', 'LineWidth', 2), xlabel('\theta_Q (rad)'), ylabel('\theta_2 (deg)'), grid on;
subplot(3,3,2), plot(thQ, w2, 'r', 'LineWidth', 2), xlabel('\theta_Q (rad)'), ylabel('\omega_2 (rad/s)'), grid on;
subplot(3,3,3), plot(thQ, acc2, 'r', 'LineWidth', 2), xlabel('\theta_Q (rad)'), ylabel('\alpha_2 (rad/s^2)'), grid on;
subplot(3,3,4), plot(thQ, th3d, 'r', 'LineWidth', 2), xlabel('\theta_Q (rad)'), ylabel('\theta_3 (deg)'), grid on;
subplot(3,3,5), plot(thQ, w3, 'r', 'LineWidth', 2), xlabel('\theta_Q (rad)'), ylabel('\omega_3 (rad/s)'), grid on;
subplot(3,3,6), plot(thQ, acc3, 'r', 'LineWidth', 2), xlabel('\theta_Q (rad)'), ylabel('\alpha_3 (rad/s^2)'), grid on;

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