I understand that you are looking to optimize the MATLAB code for determining the link lengths of a six-bar mechanism. Here are some key improvements that you can make to optimize the code:
- Use 'lsqnonlin' to minimize the error between the actual and computed trajectory.
- Replace symbolic calculations with numeric solvers like 'fsolve' to improve the performance and convergence speed.
- Ensure that (x,y) coordinates are calculated for each input angle using accurate loop-closure equations.
- Provide good initial guesses for the solver, as they are crucial for ensuring convergence.
You can refer to the below MATLAB code for incorporating the above optimizations:
clc;
clear;
close all;
angle = [10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100];
x = [26.6 30.5 32.2 32 31.3 31.4 32.3 35.1 37.3 35 28.9 20.9 13.3 7.9 5.7 2.6 -0.3 -1 0];
y = [75.5 73.6 67.6 60.6 54.8 50.8 47.1 43 36.2 25.7 14.1 4.2 -2.6 -6.2 -7 -6.8 -5.4 -2.9 0];
theta = deg2rad(angle);
L0 = [20, 30, 40, 35, 25, 30, 50, 45];
objective = @(L) compute_error(L, theta, x, y);
options = optimoptions('lsqnonlin', 'Display', 'iter', 'MaxIterations', 500);
L_opt = lsqnonlin(objective, L0, [], [], options);
disp('Optimized Link Lengths:');
disp(L_opt);
figure;
hold on;
plot(x, y, 'bo-', 'LineWidth', 2, 'MarkerSize', 6, 'MarkerFaceColor', 'b');
[~, x_calc, y_calc] = compute_error(L_opt, theta, x, y);
plot(x_calc, y_calc, 'r--', 'LineWidth', 2);
legend('Given Trajectory', 'Optimized Mechanism');
grid on;
xlabel('x(mm)');
ylabel('y(mm)');
title('Optimized Six-Bar Mechanism Fit');
axis equal;
hold off;
function [error, x_calc, y_calc] = compute_error(L, theta, x_desired, y_desired)
r1 = L(1);
r2 = L(2);
r3 = L(3);
r4 = L(4);
r5 = L(5);
r6 = L(6);
r7 = L(7);
r8 = L(8);
x_calc = zeros(size(theta));
y_calc = zeros(size(theta));
for i = 1:length(theta)
phi2 = theta(i);
fn = @(phi) loop_closure_eqs(phi, phi2, r1, r2, r3, r4, r5, r6, r7, r8);
phi0 = [0, pi/4, pi/3, pi/6]; % Initial guess for phi
phi_sol = fsolve(fn, phi0);
phi3 = phi_sol(1);
phi4 = phi_sol(2);
phi6 = phi_sol(3);
phi7 = phi_sol(4);
x_calc(i) = r3 * cos(phi4) + r6 * cos(phi6);
y_calc(i) = r3 * sin(phi4) + r6 * sin(phi6);
end
error = [(x_calc - x_desired), (y_calc - y_desired)];
end
function F = loop_closure_eqs(phi, phi2, r1, r2, r3, r4, r5, r6, r7, r8)
phi3 = phi(1);
phi4 = phi(2);
phi6 = phi(3);
phi7 = phi(4);
F(1) = r1 * cos(phi2) + r2 * cos(phi3) - r3 * cos(phi4) - r4;
F(2) = r1 * sin(phi2) + r2 * sin(phi3) - r3 * sin(phi4);
phi5 = atan(r6 / r3);
F(3) = (r3 + r6) * cos(phi5) + r7 * cos(phi7) - r8 * cos(phi7 + pi/2);
F(4) = (r3 + r6) * sin(phi5) + r7 * sin(phi7) - r8 * sin(phi7 + pi/2);
end
You can refer to the given documentation of 'lsqnonlin' to get a better understanding:
Hope this helps!
