Question

I have been trying this problem for over 8 hours. How do I make the Matlab code for the given problem. It has to move.

- Use the . You may use cif to clear the figure for the next instant of time The goal is the same as before except this time you will plot a moving 3 bar lin mechanism shown below kage. Use the L2 (k2,ya L3 The equations that govern the motion of this linkage are: x1 11 cos(wt) y = L1 sin(ωt) (x2-X1)2 + (y2-y1)2 Y. Here ω is the angular velocity of link 1. Take it as 0.5 rad/s, d is also known. Take d = 5 m. Solve for x, y, X2 and Y2 for multiple instants of time t. As for the length of the links, you can use L 3m, L2 = 5 m and La = 3.5 m. Use function fsolve to solve this system of 4 nonlinear equations. Once you have coordinates xi, V1, x2 and y2 for multiple instants of time, plot the linkage one instant of time at a time so that you can see how it moves. Same as the previous case, take advantage of the drawnow and cif commands to generate the animation. | 2.7x

Answer 1

%%
clear
clc
time = 0:0.01:20;

%% Equations of motion
options = optimoptions('fsolve','Display','off');
x0 = [0 0 0 0]';
for i = 1:length(time)
t = time(i);
[x,fval] = fsolve(@(x) fun(x,t), x0, options);
x1(i) = x(1);
y1(i) = x(2);
x2(i) = x(3);
y2(i) = x(4);
  
end

%% Animation

link1_x = [0 x1(1)];
link1_y = [0 y1(1)];

link2_x = [x1(1) x2(1)];
link2_y = [y1(1) y2(1)];

link3_x = [x2(1) 5];
link3_y = [y2(1) 0];

link1 = plot(link1_x,link1_y, 'b' ,'linewidth',1.25);
hold on
link2 = plot(link2_x,link2_y, 'b' ,'linewidth',1.25);
hold on
link3 = plot(link3_x,link3_y, 'b' ,'linewidth',1.25);
hold off

axis([-4 8 -5 5]);
grid on

for i = 2:length(time)
link1_x(2) = x1(i);
link1_y(2) = y1(i);
link2_x = [x1(i) x2(i)];
link2_y = [y1(i) y2(i)];
link3_x(1) = x2(i);
link3_y(1) = y2(i);
  
link1.XData = link1_x;
link1.YData = link1_y;
link2.XData = link2_x;
link2.YData = link2_y;
link3.XData = link3_x;
link3.YData = link3_y;
  
title(sprintf('t = %f sec',time(i)))
drawnow limitrate
pause(0.005)
end

Function 'fun' to pass to fsolve (save as new script)

function F = fun(x, t)
%% Parameters
w = 0.5;
d = 5;
l1 = 3;
l2 = 5;
l3 = 3.5;
%% Equations
x1 = x(1);
y1 = x(2);
x2 = x(3);
y2 = x(4);
  
F = [x1 - l1*cos(w*t);
y1 - l1*sin(w*t);
(x2 - x1)^2 + (y2 - y1)^2 - l2^2;
(x2 - d)^2 + (y2)^2 - l3^2];
end