Question

animate on matlab

has to be a simple 4 bar mechanism

Lab Sessioh 2 Animate the 4-bar Mo tion e ena.8 mat lab Crant rock er Doubit Cronk Doo ble rocker

Answer 1

Double Crank: C+D A+B, D is B the shortest Link C A Double Rocker: A+B>C+D, B is the D shortest link Crank Rocker: C+D A B, A is the shortest link

For Crank rocker

Take : A = 1 , B = 2, C = 3,D= 4

For Double Crank

Take : A = 3 , B = 3, C = 5,D= 2

For Double Rocker

Take : A = 6 , B = 3, C = 4,D= 4

We can run the following matlab code 3 times for 3 cases with various lengths.

Matlab Code:

clc; clear;
% Parameters
A = 1; B = 2; C = 3; D = 4;

t = 0:0.05:10;

ang_speed = 2;
theta = ang_speed*t;

P1 = [0;0];
P4 = D*[1;0];

P2 = A*[cos(theta); sin(theta)];
E = sqrt(A^2 + D^2 - 2*A*D*cos(theta));
alfa = asin(A*sin(theta)./E);
beta = acos((E.^2 + C^2 - B^2)./(2*E*C));
P3 = [D - C*cos(alfa+beta); C*sin(alfa+beta)];

P3_x = P3(1,:);
P3_y = P3(2,:);

P3_vx = diff(P3_x)./diff(t);
P3_vy = diff(P3_y)./diff(t);

P3_v = sqrt(P3_vx.^2 + P3_vy.^2);

for i=1:length(t)

ani = subplot(2,1,1);
P1_circle = viscircles(P1',0.05);
P2_circle = viscircles(P2(:,i)',0.05);
P3_circle = viscircles(P3(:,i)',0.05);
P4_circle = viscircles(P4',0.05);

A_bar = line([P1(1) P2(1,i)],[P1(2) P2(2,i)]);
B_bar = line([P2(1,i) P3(1,i)],[P2(2,i) P3(2,i)]);
C_bar = line([P3(1,i) P4(1)],[P3(2,i) P4(2)]);

axis(ani,'equal');
set(gca,'XLim',[-5 8],'YLim',[-2 7]);

str1 = 'P3';
str2 = ['Time elapsed: ' num2str(t(i)) ' s'];
P3_text = text(P3(1,i),P3(2,i)+0.4,str1);
Time = text(-2,6,str2);
pause(0.005);
if i<length(t)
delete(P1_circle);
delete(P2_circle);
delete(P3_circle);
delete(P4_circle);
delete(A_bar);
delete(B_bar);
delete(C_bar);
delete(P3_text);
delete(Time);
vel = subplot(2,1,2);
plot(vel,t(1:i),P3_v(1:i));
set(vel,'XLim',[0 10],'YLim',[0 10]);
xlabel(vel, 'Time (s)');
ylabel(vel, 'Amplitude (m/s');
title(vel,'Speed of P3');
grid on;
end

end

Time elapsed: 10s 6 4 P3 2 0 2 -5 5 0 Speed of P3 5 C 10 9 8 7 6 5 3 4 2 1 0 Time (s) LO st LC 10 Amplitude (m/s