Stephenson 6 bar mechanism example help me matlab codes

Hi,

I did my programming, but my program is not working. Can you help? Where couldn't I find my fault and solve it.

[darova]

Can you attach a scheme or something? How this mechanism looks

[Burak Berk]

Answer 1

[Dheeraj Kumar]

clc

clear

L4=6.5;

L5=17.5;

th4=30*pi/180;

q=[th4 165*pi/180 1.8]';

f=1;

qroots=poscrankslid21(q,L4,L5,f,th4) % the results

theta4=qroots(1)*180/pi

theta5=qroots(2)*180/pi

s6=qroots(3)

function Phi=crankslid2(q,L4,L5,f,theta2)

% constraint equations

Phi=[L4*cos(q(1))-L5*cos(q(2))-q(3);...

L4*sin(q(1))-L5*sin(q(2))- f;...

q(1)-theta2];

end

function J=gradcrankslid2(q,L4,L5)

% the Jacobian matrix

J=[-L4*sin(q(1)) L5*sin(q(2)) -1;...

L4*cos(q(1)) -L5*cos(q(2)) 0;...

1 0 0];

end

function q=poscrankslid21(q,L4,L5,f,theta2)

% Newton-Raphson algorithm

epsilon=1.e-3;

Phi=crankslid2(q,L4,L5,f,theta2);

while norm(Phi)>epsilon

J=gradcrankslid2(q,L4,L5);

dq=-inv(J)*Phi;

q=q+dq;

Phi=crankslid2(q,L4,L5,f,theta2);

norm(Phi);

end

end

Results,

4=30°

5=172.61°

S6=22.984

2=72.08°

3=28.317°

q = [2, 3, 4, 5, S6]T = [ 72.08°, 28.317°, 30°, 172.61°, 22.984]T

(Mohammadzadeh, 2007)

C) Simulation of a kinematic behavior of the system

% sewing machine kinematic analysis

clc

clear

close all

d2r=pi/180;

d=10;

L2=10;

L3=9;

L4=6.5;

L5=17.5;

e=7;

f=1;

th40=30*d2r; % crank at 30 deg %180*d2r; %

q=[72.082*d2r 28.317*d2r th40 172.61*d2r 22.984]';

omega4=0.1;

qa=75*d2r;% angle of ternary link th4 + 45 deg*d2r %;

tf=5; h=0.02; t=0:h:tf; N=length(t); % over 5 cycles

qq=zeros(N,5);

dqq=zeros(N,5);

ddqq=zeros(N,5);

h = waitbar(0,'Please wait...');

for i=1:N

theta4=th40+omega4*t(i);

q=posfourbar(q,L2,L3,L4,L5,d,e,f,qa,theta4);

qq(i,:)=q';

J=gradfourbar(q,L2,L3,L4,L5,qa);

dq=J\[0 0 omega4 0 0]';

dqq(i,:)=dq';

gam=gamfourbar(q,dq,L2,L3,L4,L5,qa);

ddq=J\gam;

ddqq(i,:)=ddq';

waitbar(i/N)

end

close(h)

save fourbar

figure(1)

clf

subplot(5,1,1)

plot(t,qq(:,1)/d2r)

ylabel('\theta_2 deg')

xlabel('\ittime s')

grid

subplot(5,1,2)

plot(t,qq(:,2)/d2r)

ylabel('\theta_3 deg')

xlabel('\ittime s')

grid

subplot(5,1,3)

plot(t,qq(:,3)/d2r)

ylabel('\theta_4 deg')

xlabel('\ittime s')

grid

subplot(5,1,4)

plot(t,qq(:,4)/d2r)

ylabel('\theta_5 deg')

xlabel('\ittime s')

grid

subplot(5,1,5)

plot(t,qq(:,5)/d2r)

ylabel('S6')

xlabel('\ittime s')

grid

figure(2)

clf

subplot(5,1,1)

plot(qq(t,dqq(:,1)/d2r))

ylabel('\omega_2 rad/s')

xlabel('\ittime s')

grid

subplot(5,1,2)

plot(qq(t,dqq(:,2)/d2r))

ylabel('\omega_3 rad/s')

xlabel('\ittime s')

grid

subplot(5,1,3)

plot(qq(t,dqq(:,3)/d2r))

ylabel('\omega_4 rad/s')

xlabel('\ittime s')

grid

subplot(5,1,4)

plot(qq(t,dqq(:,4)/d2r))

ylabel('\omega_5 rad/s')

xlabel('\ittime s')

grid

subplot(5,1,5)

plot(qq(t,dqq(:,5)/d2r))

ylabel('V6 rad/s')

xlabel('\ittime s')

grid

figure(3)

clf

subplot(5,1,1)

plot(qq(t,ddqq(:,1)))

ylabel('\epsilon_2 rad/s^2')

xlabel('\ittime s')

grid

subplot(5,1,2)

plot(qq(t,ddqq(:,2)))

ylabel('\epsilon_3 rad/s^2')

xlabel('\ittime s')

grid

subplot(5,1,3)

plot(qq(t,ddqq(:,3)))

ylabel('\epsilon_4 rad/s^2')

xlabel('\ittime s')

grid

subplot(5,1,4)

plot(qq(t,ddqq(:,4)))

ylabel('\epsilon_5 rad/s^2')

xlabel('\ittime s')

grid

subplot(5,1,5)

plot(qq(t,ddqq(:,5)))

ylabel('A6 rad/s^2')

xlabel('\ittime s')

grid

function Phi=fourbar(q,L2,L3,L4,L5,d,e,f,qa,theta4)

Phi=[L2*cos(q(1))+L3*cos(q(2))-L4*cos(qa)-d;...

L2*sin(q(1))+L3*sin(q(2))-L4*sin(qa)-e;...

L4*cos(q(3))-L5*cos(q(4))-q(5);...

L4*sin(q(3))-L5*sin(q(4))-f;...

q(4)-theta4];

end

function J=gradfourbar(q,L2,L3,L4,L5,qa)

J=[-L2*sin(q(1)) -L3*sin(q(2)) L4*sin(qa) 0 0;...

L2*cos(q(1)) L3*cos(q(2)) -L4*cos(qa) 0 0;...

0 0 -L4*sin(q(3)) L5*sin(q(4)) -1;...

0 0 L4*cos(q(3)) -L5*cos(q(4)) 0;...

0 0 1 0 0];

end

function q=posfourbar(q,L2,L3,L4,L5,d,e,f,qa,theta4)

epsilon=1.e-6;

Phi=fourbar(q,L2,L3,L4,L5,d,e,f,qa,theta4);

while norm(Phi)>epsilon

J=gradfourbar(q,L2,L3,L4,L5,qa);

dq=-inv(J)*Phi;

q=q+dq;

Phi=fourbar(q,L2,L3,L4,L5,d,e,f,qa,theta4);

end

end

function gam=gamfourbar(q,dq,L2,L3,L4,L5,qa)

gam=[L2*cos(q(1))*dq(1)^2+L3*cos(q(2))*dq(2)^2-L4*cos(qa)*d(qa^2);...

L2*sin(q(1))*dq(1)^2+L3*sin(q(2))*dq(2)^2-L4*sin(qa)*d(qa^2);...

L4*cos(q(3))*dq(3)^2-L5*cos(q(4))*dq(4)^2;...

L4*sin(q(3))*dq(3)^2-L5*sin(q(4))*dq(4)^2;...

0];

end

[Dheeraj Kumar]

this program is not working please help

[DGM]

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