Question

An internal combustion engine slider-crank mechanism is shown in the figure. Crank AB rotates in selected clockwise positive direction as shown. Piston position is Y=AD. e(t) is angular position of the crank, ó(t) is angular velocity of the crank, ő is angular acceleration of the crank,

Answer 1

LAB 0.25 rad's is dWAB 0.25 2 WADDE Jawaba Jouset l=isomm 1... WAB = 0.25% e, sino=l sind titisa RH.S B 10 ylie somm *position of the piston". AI pepa = e, caso a la cosa! tre dO AB TE orast DAB I do ng Joorstedt Өelp - 0.25t2 **Velouty: E = TP + V Vp ja w BB + WAB XAB 1 X BF Bp Vp j = W Bp kx|-22 Sindi +22c05dj) + Wagk* ( l, sine i tlocosoj) =-l2W Bp sind j e, WAB sinoj - l, WARLOSO i lz webp cosa i vpj = coso ;-) O= -lz W Bp cosa e, WAS j-> l wap cose = l, WAB Logo vp=-lz WBP sind tl, WAB sino up + lz Wapsino = l, WABsino

e sino jadi dapo * Matrix Jorms: l cosa -d, WARCOSO WBP l, WAB sino lz sind x = B 2 (AR) LAB 2 Acelerators ap = a pusta ap j = 2Bp* BP - war (BP) + 2 * AB - Wars apja dop kx4d2 sind i +4.605j ) - web (-fesindi tdscootj) kx(+4, sin dith, cos8j)-Wall, sinoi thi coroj) ap j = = 12 & pp sind j-lz Abp corpi + d2 wep singine wa a conej ;-) 0 =-224 Bp wsd + d2 w Bp sinone, CAB Coso e, assing la cos& dBp = la wapo sinde, "ABoso e, wala sina. j -) ap=l&Bp sind -la wey losore, dagsino-1, wh rogol cep -lsind & Bp = l, dabsino-l₂ WB y lose -e, wat hy org. * matrix form lzcosa Tap ilzw sind - le dag novo - doch marino Bele, dagsino - 12 we are cost-1, what is cose. 0 2 - lasing X

clc;clear all;close all;
l1=50;%length of the crank
l2=150;%length of the lever
t(1)=0;
alphaAB=0.25;%angular acceleration
w0=0;%initial angular velocity
theta0=0;%initial anglular position
theta(1)=theta0+w0*t(1)+0.5*alphaAB*t(1).^2;
dt=0.01;
i=1;
t(i+1)=t(i)+dt;
theta(i+1)=theta0+w0*t(i+1)+0.5*alphaAB*t(i+1).^2;
while theta(i+1)<4*pi
i=i+1;
t(i+1)=t(i)+dt;
theta(i+1)=theta0+w0*t(i+1)+0.5*alphaAB*t(i+1).^2;
end
figure
plot(t,theta)
xlabel('time in sec')
ylabel('Theta in rad')
title('Crank angular position Vs time')
%Position
for i=1:1004
phi1=-pi/4;
LHS=l1*sin(theta(i));
RHS=l2*sin(phi1);
while round(LHS,1)~=round(RHS,1)
phi1=phi1+0.0001;
RHS=l2*sin(phi1);
end
phi(i)=phi1;
end
Xp=l1*cos(theta)+l2*cos(phi);
figure
plot(t,Xp)
xlabel('Time in sec')
ylabel('Y in mm')
title('Piston displacement Vs time')
wAB=alphaAB*t+w0;
%piston velocity
for i=1:1004
A=[0 l2*cos(phi(i));1 l2*sin(phi(i))];
B=[-l1*wAB(i)*cos(theta(i));l1*wAB(i)*sin(theta(i))];
X=inv(A)*B;
Vp(i)=X(1);
wBP(i)=X(2);
end
figure
plot(t,Vp)
xlabel('Time in sec')
ylabel('Ydot in mm/sec')
title('Piston velocity Vs time')

figure
plot(theta,Vp)
xlabel('theta in rad')
ylabel('Ydot in mm/sec')
title('Piston velocity Vs angle theta')

%piston Acceleration
for i=1:1004
C=[0 l2*cos(phi(i));1 -l2*sin(phi(i))];
D=[l2*wBP(i).^2*sin(phi(i))-l1*alphaAB*cos(theta(i))-l1*wAB(i).^2*sin(theta(i));
l1*alphaAB*sin(theta(i))-l2*wBP(i).^2*cos(phi(i))-l1*wAB(i).^2*cos(theta(i))];
X=inv(C)*D;
ap(i)=X(1);
alphaBP(i)=X(2);
end
figure
plot(t,ap)
xlabel('Time in sec')
ylabel('accelaration in mm/sec^2')
title('Piston acceleration Vs time')

figure
plot(theta,ap)
xlabel('theta in rad')
ylabel('accelaration in mm/sec^2')
title('Piston accelaration Vs angle theta')

Crank angular position Vs time 14 Piston displacement Vs time 200 190 12 180 10 170 160 Theta in rad Y in mm 150 140 4 130 120 2. 110 0 0 2 4 6 10 12 100 0 2 4 8 10 12 time in sec 6 Time in sec Piston velocity Vs time Piston velocity Vs angle theta 150 150 100 100 50 50 Ydot in mm/sec 0 Ydot in mm/sec 0 -50 -50 -100 -100 - 150 - 150 0 2 4 6 8 10 12 0 4 6 8 10 14 Time in sec theta in rad Piston acceleration Vs time Piston accelaration Vs angle theta 200 200 100 100 0 0 -100 -100 accelaration in mm/sec2 accelaration in mm/sec2 -200 -200 -300 -300 400 -400 -500 -500 0 0 2 4 8 10 12 2 4 10 12 14 6 Time in sec 6 8 theta in rad