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Theory of Machines

Theory of Machines. Lecture 15. Four Bar Mechanism. F.  3.  3. A. 3.  2.  2. B. k.  4.  4. 4. 2. C. e. O. d. The Equation.  3. F.  3. A. 3.  2.  2. B.  4. 2.  4. 4. C. e. O. d. k. Mass Matrix.  3. F.  3. A. 3.  2.  2. B.  4. 2.  4.

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Theory of Machines

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  1. Theory of Machines Lecture 15

  2. Four Bar Mechanism F 3 3 A 3 2 2 B k 4 4 4 2 C e O d

  3. The Equation

  4. 3 F 3 A 3 2 2 B 4 2 4 4 C e O d k Mass Matrix

  5. 3 F 3 A 3 2 2 B 4 2 4 4 C e O d k Four bar Mechanism Joint O i=1 j=2 Joint A i=2 j=3 Joint B i=3 j=4 Joint C i=4 j=1

  6. Jacobian

  7. 3 F 3 A 3 2 2 B 4 2 4 4 C e O d k Force Vector

  8. 3 F 3 A 3 2 2 B 4 2 4 4 C e O d k Acceleration

  9. Matlab code global m2,i2,m3,i3,m4,i4, L2,L3,L4,L0,k,F % Define const L2= ___ ;L3=___ ;L4=___;d=___;e=_____; m2=___;m3=___;m4=___;L0=___;k=____; i2=m2*L2^2/12;i3=m3*L3^2/12;i4=m4*L4^2/12; F=____; % Initial geometry % calculate x2,y2 etc . . . y0=[x2;y2;th2;x3;y3;th3;x4;y4;th4;zeros(9:1)]; [t,y]=ode45(@difffour,[0,2],y0); figure(1) plot(t,y(:,9) xlabel(‘Time s’) ylabel(‘Theta 4’)

  10. Matlab Code function ydot=difffour(y,t) global m2,i2,m3,i3,m4,i4, L2,L3,L4,L0,k,F m=massfour(m2,i2,m3,i3,m4,i4); J=gradfour(q,L2,L3,L4); f=forcefour(q,m2,m3,m4,L0,k,F); gam=zeros(8,1); A=[m –J’;J zeros(8)]; b=[f;gam]; X=A\b; ydot=[y(10:18);X(1:9)];

  11. Matlab Code function f=forcefour(y,m2,m3,m4,L,L0,k,F) brac=k*(sqrt((y(4)-y(1))^2+(y(5)-y(4))^2)-L0)/ sqrt((y(4)-y(1))^2+(y(5)-y(4))^2)) g=9.81; f=[(y(1)-y(4))*brac;… -F-m2*g- +(y(2)-y(5))*brac;… -F*L/2*cos(y(3);… (y(4)-y(1))*brac;… -m3*g-(y(5)-y(2))*brac;… 0;… 0;… -m4*g;… 0];

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