Six-Linked Bars Mechanism

Lateef Adewale Kareem
/
Six-Linked Bars Mechanism

on 29 Nov 2023

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drawframe(1);

Equation solved. fsolve completed because the vector of function values is near zero as measured by the value of the function tolerance, and the problem appears regular as measured by the gradient.

Write your drawframe function below

function drawframe(f)
    persistent L1 L2 L3 L4 L5 L6 L7 L8 t2 t3 t4 t5 t6 ...
        Bar2 Bar3 Bar4 Bar5 Bar6 f1 f2 
    if f==1
        L1=5;
        L2=2;
        L3=6;
        L4=4;
        L5=6;
        L6=4;
        L7=5;
        L8=1;
        f1=@(t2,t)(L2*cos(t2)-(L1+L4*cos(t)))^2+(L2*sin(t2)-L4*sin(t))^2-L3^2;
        f2=@(x5,y5,T)[x5+L5*cos(T(1))-(L1+L7+0.9*L6*cos(T(2)))
            y5+L5*sin(T(1))-(L8+0.9*L6*sin(T(2)))];
        t=linspace(0,2*pi,7); 
        brown=[206,179,140]/255;
        s=sin(t);
        c=cos(t);
        R=1.15;
        wclr=0.7*[1,1,1];
        hold on;
        fill(R*c,R*s,wclr); 
        fill(L1+R*c,R*s,wclr); 
        fill((L1+L7)+R*c,L8+R*s,wclr);
        xline(0);
        yline(0);
        axis equal
        t4=acos(((L2+L3)^2-L1^2-L4^2)/(2*L1*L4));
        c4=cos(t4);
        s4=sin(t4);
        t2=asin(sin(t4*L4/(L2+L3)));
        c2=cos(t2);
        s2=sin(t2);
        x3=L2*c2;
        y3=L2*s2;
        t3=atan2(L4*s4-L2*s2,L1+L4*c4-L2*c2);
        x5=L2*c2+(2/3)*((L1+L4*c4)-L2*c2);
        y5=L2*s2+(2/3)*(L4*s4-L2*s2);
        t56=fsolve(@(T)f2(x5,y5,T),[1.5*pi;1.5*pi]);
        t5=t56(1);
        t6=t56(2);
        Bar2=BarMaker(L2,'g',0); 
        Bar2.Rotate(t2);
        Bar3=BarMaker(L3,'b',[0,0.45]); 
        Bar3.Rotate(t3);
        Bar3.Trans([x3,y3]);
        Bar4=BarMaker(L4,'g',0);
        Bar4.Rotate(t4);
        Bar4.Trans([L1,0]);
        Bar5=BarMaker(L5,brown,0.3); 
        Bar5.Rotate(t5);
        Bar5.Trans([x5,y5]);
        Bar6=BarMaker(L6,'r',0); 
        Bar6.Rotate(t6);
        Bar6.Trans([L1+L7,L8]);
        axis([-2.6,11.4,-5,5])
    else
        t2=t2+2*pi/48; 
        c2=cos(t2);
        s2=sin(t2);
        x3=L2*c2;
        y3=L2*s2;
        t4=fzero(@(t)f1(t2,t),t4); 
        c4=cos(t4);
        s4=sin(t4);
        t3=atan2(L4*s4-L2*s2,L1+L4*c4-L2*c2);
        x5=L2*c2+(2/3)*((L1+L4*c4)-L2*c2);
        y5=L2*s2+(2/3)*(L4*s4-L2*s2);
        t56=fsolve(@(T)f2(x5,y5,T),[t5;t6]); 
        t5=t56(1);
        t6=t56(2);
        Bar2.Rotate(t2);  
        Bar3.Rotate(t3);
        Bar3.Trans([x3,y3]); 
        Bar4.Rotate(t4);
        Bar5.Rotate(t5); 
        Bar5.Trans([x5,y5]); 
        Bar6.Rotate(t6);
    end
end
function B=BarMaker(L,clr,F)
    t1=pi/2+linspace(0,pi); 
    t2=t1+pi; 
    s1=sin(t1);
    s2=sin(t2);
    c1=cos(t1);
    c2=cos(t2);
    Xl=[0.5*c1,L+0.5*c2];
    Yl=[0.5*s1,0.5*s2];
    X=Xl; 
    Y=Yl;
    Xl=[Xl,Xl(1)]; 
    Yl=[Yl,Yl(1)]; 
    for n=1:numel(F)
        f=F(n);
        X=[X,f*L,f*L+0.3*[c1,c2],f*L];
        Y=[Y,0.5,0.3*[s1,s2],0.5];
        Xl=[Xl,nan,f*L+0.3*[c1,c2]];
        Yl=[Yl,nan,0.3*[s1,s2]];
    end
    ax=gca;
    H=hgtransform('Parent',ax);
    K=hgtransform('Parent',H);
    B.line=plot(Xl,Yl,'k','Parent',K);
    B.fill=fill(X,Y,clr,'EdgeColor','none','Parent',K);
    B.Rotate=@(t)set(K,'Matrix',makehgtform('zrotate',t));
    B.Trans=@(p)set(H,'Matrix',makehgtform('translate',[p,0]));
end

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Six-Linked Bars Mechanism
Lateef Adewale Kareem