Four Bars Mechanism: i cannot understand why CP modifies his length.

clear all;
clc;

AB=1;
CD=1;
BP=AB;
CP=AB; %[m]

xD=2*AB
yD=0;

incr=1

for phi=0:1/30:2*pi      
    xA=0;
    yA=0;
    rA=[xA,yA,0];
    xB=AB*cos(phi);
    yB=AB*sin(phi);
    rB=[xB,yB,0];
    rD=[xD,yD,0];
    yP=0;
    yPb=yP;
    yPc=yP;
    yD=0;
    xC=2-CD*cos(pi/2-phi);
    yC=CD*sin(pi/2-phi);
    rD=[xD,yD,0];
    rC=[xC,yC,0];
    
    
    syms xPsol   xPcsol
    
    solP=solve((xPsol-xB)^2+(yB-yP)^2==BP^2);
    
    solPc=solve((xPcsol-xC)^2+(yC-yP)^2==CP^2);
    
    xP1=eval(solP(1));
    xP2=eval(solP(2));
    
    
    yP1=eval(solP(1));
    yP2=eval(solP(2));
    
    
    xP3=eval(solPc(1));
    xP4=eval(solPc(2));
    
    yP3=eval(solPc(1));
    yP4=eval(solPc(2));
    
    
    if xP1>xB
        xP=xP1;
    else
        xP=xP2;
    end
    
    
    
    if xP3<xC
        xPc=xP3;
    else
        xPc=xP4;  
    end
    
    rP=[xP,yP,0];
    rP=[xPc,yPc,0];
    
    
    
    
    
    plot([xA,xB],[yA,yB],'k-',[xB,xP],[yB,yP],'b-',[xD,xC],[yD,yC],[xC,xP],[yC,yP],'g-')
    
    text(xA,yA,'A');
    text(xB,yB,'B');
    text(xP,yP,'P');
    text(xC,yC,'C');
    text(xD,yD,'D');
    grid
    axis([-2 4 -2 2])
    
    manovellismoroberts(:,incr)=getframe;
    incr=incr+1;
    
end
hold on


movie(manovellismoroberts,3,200)

vidobj=VideoWriter('manovellismoroberts.avi')
open(vidobj)
writeVideo(vidobj,manovellismoroberts)
close(vidobj)

Answer 1

[Pratyush]

Hi @Joe Propp,

I understand that you want to know the reason behind why does CP keep changing its length.The length of CP is initially set to AB at the beginning of the code: CP=AB; %[m]. However, as the loop iterates through different values of phi, the length of CP is modified using the following line of code:

xC=2-CD*cos(pi/2-phi);
yC=CD*sin(pi/2-phi);

Here, the x and y coordinates of point C are calculated based on the value of phi and the length of CD. Since phi changes in each iteration, the position of point C changes accordingly, which in turn affects the length of CP. Therefore, CP appears to change its length because it is being dynamically updated based on the value of phi during each iteration of the loop.

[Joe Propp]

I think the problem lies in the mechanism, point P has a sinusoidal speed. I can't find a way to make these 4 rods move. would you have an idea?