Question

- Animate 4-bar Greshof’s mechanisms crank-rocker , double rocker , double crank

- matlab coding

Answer 1

Note- Keep pressing on the ENTER key to visualize animation.

%% Plot Any Four Bar Linkage

clc;clear;close all

X = [150 110 100 90 40 120];

% X = [180 100 185 220 55 0];

% X = [r1 r2 r3 r4 Cx Cy ];

% r1: Crank (make sure its always the smallest, also r3+r4>=r1+r2)

% r2: Coupler

% r3: Lever (Rocker)

% r4: Frame

% Cu: x coordinate for coupler point wrt crank-coupler point

% Cv: y coordinate for coupler point wrt crank-coupler point

cycles = 2;% number of crank rotations

INCREMENTS = 100;% divide a rotation into this number

%% check the geometry

P = X(1:4);

check = P;

[L locL] = max(check);

check(locL) = [];

[S locS] = min(check);

check(locS) = [];

R = check;

flag = 0;

if S==X(4) & sum(check)>(L+S)

TITLE = 'This is a Double-Crank Mechanism';

elseif (S==X(1)|S==X(3)) & sum(check)>(L+S)

TITLE = 'This is a Rocker-Crank Mechanism';

elseif S==X(2) & sum(check)>(L+S)

TITLE = 'This is a Double-Rocker Mechanism';

flag = 1;

elseif sum(check)==(L+S)

TITLE = 'This is a Change Point Mechanism';

elseif sum(check)<(L+S)

flag = 1;

TITLE = 'This is a Double-Rocker Mechanism';

end

%%

TH1 = linspace(0,2*pi,INCREMENTS);% Input angle theta1

dig = 10;% divide links into this number

R1 = X(1); r1 = linspace(0,R1,dig);

R2 = X(2); r2 = linspace(0,R2,dig);

R3 = X(3); r3 = linspace(0,R3,dig);

R4 = X(4); r4 = linspace(0,R4,dig);

Cu = X(5); cu = linspace(0,Cu,dig);

Cv = X(6); cv = linspace(0,Cv,dig);

%% check valid region

D = sqrt(R1^2 + R4^2 - 2*R1*R4*cos(TH1));% diagonal distance between

% crank-coupler point and rocker-frame point

TH5 = acos((R3^2+D.^2-R2^2)./(2*R3*D));% angle between rocker and diagonal

% link (d)

IMAG = imag(TH5);

[VALUES LOCATION] = find(IMAG==0);

%%

IMAG = imag(TH5);

LOCATION = IMAG==0;

LOCATION1 = find(IMAG==0);

LOC = LOCATION;

n = length(LOCATION);

n1 = length(LOCATION1);

Check = 0;

direction = 1;

for i=1:n-1

if LOC(i+1)~=LOC(i)

if Check==0

direction = LOC(i);

end

Check = Check+1;

end

end

%%

Rotate = 0;

if isempty(LOCATION1)

error('This is not a valid linkage');

elseif direction==0 & Check==2

LOC1 = find(LOCATION==1);

th1 = [TH1(LOC1) TH1(fliplr(LOC1))];

elseif n1==n

th1 = TH1;

elseif direction==1 & Check==2

Rotate = 1;

loc1 = LOC(1:end-1);

loc2 = LOC(2:end);

[Value deadpoint] = find((loc2-loc1)~=0);

deadp = deadpoint + [0 1];

LOC2 = [deadp(2):n 1:deadp(1)];

th1 = [TH1(LOC2) TH1(fliplr(LOC2))];

elseif Check==4

Rotate = 1;

loc1 = LOC(1:end-1);

loc2 = LOC(2:end);

[Value deadpoint] = find((loc2-loc1)~=0);

deadp1 = deadpoint(1:2) + [1 0];

deadp2 = deadpoint(3:4) + [1 0];

fprintf('This mechanism has two disconnected upper and lower regions\n');

DIREC = 1;

DIREC = input('Select [1] for upper, [2] for lower Default = [1] ');

if DIREC == 1

LOC3 = [deadp1(1):deadp1(2)];

else

LOC3 = [deadp2(1):deadp2(2)];

end

th1 = [TH1(LOC3) TH1(fliplr(LOC3))];

end

d = sqrt(R1^2 + R4^2 - 2*R1*R4*cos(th1));

th5 = acos((R3^2+d.^2-R2^2)./(2*R3*d));% angle between rocker and

%%

if Rotate == 1

d = sqrt(R1^2 + R4^2 - 2*R1*R4*cos(th1));

th5 = acos((R3^2+d.^2-R2^2)./(2*R3*d));% angle between rocker and diagonal link (d)

th5 = [th5(1:end/2) -th5(end/2+1:end)];

end

Ax = R1*cos(th1);% x coordinate for the crank-coupler point

Ay = R1*sin(th1);% y coordinate for the crank-coupler point

a = R4 - R1*cos(th1);% horizontal distance between rocker-frame point and

% projection of crank-coupler point

b = Ay;% vertical projection of crank-coupler point

th6 = atan2(b,a);% angle between frame and diagonal link (d)

th4 = pi - th5 - th6;% angle the rocker makes with horizon

Bx = R3*cos(th4) + R4;% horizontal distance between frame-crank point and

% projection of coupler-rocker point

By = R3*sin(th4);% vertical projection of coupler-rocker point

th2 = atan2((By-Ay),(Bx-Ax));% angle the coupler makes with the horizon

Cx = Ax + Cu*cos(th2) - Cv*sin(th2);% horizontal projection of coupler

% point wrt coupler

Cy = Ay + Cu*sin(th2) + Cv*cos(th2);% vertical projection of coupler

% point wrt coupler

% calculate display (figure) limits

xmin = 1.2*min([min(Cx) -R1 -R3]);

xmax = 1.2*max([max(Cx) R4+max([R3 max(R3*cos(th4))])]);

ymin = 1.2*min([min(Cy) -R1 -R3]);

ymax = 1.2*max([max(Cy) max([R1 R3 R3+Cv])]);

%%

increments = length(th1);

for i=1:increments

link1x(i,:) = r1*cos(th1(i));

link1y(i,:) = r1*sin(th1(i));

link2x(i,:) = linspace(Ax(i),Bx(i),dig);

link2y(i,:) = linspace(Ay(i),By(i),dig);

link3x(i,:) = R4 + r3*cos(th4(i));

link3y(i,:) = r3*sin(th4(i));

Couplx1(i,:) = linspace(Ax(i),Cx(i),dig);

Couply1(i,:) = linspace(Ay(i),Cy(i),dig);

Couplx2(i,:) = linspace(Cx(i),Bx(i),dig);

Couply2(i,:) = linspace(Cy(i),By(i),dig);

end

for k=1:cycles

for i = 1:increments

plot(link1x(i,:),link1y(i,:),'b',link2x(i,:),link2y(i,:),'r',...

link3x(i,:),link3y(i,:),'k',Couplx1(i,:),Couply1(i,:),'r',...

Couplx2(i,:),Couply2(i,:),'r')

hold on

plot([link2x(i,:) ;Couplx1(i,:)],[link2y(i,:); Couply1(i,:)],'g','linewidth',2)

plot([link2x(i,:) ;Couplx2(i,:)],[link2y(i,:); Couply2(i,:)],'g','linewidth',2)

plot(0,0,'sk',R4,0,'sk','MarkerSize',12)

plot(0,0,'ok',R4,0,'ok')

plot(Couplx1(i,end),Couply1(i,end),'ok','MarkerSize',6,...

'MarkerFaceColor','g')

axis([xmin xmax ymin ymax])

if Rotate == 1 & i<=increments/2

plot(Couplx1(1:i,end),Couply1(1:i,end),'--g','linewidth',2)

elseif Rotate == 1

plot(Couplx1(1:increments/2,end),Couply1(1:increments/2,end),'--g','linewidth',2)

plot(Couplx1(increments/2:i,end),Couply1(increments/2:i,end),'--r','linewidth',2)

else

plot(Couplx1(1:i,end),Couply1(1:i,end),'--g','linewidth',2)

end

clc

title(['\bf',TITLE])

fprintf('Th1 = %5.2f, th5 = %5.2f, D = %7.2f\n',th1(i),th5(i),d(i))

YY = input('Hit Enter ');

hold off

end

end

if Rotate==1

hold on

plot(Couplx1([1 end/2],end),Couply1([1 end/2],end),'hr','MarkerSize',10)

end