MATLAB Position and Velocity Analysis

%Kinematic Analysis of Treadle Sewing Machine

clear;

a=6;

b=11.5;

c=1.25;

d=12;

e=6;

g=1.5;

h=22.38;

f=((e-g)^2+h^2)^.5;

%%%%% Calculate toggle point of Grashoff rocker-crank

tog1=acosd((a^2+d^2-(b+c)^2)/(2*a*d));

tog2=acosd((a^2+d^2-(b-c)^2)/(2*a*d));

theta2d_1=[tog1-.005:-.005:tog2+.005];

theta2d_2=[tog2+.005:.005:tog1-.005];

%%%%% Calculate position of rocker-crank

delta=1;

[theta3d_1,theta4d_1]=fourbarpos2(a,b,c,d,theta2d_1,delta);

delta=-1;

[theta3d_2,theta4d_2]=fourbarpos2(a,b,c,d,theta2d_2,delta);

theta2d=[theta2d_1 theta2d_2];

theta3d=[theta3d_1 theta3d_2];

theta4d=[theta4d_1 theta4d_2];

max(theta3d);

min(theta3d);

%%%%% Create Plots

figure(1)

plot(theta2d,theta3d,theta2d,theta4d,'k')

xlabel('Input Angle (deg)')

ylabel('Coupler & Crank Position (deg)')

%axis([55 85 -50 -20])

legend('theta3','theta4','Location','northwest')

title('Sewing Machine Position')

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%Velocity Analysis

w2=1;  %assumed value

w3=(a*w2.*sind(theta4d-theta2d))./(b.*sind(theta3d-theta4d));

w4=abs((a*w2.*sind(theta2d-theta3d))./(c.*sind(theta4d-theta3d)));

%%%%% Create Plot

figure(2)

plot(theta2d,w3,'r',theta2d,w4,'k')

axis([55 85 -20 20])

xlabel('Input Angle (deg)')

ylabel('Coupler and Crank Velocity')

legend('w3','w4')

title('Sewing Machine Angular Velocity')

w5=abs(w4);

m_G=g/e;

w7=w5./m_G;

MA=(w2./w7).*(a/g);

%Create Plot

figure(3)

plot(theta2d,w4,'k',theta2d,w7,'b')

axis([55 85 0 40])

xlabel('Input Angle (deg)')

ylabel('Pulley Input and Output Speeds')

legend('w4','w7')

title('Sewing Machine Angular Velocity')

%Create Plot

figure(4)

plot(theta2d,MA,'k')

xlabel('Input Angle (deg)')

ylabel('MA')

title('Sewing Machine Mechanical Advantage')

Function 'fourbarpos2'

function [theta3d,theta4d]=fourbarpos2(a,b,c,d,theta2d,delta)

%input and output in degrees

%Calculate position of 4-bar mechanism

K1=d/a;                                   %4.8a textbook

K2=d/c;   

K3=(a^2-b^2+c^2+d^2)/(2*a*c);

K4=d/b;

K5=(c^2-d^2-a^2-b^2)/(2*a*b);

A=cosd(theta2d)-K1-K2.*cosd(theta2d)+K3;       %4.10a textbook

B=-2.*sind(theta2d);

C=K1-(K2+1).*cosd(theta2d)+K3;

D=cosd(theta2d)-K1+K4.*cosd(theta2d)+K5;

E=-2.*sind(theta2d);

F=K1+(K4-1).*cosd(theta2d)+K5;

theta3_1=2.*atand((-E-((E.^2)-4.*D.*F).^.5)./(2.*D));    %calculate open solution

theta3_2=2.*atand((-E+((E.^2)-4.*D.*F).^.5)./(2.*D));    %calculate crossed solution

theta4_1=2.*atand((-B-((B.^2)-4.*A.*C).^.5)./(2.*A));    %calculate open solution

theta4_2=2.*atand((-B+((B.^2)-4.*A.*C).^.5)./(2.*A));    %calculate crossed solution

if delta==1

    theta3d=theta3_1;

    theta4d=theta4_1;

else

    theta3d=theta3_2;

    theta4d=theta4_2;

end