gear_curve.asv

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% gear
% unit: mm
% press ang: 20deg
clear;

m=2;
z=50;
h=.5;% 1*m
rb=.5*m*z*cos(20*pi/180);
ra=m*(.5*z+h);
N=100;
delr=(ra-rb)/N;

% cal one side
rk=rb:delr:ra;
alphak=acos(rb./rk);
thetak=tan(alphak)-alphak;

% circle
for n=1:361
    xc(n)=rb*cos(n*pi/180);
    yc(n)=rb*sin(n*pi/180);
end
plot(xc,yc);
hold on;
axis equal
%axis square

% plot one side
for n=0:z-1
x=rk.*cos(n*360/z*pi/180+thetak);
y=rk.*sin(n*360/z*pi/180+thetak);
plot(x,y,'r');
end

% cal ang at contact point of one side
rc=.5*m*z;
alphac=acos(rb/rc);
thetac=tan(alphac)-alphac;
theta_width=2*pi/z/2;
theta_otherside=thetac*2+theta_width;

% cal other side
rk2=rb:delr:ra;
alphak2=-acos(rb./rk);       % negative
thetak2=tan(alphak2)-alphak2;

% plot other side
for n=0:z-1
x=rk2.*cos(n*360/z*pi/180+theta_otherside+thetak2);
y=rk2.*sin(n*360/z*pi/180+theta_otherside+thetak2);
plot(x,y,'r');
end

% close the gear
i=1;
for n=linspace(max(thetak),theta_otherside+min(thetak2),10)
    xg(i)=ra*cos(n);
    yg(i)=ra*sin(n);
    i=i+1;
end
clear x
clear y
for n=0:z-1
x=xg*cos(n*360/z*pi/180)-yg*sin(n*360/z*pi/180);
y=xg*sin(n*360/z*pi/180)+yg*cos(n*360/z*pi/180);
plot(x,y,'r');
end