create the whole geomtery of boggenzahn kupplung and also show its gear profile and tooth profile in matlab

main.m
% Define the parameters of the bogenzahn kupplung
module = 1;
z1 = 20;
z2 = 30;
alpha = 20; % Pressure angle in degrees

% Calculate the base circle radius
rb = module * z1 / 2;

% Calculate the pitch circle radius
rp1 = rb / cosd(alpha);
rp2 = rp1;

% Calculate the number of teeth in contact
b = rb * (sqrt((rp2^2 - (rp1 - 2*module)^2)) - sqrt(rp1^2 - (rp1 - 2*module)^2)) / ((rp1 + rp2) * sind(alpha)); % Approximation

% Calculate the reference circle radius
rf = rp1 + module;

% Draw the gear profile
t = linspace(0, 2*pi, 1000);
x = rb*cos(t) - module*sin(t);
y = rb*sin(t) + module*cos(t);
plot(x, y);
hold on;
x1 = rp1*cos(t) - module*sin(t);
y1 = rp1*sin(t) + module*cos(t);
plot(x1, y1, 'r');
x2 = rp2*cos(t) - module*sin(t);
y2 = rp2*sin(t) + module*cos(t);
plot(x2, y2, 'g');
axis equal;
xlabel('X');
ylabel('Y');
title('Gear Profile');

% Draw the tooth profile
tooth_angle = asind(module / (2*rf));
tooth_theta = linspace(-tooth_angle, tooth_angle);
tooth_x = rf * cosd(tooth_theta) - module * sind(tooth_theta);
tooth_y = rf * sind(tooth_theta) + module * cosd(tooth_theta);
plot(tooth_x, tooth_y, 'm', 'LineWidth', 2);

legend('Base Circle', 'Pitch Circle 1', 'Pitch Circle 2', 'Tooth Profile', 'Location', 'Best');
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