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is it possible to convert equation variable (polar to Cartesian coordinate)?

hi everyone!!

my project is related spur gear and i draw the involute profile by using matlab program .

this is the program only for better understanding (graph also attached with post)

is it possible to make such kind of equation Y=f(x) for involute profile?

because i want to use this equation in bending, deflection, stress calculation

thanks in advance !!!

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clear

rad = pi/180;

r_p = 50;

r_p2 = r_p;

phi = 20*rad;

P = 0.25;

a = 1/P;

d = 1.25/P;

p = pi/P;

t_p = p/2; % arc tooth thickness @ r_p ---- [mm]

r_b = r_p*cos(phi); % base circle radius ----------- [mm]

inv_phi = tan(phi)-phi; % derived angle ---------------- [rad]

r = r_b:0.01:r_p+a;

chi = acos(r_b./r); % pressure angle @ r ----------- [rad]

inv_chi = tan(chi)-chi; % derived angle ---------------- [rad]

t = 2*r.*((t_p/(2*r_p))+inv_phi-inv_chi);

beta = t./(2*r);

x = r.*sin(beta); % x-coor of tooth profile ------ [mm]

y = (r.*cos(beta)); % y-coor of tooth profile ------ [mm]

N = P*2*r_p; % number of teeth

figure(1)

clf

hold on

plot(x,y)

grid on

axis equal

xlabel('x [mm]')

ylabel('y [mm]')

title('involute spur gear tooth profile')

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