Thread: 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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why 35 views and 0 reply?
plz guide where m i wrong in problem statement ?