Involute

%       The equations of the involute.

axis([-1.7 1.7 -1.7 1.7]), axis(‘square’), axis(‘off’)
hold on
phi1 = 0: pi/30: 2*pi;
a = 1;
rho = a*ones(phi1);
alpha1 = pi/3;
phi2 = tan(alpha1) – alpha1;
phi3 = phi2 + alpha1;polar(phi1, rho, ‘-‘) % base circle
polar( [phi3 phi3 ], [ 0 a ])              % radius OA
polar([ phi3 phi2 ], [ a a/cos(alpha1) ])  % tangent AB
gtext(‘A’)
gtext(‘B’)
gtext(‘a’)
polar([ phi2 phi2 ], [ 0 a/cos(alpha1) ])  % OB
gtext(‘O’)
gtext(‘r’)
polar([ 0 0 ], [ 0 a ])
gtext(‘C’)
gtext(‘D’)
hold off