I would suggest pulling all the calculations out of the for loop. You can take advantage of MATLAB's vector math to calculate all the results and even plot the starting configuration. Then use a loop to update the XData and YData values of the links. This way, you have access to all the data and can follow a similar approach to create a line that traces P.
L0 = 7; L1 = 3; L2 = 7.5; L3 = 4.5;
L_PA = 4; alpha =35;
w2 = 5; theta2 = 0:2:360;
% Convert operators on vectors to elementwise operators
AC = sqrt(L0^2+L1^2 - 2*L0*L1*cosd(theta2));
beta = acosd((L0^2+AC.^2-L1^2)./(2*L0*AC));
psi = acosd((L2^2+AC.^2-L3^2)./(2*L2*AC));
lamda = acosd((L3^2+AC.^2-L2^2)./(2*L3*AC));
% These 2 lines might be a little tricky. Break it into parts to figure out how it works.
theta3 = (theta2<=180).*(psi-beta) + (theta2>180).*(psi+beta);
theta4 = (theta2<=180).*(180-lamda-beta) + (theta2>180).*(180-lamda+beta);
Ox = 0; Oy = 0;
Ax = Ox + L1*cosd(theta2);
Ay = Oy + L1*sind(theta2);
Bx = Ox +Ax + L2*cosd(theta3);
By = Oy +Ay + L2*sind(theta3);
Cx = L0; Cy = 0;
Px = Ax +L_PA *cosd(alpha + theta3);
Py = Ay +L_PA *sind(alpha + theta3);
theta5 = alpha + theta3;
% Create the original figure by plotting just the first points in the vectors
AB = plot([Ox Ax(1)],[Oy Ay(1)], ...
[Ax(1) Bx(1)],[Ay(1) By(1)],...
[Bx(1) Cx],[By(1) Cy],'LineWidth',3);
hold on
ABP = plot([Ax(1) Px(1)],[Ay(1) Py(1)],...
[Bx(1) Px(1)],[By(1) Py(1)],'LineWidth',3);
hold off
grid on;
axis equal;
axis([-5 15 -5 10]);
% Use the loop to step though all the link positions, updating the corresponding X and Y values
for i = 2:length(theta2)
AB(1).XData = [Ox Ax(i)];
AB(1).YData = [Oy Ay(i)];
AB(2).XData = [Ax(i) Bx(i)];
AB(2).YData = [Ay(i) By(i)];
AB(3).XData = [Bx(i) Cx];
AB(3).YData = [By(i) Cy];
ABP(1).XData = [Ax(i) Px(i)];
ABP(1).YData = [Ay(i) Py(i)];
ABP(2).XData = [Bx(i) Px(i)];
ABP(2).YData = [By(i) Py(i)];
drawnow
end
