clear all;
    clc;
    g = 9.81;
    m = 4000;
    L = 4;
    r_max = 2.2;
    r_min = 1.2;
    theta_min = -20;
    theta_max = 80;

    %values to remember mins and maxs
    F_max = 10000;
    tempFExtension = 0;

    %values to remember angles where you minimise the maximum hydrulic ram
    %force
      thetaFinal =0;
      phiFinal = 0;
      aFinal = 0;
      bFinal = 0;

    for phi = 0:0.5:180
        gamma = phi +20;
        C_2 = (r_max.^2 - r_min.^2)./((cos(gamma + theta_min) - cos(gamma + theta_max)));
        C_1 = r_max.^2 + C_2.*cos(gamma + theta_max);
        a = ((C_1 +C_2).^(1/2)+(C_1-C_2))./2;
        b = C_2./2.*a;

        for theta = -20:10:80
            r = linspace(1.2,2.2,10); % taking all possible values of ram length
            F = (r./(b.*a)).*((m.*g.*L.*cos(theta))./(sin(gamma + theta)));

           % find maximum value of force in vector F
           tempFExtension = max(F);
           if tempFExtension > 0 && tempFExtension < F_max;
               F_max = tempFExtension
               thetaFinal = theta
               aFinal = a
               phiFinal = phi
               bFinal = b
           end
        end
    end
     a
     b
     thetaFinal
     phiFinal