Solve command breaking when certain numbers are inserted?

I am working on a 6-bar mechanism code for school, and I've run across an issue. I've got this code that is supposed to figure the positions of each link and plot them, but whenever the values for angle_2 are equal to 60 or 45, the code breaks, and I either get an error message or the plot is wrong. Works great for every other value so I am not sure what is the matter? I tried to use the assume command to make sure the angle values were right, but that broke the code as well. Any help would be appreciated!

clear;clc;
R1 = 12.8062; %O2-O4
R1a_ = [10,-8,0];
R1b_ = [-7,10.5,0];
R2 = 5; %OA
R3 = 7.5; %AB
R3_2 = 15; %AC
R4 = 15;    %O4-B
R6 = 12.6194;  
DO6 = 8;
angle_2 = 0:45:360;
thetag = 321.34;
thetag2 = 180 + atand(10.5/-7);

for i=1:length(angle_2)
    syms angle_3 angle_4 R5_1 angle_5   
    
    Angle_eqs = [R2*cosd(angle_2(i))+R3*cosd(angle_3) == R4*cosd(angle_4)+R1*cosd(thetag);
        R2*sind(angle_2(i))+R3*sind(angle_3) == R4*sind(angle_4)+R1*sind(thetag)];
    
    Angle = solve(Angle_eqs,[angle_3 angle_4]);
    angle_3 = eval(Angle.angle_3)
    angle_4 = eval(Angle.angle_4)
    
    angle_3_ = angle_3(1)
    angle_4_ = angle_4(1)
    OA = [R2*cosd(angle_2(i)),R2*sind(angle_2(i)),0];
    AB = [OA(1)+R3*cosd(angle_3_),OA(2)+R3*sind(angle_3_),0];
    AC = R3_2*[cosd(angle_3_),sind(angle_3_),0]+[OA(1),OA(2),0];
    O4B = [R1a_(1)+R4*cosd(angle_4_),R1a_(2)+R4*sind(angle_4_)];
    
    Angle_eqs2 = [R2*cosd(angle_2(i))+R3_2*cosd(angle_3_)==R5_1*cosd(angle_5)+R6*cosd(thetag2); 
        R2*sind(angle_2(i))+R3_2*sind(angle_3_)== R5_1*sind(angle_5)+R6*sind(thetag2)]; % %*cosd(thetag2)
    
    Angle2 = solve(Angle_eqs2,[R5_1 angle_5]);
    R5_1 = eval(Angle2.R5_1);
    angle_5 = eval(Angle2.angle_5);
    R5 = R5_1(1);
    angle_5_ = angle_5(1);
    R5val = R5;
    R5 = R5*[cosd(angle_5_),sind(angle_5_),0]+R1b_;
    
    D_O6 = R1b_- DO6*[cosd(angle_5_),sind(angle_5_),0];
    CE = (27-R5val)*[cosd(angle_5_),sind(angle_5_),0]+AC;
    
    plot([0,OA(1)],[0,OA(2)],[OA(1),AB(1)], ...
        [OA(2),AB(2)],[AB(1),R1a_(1)],[AB(2),R1a_(2)] ...
        ,[OA(1),AC(1)],[OA(2),AC(2)],[R1b_(1),R5(1)],[R1b_(2),R5(2)],[R1b_(1),D_O6(1)],[R1b_(2),D_O6(2)] ...
        ,[AC(1),CE(1)],[AC(2),CE(2)])
    axis ( [ -20 20 -20 20])
    hold on
end

Answer 1

[Walter Roberson]

Never eval() a symbolic expression. There is no documented eval() for symbolic expressions.

In practice, eval() of a symbolic expression is the same as eval() of char() of the symbolic expression. But char() of a symbolic expression does not generally turn the symbolic expression into MATLAB code: it generally turns it into human-readable form that is not accepted as code.

Use subs() if you need to evaluate a symbolic expression after you have changed a symbolic variable to numeric. double() the result of subs() if you need double precision.

R1 = 12.8062; %O2-O4
R1a_ = [10,-8,0];
R1b_ = [-7,10.5,0];
R2 = 5; %OA
R3 = 7.5; %AB
R3_2 = 15; %AC
R4 = 15;    %O4-B
R6 = 12.6194;  
DO6 = 8;
angle_2 = 0:45:360;
thetag = 321.34;
thetag2 = 180 + atand(10.5/-7);

for i=1:length(angle_2)
    syms angle_3 angle_4 R5_1 angle_5   
    
    Angle_eqs = [R2*cosd(angle_2(i))+R3*cosd(angle_3) == R4*cosd(angle_4)+R1*cosd(thetag);
        R2*sind(angle_2(i))+R3*sind(angle_3) == R4*sind(angle_4)+R1*sind(thetag)];
    
    Angle = solve(Angle_eqs,[angle_3 angle_4]);
    angle_3 = double(subs(Angle.angle_3))
    angle_4 = double(subs(Angle.angle_4))
    
    angle_3_ = angle_3(1)
    angle_4_ = angle_4(1)
    OA = [R2*cosd(angle_2(i)),R2*sind(angle_2(i)),0];
    AB = [OA(1)+R3*cosd(angle_3_),OA(2)+R3*sind(angle_3_),0];
    AC = R3_2*[cosd(angle_3_),sind(angle_3_),0]+[OA(1),OA(2),0];
    O4B = [R1a_(1)+R4*cosd(angle_4_),R1a_(2)+R4*sind(angle_4_)];
    
    Angle_eqs2 = [R2*cosd(angle_2(i))+R3_2*cosd(angle_3_)==R5_1*cosd(angle_5)+R6*cosd(thetag2); 
        R2*sind(angle_2(i))+R3_2*sind(angle_3_)== R5_1*sind(angle_5)+R6*sind(thetag2)]; % %*cosd(thetag2)
    
    Angle2 = solve(Angle_eqs2,[R5_1 angle_5]);
    R5_1 = double(subs(Angle2.R5_1));
    angle_5 = double(subs(Angle2.angle_5));
    R5 = R5_1(1);
    angle_5_ = angle_5(1);
    R5val = R5;
    R5 = R5*[cosd(angle_5_),sind(angle_5_),0]+R1b_;
    
    D_O6 = R1b_- DO6*[cosd(angle_5_),sind(angle_5_),0];
    CE = (27-R5val)*[cosd(angle_5_),sind(angle_5_),0]+AC;
    
    plot([0,OA(1)],[0,OA(2)],[OA(1),AB(1)], ...
        [OA(2),AB(2)],[AB(1),R1a_(1)],[AB(2),R1a_(2)] ...
        ,[OA(1),AC(1)],[OA(2),AC(2)],[R1b_(1),R5(1)],[R1b_(2),R5(2)],[R1b_(1),D_O6(1)],[R1b_(2),D_O6(2)] ...
        ,[AC(1),CE(1)],[AC(2),CE(2)])
    axis ( [ -20 20 -20 20])
    hold on
end

angle_3 = 2×1

66.3082 177.7019

angle_4 = 2×1

97.6095 146.4006

angle_3_ = 66.3082

angle_4_ = 97.6095

angle_3 = 2×1

27.5015 -148.9698

angle_4 = 2×1

89.2815 149.2502

angle_3_ = 27.5015

angle_4_ = 89.2815

angle_3 = 2×1

13.5214 -118.3846

angle_4 = 2×1

100.4001 154.7367

angle_3_ = 13.5214

angle_4_ = 100.4001

angle_3 = 2×1

15.9858 -96.8641

angle_4 = 2×1

114.9419 164.1798

angle_3_ = 15.9858

angle_4_ = 114.9419

angle_3 = 2×1

33.7916 -89.9368

angle_4 = 2×1

125.7650 178.0898

angle_3_ = 33.7916

angle_4_ = 125.7650

angle_3 = 2×1

62.4888 -98.9975

angle_4 = 2×1

132.1755 -168.6842

angle_3_ = 62.4888

angle_4_ = 132.1755

angle_3 = 2×1

95.7300 -129.1287

angle_4 = 2×1

135.7731 -169.1718

angle_3_ = 95.7300

angle_4_ = 135.7731

angle_3 = 2×1

170.1066 120.6336

angle_4 = 2×1

157.4469 133.2933

angle_3_ = 170.1066

angle_4_ = 157.4469

angle_3 = 2×1

66.3082 177.7019

angle_4 = 2×1

97.6095 146.4006

angle_3_ = 66.3082

angle_4_ = 97.6095