A. Appendix for MATLAB script

clear all

theta = 0:.01:14.32;

Bx = [0,0];

By = [0,0];

Bz = [0,0];

Cx = [0,0];

Cy = [0,0];

Cz = [0,0];

Ax = [0];

Ay = 4.85*sind(theta);

Az = -4.85*cosd(theta);

for i = 1:length(theta)

    Ax(i) = -2.3;

    x = theta(i);

    syms bx by bz cx cy cz

    eqn1 = bx^2 + by^2 + bz^2 == 4.1^2;

    eqn2 = cx^2 + cy^2 + cz^2 == 0.85^2;

    eqn3 = bx + cx == -0.7;

    eqn4 = by + cy == 4.8-4.85*sind(x);

    eqn5 = bz + cz == 4.85*cosd(x)-4;

    eqn6 = cz/cx == tand(18);

    [Sbx, Sby, Sbz, Scx, Scy, Scz] = solve(eqn1, eqn2, eqn3, eqn4, eqn5, eqn6);

    format short

    temp1 = vpa(Sbx);

    temp2 = vpa(Sby);

    temp3 = vpa(Sbz);

    temp4 = vpa(Scx);

    temp5 = vpa(Scy);

    temp6 = vpa(Scz);

    Bx(i) = temp1(1);

    By(i) = temp2(1);

    Bz(i) = temp3(1);

    Cx(i) = temp4(1);

    Cy(i) = temp5(1);

    Cz(i) = temp6(1);

end

o = [0,0,0];

for i = 1:length(theta)

    A = [Ax(i), Ay(i), Az(i)];

    B = [(Bx(i)+Ax(i)), (By(i) + Ay(i)), (Bz(i) + Az(i))];

    C = [(Cx(i) + Bx(i)+Ax(i)), (Cy(i) + By(i) + Ay(i)), (Cz(i) + Bz(i) + Az(i))];

    figure(1)

    vectarrow(o,A)

    hold on 

    vectarrow(A,B)

    vectarrow(B,C)

    axis([-5 0 0 7.5 -5 0])

    legend('Link A [input]', 'Link B', 'Link C [output]', 'location', 'southeast')

    hold off

    drawnow

    frame = getframe(1);

    im = frame2im(frame);

    [ind,cm] = rgb2ind(im,256);

    filename = 'ME350RProject.gif';

    if i == 1 

        imwrite(ind,cm,filename,'gif', 'DelayTime', 0, 'Loopcount',inf);

    else

        imwrite(ind,cm,filename,'gif','WriteMode','append');

    end

end

figure(2)

plot3(Ax, Ay, Az)

hold on

subx = Ax + Bx;

suby = Ay + By;

subz = Az + Bz;

plot3(subx, suby, subz)

subx = subx + Cx;

suby = suby + Cy;

subz = subz + Cz;

plot3(subx, suby, subz)

hold off

legend('Link A [input]', 'Link B', 'Link C [output]', 'location', 'southwest')

saveas(2, 'ME350RProject.jpg')

o = [0,0];

Cxref = sqrt(Cx.^2 + Cz.^2);

for i = 1:length(theta)

    subC = sqrt(Cx(i)^2 + Cz(i)^2);

    Cref = [subC, -Cy(i)];

    figure(3)

    vectarrow(o, Cref)

    hold on

    plot(Cxref, -Cy)

    axis([0 2 -1 0.5])

    title('Output Link')

    hold off

    drawnow

    frame = getframe(3);

    im = frame2im(frame);

    [ind,cm] = rgb2ind(im,256);

    filename = 'ME350RProjectDemo.gif';

    if i == 1 

        imwrite(ind,cm,filename,'gif', 'DelayTime', 0, 'Loopcount',inf);

        angle1 = abs(atand(Cy(i)/subC));

    else

        imwrite(ind,cm,filename,'gif','WriteMode','append');

    end

end

outputangle = angle1 + abs(atand(Cy(i)/subC));