% %%%%%%%%%%%%
% Problem 6.1 
%%%%%%%%%%%%%%
% Results 
% rA =  [ 0, 0, 0 ] (m)
% rD =  [ 0.09, 0, 0 ] (m)
% rB =  [ 0.034641, 0.02, 0 ] (m)
% rC =  [ 0.103859, -0.0375222, 0 ] (m)
% phi1 = 30 (degrees) 
% phi2 = -39.7274 (degrees) 
% phi3 = -69.7274 (degrees) 
% rC1 = rB/2 = [ 0.0173205, 0.01, 0 ] (m)
% rC2 = (rB+rC)/2 = [ 0.0692503, -0.00876109, 0 ] (m)
% rC3 = (rC+rD)/2 = [ 0.0969297, -0.0187611, 0 ] (m)
% Velocity and acceleration analysis 
% omega1 =  [ 0, 0, 12.5664 ] (rad/s)
% alpha1 =  [ 0, 0, 0 ] (rad/s^2)
% vB = vB1 = vB2 =  [ -0.251327, 0.435312, 0 ] (m/s)
% aB = aB1 = aB2 =  [ -5.47029, -3.15827, 0 ] (m/s^2)
% vC = vB + omega2 x rBC = vD + omega3 x rDC  => 
% x-axis: -.251327412+.575221840e-1*omega2z-.375221840e-1*omega3z = 0 
% y-axis: .435311847+.692184827e-1*omega2z-.138594989e-1*omega3z = 0 
% =>
% omega2z =  -11.0095 (rad/s)
% omega3z =  -23.5759 (rad/s)
% omega2 = [ 0, 0, -11.0095 ] (rad/s)
% omega3 = [ 0, 0, -23.5759 ] (rad/s)
% vC =  [ -0.884619, -0.32675, 0 ] (m/s)
% aC = aC2 = aB + omega2 x rBC - (omega2.omega2)rBC 
% aC = aC3 = aD + omega3 x rDC - (omega3.omega3)rDC 
% x-axis: -6.15680068+.575221840e-1*alpha2z-.375221840e-1*alpha3z = 0 
% y-axis: -17.0417115+.692184827e-1*alpha2z-.138594989e-1*alpha3z = 0 
% =>
% alpha2z =  307.84 (rad/s^2)
% alpha3z =  307.84 (rad/s^2)
% alpha2 = [ 0, 0, 307.84 ] (rad/s^2)
% alpha3 = [ 0, 0, 307.84 ] (rad/s^2)
% aC =  [ 3.84741, 25.1222, 0] (m/s^2)
% aC1 = aB/2 = [ -2.73515, -1.57914, 0] (m/s^2)
% aC2 = (aB+aC)/2 = [ -0.811439, 10.982, 0] (m/s^2)
% aC3 = (aC+aD)/2 = [ 1.92371, 12.5611, 0] (m/s^2)
% external moment Me = [ 0, 0, 500 ] (N m)
% Inertia forces and moments 
%  link 1 
% m1 = 0.0032 (kg)
% IC1 = 4.53333e-07 (kg m^2)
% G1 = [ 0, -0.0313824, 0 ] (N)
% m1*aC1 = [ -0.00875246, -0.00505324, 0 ] (N)
% IC1*alpha1 = [ 0, 0, 0 ] (N m)
%  link 2 
% m2 = 0.0072 (kg)
% IC2 = 4.92e-06 (kg m^2)
% G2 = [ 0, -0.0706104, 0 ] (N)
% m1*aC2 = [ -0.00584236, 0.07907, 0 ] (N)
% IC2*alpha2 = [ 0, 0, 1.514573e-03 ] (N m)
%  link 3 
% m3 = 0.0032 (kg)
% IC3 = 4.53333e-07 (kg m^2)
% G3 = [ 0, -0.0313824, 0 ] (N)
% m3*aC3 = [ 0.00615586, 0.0401955, 0 ] (N)
% IC3*alpha3 = [ 0, 0, 1.395541e-04 ] (N m)
% eom link 3 
% F03x+F23x-.615585933e-2 = 0 (1)
% F03y+F23y-.715778793e-1 = 0 (2)
% -.692974943e-2*F03y-.187610920e-1*F03x+.692974943e-2*F23y+.187610920e-1*F23x+499.999860 = 0 (3)
% eom link 2 
% -1.*F23x+F12x+.584236053e-2 = 0 (4)
% -1.*F23y+F12y-.149680444 = 0 (5)
% -.346092414e-1*F23y-.287610920e-1*F23x-.346092414e-1*F12y-.287610920e-1*F12x-.151457297e-2 = 0 (6)
% Eqs(1)-(6) => F03x, F03y, F23x, F23y, F12x, F12y 
% F03 = [ 19227.3, -15978.2, 0] (N)
% F23 = [ -19227.3, 15978.2, 0] (N)
% F12 = [ -19227.3, 15978.4, 0] (N)
% eom link 1 
% F01 = [ -19227.3, 15978.4, 0] (N)
% Mm = [ 0, 0, 938.053] (N m)
%
%
%
%%%%%%%%%%%%%%
% Problem 6.1 
%%%%%%%%%%%%%%
% Dyad method
%%%%%%%%%%%%%
% Results
% rA =  [ 0, 0, 0 ] (m)
% rD =  [ 0.09, 0, 0 ] (m)
% rB =  [ 0.034641, 0.02, 0 ] (m)
% rC =  [ 0.103859, -0.0375222, 0 ] (m)
% phi2 = -39.7274 (degrees) 
% phi3 = -69.7274 (degrees) 
% rC1 = rB/2 = [ 0.0173205, 0.01, 0 ] (m)
% rC2 = (rB+rC)/2 = [ 0.0692503, -0.00876109, 0 ] (m)
% rC3 = (rC+rD)/2 = [ 0.0969297, -0.0187611, 0 ] (m)
% Velocity and acceleration analysis 
% omega1 =  [ 0, 0, 12.5664 ] (rad/s)
% alpha1 =  [ 0, 0, 0 ] (rad/s^2)
% vB = vB1 = vB2 =  [ -0.251327, 0.435312, 0 ] (m/s)
% aB = aB1 = aB2 =  [ -5.47029, -3.15827, 0 ] (m/s^2)
% vC = vB + omega2 x rBC = vD + omega3 x rDC  => 
% x-axis: -.251327412+.575221840e-1*omega2z-.375221840e-1*omega3z = 0 
% y-axis: .435311847+.692184827e-1*omega2z-.138594989e-1*omega3z = 0 
% =>
% omega2z =  -11.0095 (rad/s)
% omega3z =  -23.5759 (rad/s)
% omega2 = [ 0, 0, -11.0095 ] (rad/s)
% omega3 = [ 0, 0, -23.5759 ] (rad/s)
% vC =  [ -0.884619, -0.32675, 0 ] (m/s)
% aC = aC2 = aB + omega2 x rBC - (omega2.omega2)rBC 
% aC = aC3 = aD + omega3 x rDC - (omega3.omega3)rDC 
% x-axis: -6.15680068+.575221840e-1*alpha2z-.375221840e-1*alpha3z = 0 
% y-axis: -17.0417115+.692184827e-1*alpha2z-.138594989e-1*alpha3z = 0 
% =>
% alpha2z =  307.84 (rad/s^2)
% alpha3z =  307.84 (rad/s^2)
% alpha2 = [ 0, 0, 307.84 ] (rad/s^2)
% alpha3 = [ 0, 0, 307.84 ] (rad/s^2)
% aC =  [ 3.84741, 25.1222, 0] (m/s^2)
% aC1 = aB/2 = [ -2.73515, -1.57914, 0] (m/s^2)
% aC2 = (aB+aC)/2 = [ -0.811439, 10.982, 0] (m/s^2)
% aC3 = (aC+aD)/2 = [ 1.92371, 12.5611, 0] (m/s^2)
% external moment Me = [ 0, 0, 500 ] (N m)
% Inertia forces and moments 
%  link 1 
% m1 = 0.0032 (kg)
% IC1 = 4.53333e-07 (kg m^2)
% G1 = [ 0, -0.0313824, 0 ] (N)
% m1*aC1 = [ -0.00875246, -0.00505324, 0 ] (N)
% IC1*alpha1 = [ 0, 0, 0 ] (N m)
%  link 2 
% m2 = 0.0072 (kg)
% IC2 = 4.92e-06 (kg m^2)
% G2 = [ 0, -0.0706104, 0 ] (N)
% m1*aC2 = [ -0.00584236, 0.07907, 0 ] (N)
% IC2*alpha2 = [ 0, 0, 1.514573e-03 ] (N m)
%  link 3 
% m3 = 0.0032 (kg)
% IC3 = 4.53333e-07 (kg m^2)
% G3 = [ 0, -0.0313824, 0 ] (N)
% m3*aC3 = [ 0.00615586, 0.0401955, 0 ] (N)
% IC2*alpha3 = [ 0, 0, 1.395541e-04 ] (N m)
% eom links 2 and 3: RRR dyad 
% F03x+F12x-.313498807e-3 = 0 (1)
% F03y-.221258324+F12y = 0 (2)
% -.138594989e-1*F03y-.375221840e-1*F03x+500.000472 = 0 (3)
% -.692184827e-1*F12y-.575221840e-1*F12x+.349772099e-2 = 0 (4)
% Eqs(1)-(4) => F03x, F03y, F12x, F12y 
% F03 = [ 19227.3, -15978.2, 0] (N)
% F12 = [ -19227.3, 15978.4, 0] (N)
% F32 = [ 19227.3, -15978.2, 0] (N)
% eom link 1 
% F01 = [ -19227.3, 15978.4, 0] (N)
% Mm = [ 0, 0, 938.053] (N m)
% 
%
%
% %%%%%%%%%%%%%
% Problem 6.2 
% %%%%%%%%%%%%%
% Results 
% rA =  [ 0, 0, 0 ] (m)
% rD =  [ 0.3, 0.45, 0 ] (m)
% rB =  [ 0.129904, 0.075, 0 ] (m)
% rC =  [ -0.0689445, 0.422073, 0 ] (m)
% rE =  [ -0.298288, 0.404712, 0 ] (m)
% rF =  [ -0.37, 0.186177, 0 ] (m)
% phi1 = 30 (degrees) 
% phi2 = -60.1903 (degrees) 
% phi3 = 4.32878 (degrees) 
% phi4 = 71.8329 (degrees) 
% rC1 = rB/2 = [ 0.0649519, 0.0375, 0 ] (m)
% rC2 = (rB+rC)/2 = [ 0.0304796, 0.248536, 0 ] (m)
% rC3 = (rD+rE)/2 = [ 0.000855797, 0.427356, 0 ] (m)
% rC4 = (rE+rF)/2 = [ -0.334144, 0.295445, 0 ] (m)
% rC5 = rF = [ -0.37, 0.186177, 0 ] (m)
% Velocity and acceleration analysis 
% omega1 =  [ 0, 0, 6.28319 ] (rad/s)
% alpha1 =  [ 0, 0, 0 ] (rad/s^2)
% vB = vB1 = vB2 =  [ -0.471239, 0.81621, 0 ] (m/s)
% aB = aB1 = aB2 =  [ -5.1284, -2.96088, 0 ] (m/s^2)
% vC = vB + omega2 x rBC = vD + omega3 x rDC  => 
% x-axis: -.471238898-.347072532*omega2z-.279274677e-1*omega3z = 0 
% y-axis: .816209714-.198848327*omega2z+.368944517*omega3z = 0 
% =>
% omega2z =  -1.1307 (rad/s)
% omega3z =  -2.82169 (rad/s)
% omega2 = [ 0, 0, -1.1307 ] (rad/s)
% omega3 = [ 0, 0, -2.82169 ] (rad/s)
% vC =  [ -0.0788027, 1.04105, 0 ] (m/s)
% vE =  [ -0.127788, 1.68819, 0 ] (m/s)
% vF = vE + omega4 x rEF  => 
% x-axis: .127788236-.218534774*omega4z = 0 
% y-axis: vFy-1.68818632+.717115942e-1*omega4z = 0 
% =>
% omega4z =  0.58475 (rad/s)
% vFy =  1.64625 (m/s)
% omega4 = [ 0, 0, 0.58475 ] (rad/s)
% vF =  [ 0, 1.64625, 0 ] (m/s)
% aC = aC2 = aB + alpha2 x rBC - (omega2.omega2)rBC 
% aC = aC3 = aD + alpha3 x rDC - (omega3.omega3)rDC 
% x-axis: -7.81168986-.347072532*alpha2z-.279274677e-1*alpha3z = 0 
% y-axis: -3.62696745-.198848327*alpha2z+.368944517*alpha3z = 0 
% =>
% alpha2z =  -22.33 (rad/s^2)
% alpha3z =  -2.20443 (rad/s^2)
% alpha2 = [ 0, 0, -22.33 ] (rad/s^2)
% alpha3 = [ 0, 0, -2.20443 ] (rad/s^2)
% aC =  [ 2.87595, 1.03567, 0] (m/s^2)
% aE =  [ 4.66371, 1.67947, 0] (m/s^2)
% aF = aE + alpha4 x rEF - (omega4.omega4)rEF 
% x-axis: -4.68823048-.218534774*alpha4z = 0 
% y-axis: aFy-1.75418998+.717115942e-1*alpha4z = 0 
% =>
% alpha4z =  -21.453 (rad/s^2)
% aFy =  3.29262 (m/s^2)
% alpha4 = [ 0, 0, -21.453 ] (rad/s^2)
% aF =  [ 0, 3.29262, 0 ] (m/s^2)
% aC1 = aB/2 = [ -2.5642, -1.48044, 0] (m/s^2)
% aC2 = (aB+aC)/2 = [ -1.12622, -0.962605, 0] (m/s^2)
% aC3 = (aD+aE)/2 = [ 2.33185, 0.839733, 0] (m/s^2)
% aC4 = (aE+aF)/2 = [ 2.33185, 2.48604, 0] (m/s^2)
% aC5 = aF = [ 0, 3.29262, 0] (m/s^2)
% alpha1 = [ 0, 0, 0 ] (rad/s^2)
% alpha2 = [ 0, 0, -22.33 ] (rad/s^2)
% alpha3 = [ 0, 0, -2.20443 ] (rad/s^2)
% alpha4 = [ 0, 0, -21.453 ] (rad/s^2)
% vF =  [ 0, 1.64625, 0 ] (m/s)
% external force Fe = [ 0, -500, 0 ] (N)
% Dynamic force analysis  
% Newton-Euler method  
%  link 1 
% m1 = 0.012 (kg)
% IC1 = 2.26e-05 (kg m^2)
% G1 = [ 0, -0.117684, 0 ] (N)
% m1*aC1 = [ -0.0307704, -0.0177653, 0 ] (N)
% IC1*alpha1 = [ 0, 0, 0 ] (N m)
%  link 2 
% m2 = 0.032 (kg)
% IC2 = 0.000426933 (kg m^2)
% G2 = [ 0, -0.313824, 0 ] (N)
% m1*aC2 = [ -0.0360391, -0.0308034, 0 ] (N)
% IC2*alpha2 = [ 0, 0, -9.533416e-03 ] (N m)
%  link 3 
% m3 = 0.048 (kg)
% IC3 = 0.0014404 (kg m^2)
% G3 = [ 0, -0.470736, 0 ] (N)
% m3*aC3 = [ 0.111929, 0.0403072, 0 ] (N)
% IC3*alpha3 = [ 0, 0, -3.175265e-03 ] (N m)
%  link 4 
% m4 = 0.0184 (kg)
% IC4 = 8.12667e-05 (kg m^2)
% G4 = [ 0, -0.180449, 0 ] (N)
% m4*aC4 = [ 0.0429061, 0.0457432, 0 ] (N)
% IC4*alpha4 = [ 0, 0, -1.743415e-03 ] (N m)
%  link 5  
% m5 =  0.008 (kg)
% IC5 =  1.93333e-06 (kg m^2)
% G5 = - m5 g = [ 0, -0.078456, 0] (N)
% m5*aC5 = [ 0, 0.026341, 0] (N)
% IC5*alpha5 = [ 0, 0, 0] (N m)
%
%
%
%%%%%%%%%%%%%%%
% Problem 6.3 
%%%%%%%%%%%%%%%
% Results 
% rA =  [ 0, 0, 0 ] (m)
% rD =  [ -1.04491, -0.154122, 0 ] (m)
% rB =  [ -0.1, 0.173205, 0 ] (m)
% rC =  [ -0.6, 0, 0 ] (m)
% rE =  [ -0.75, 0.25, 0 ] (m)
% rF =  [ -1.10369, -0.234668, 0 ] (m)
% phi1 = 120 (degrees) 
% phi2 = 19.1066 (degrees) 
% phi5 = 53.8796 (degrees) 
% rC1 = rB/2 = [ -0.05, 0.0866025, 0 ] (m)
% rC2 = (rB+rD)/2 = [ -0.572456, 0.00954166, 0 ] (m)
% rC3 = rC = [ -0.6, 0, 0 ] (m)
% rC4 = rD = [ -1.04491, -0.154122, 0 ] (m)
% rC5 = (rE+rF)/2 = [ -0.926845, 0.00766601, 0 ] (m)
% Velocity and acceleration analysis 
% omega1 =  [ 0, 0, 6.28319 ] (rad/s)
% alpha1 =  [ 0, 0, 0 ] (rad/s^2)
% vB = vB1 = vB2 =  [ -1.08828, -0.628319, 0 ] (m/s)
% aB = aB1 = aB2 =  [ 3.94784, -6.83786, 0 ] (m/s^2)
% vC2 = vB + omega2 x rBC = vC3 + vC23 (vC3=0)  => 
% x-axis: -1.08827962+.173205081*omega2z-.944911182*vC23 = 0 
% y-axis: -.628318530-.500000000*omega2z-.327326835*vC23 = 0 
% =>
% omega2z =  -0.448799 (rad/s)
% vC23 =  -1.23399 (m/s)
% omega2 = omega3 = [ 0, 0, -0.448799 ] (rad/s)
% vC2C3 = [ -1.16601, -0.403919, -0 ] (m/s)
% vD2 =  [ -1.23518, -0.204243, 0 ] (m/s)
% vD5 = vE + omega5 x rED = vD4 + vD54 (vD4=vD2)  => 
% x-axis: .404121755*omega5z+1.23518356-.589484100*vD54 = 0 
% y-axis: -.294911183*omega5z+.204243384-.807779980*vD54 = 0 
% =>
% omega5z =  -1.75371 (rad/s)
% vD23 =  0.893105 (m/s)
% omega5 = omega5 = [ 0, 0, -1.75371 ] (rad/s)
% vD2D3 = [ 0.526471, 0.721432, 0 ] (m/s)
% vF =  [ -0.849967, 0.620271, 0 ] (m/s)
% aC23cor =  [ -0.362557, 1.04661, 0 ] (m/s^2)
% aC2 = aB + alpha2 x rBC - (omega2.omega2)rBC 
% aC2 = aC3 + aC23 + aC23cor (aC3=0)  
% x-axis: 4.41110891+.173205081*alpha2z-.944911182*aC23 = 0 
% y-axis: -7.84958706-.500000000*alpha2z-.327326835*aC23 = 0 
% =>
% alpha2z =  -16.7458 (rad/s^2)
% aC23 =  1.59873 (m/s^2)
% alpha2 = [ 0, 0, -16.7458 ] (rad/s^2)
% aC2C3 = [ 1.51065, 0.523306, 0 ] (m/s^2)
% aD2 =  [ -1.34318, 9.05135, 0] (m/s^2)
% aD54cor =  [ 2.53037, -1.84656, 0 ] (m/s^2)
% aD5 = aE + alpha5 x rED - (omega4.omega4)rED (aE=0) 
% aD5 = aD4 + aD54 + aD54cor (aD4=aD2)  
% x-axis: .404121755*alpha5z-.280187945-.589484100*aD54 = 0 
% y-axis: -.294911183*alpha5z-5.96191614-.807779980*aD54 = 0 
% =>
% alpha5z =  -6.57248 (rad/s^2)
% aD54 =  -4.98108 (m/s^2)
% alpha5 = [ 0, 0, -6.57248 ] (rad/s^2)
% aD5D4 = [ -2.93627, -4.02362, -0 ] (m/s^2)
% aF =  [ -2.09769, 3.81522, 0] (m/s^2)
% alpha1 = [ 0, 0, 0 ] (rad/s^2)
% alpha2 = alpha3 = [ 0, 0, -16.7458 ] (rad/s^2)
% alpha4 = alpha5 = [ 0, 0, -6.57248 ] (rad/s^2)
% aC1 = [ 1.97392, -3.41893, 0 ] (m/s^2)
% aC2 = [ 1.30233, 1.10674, 0 ] (m/s^2)
% aC3 = [ 0, 0, 0 ] (m/s^2)
% aC4 = aD4 = aD2 = [ -1.34318, 9.05135, 0 ] (m/s^2)
% aC5 = [ -1.04885, 1.90761, 0 ] (m/s^2)
% external moment Me = [ 0, 0, 900 ] (N m)
% Dynamic force analysis  
% Newton-Euler method  
%  link 1 
% m1 = 0.016 (kg)
% IC1 = 5.34667e-05 (kg m^2)
% G1 = [ 0, -0.156912, 0 ] (N)
% m1*aC1 = [ 0.0315827, -0.0547029, 0 ] (N)
% IC1*alpha1 = [ 0, 0, 0 ] (N m)
%  link 2 
% m2 = 0.08 (kg)
% IC2 = 0.00666733 (kg m^2)
% G2 = [ 0, -0.78456, 0 ] (N)
% m2*aC2 = [ 0.104187, 0.0885394, 0 ] (N)
% IC2*alpha2 = [ 0, 0, -1.116497e-01 ] (N m)
%  link 3 
% m3 = 0.008 (kg)
% IC3 = 1.93333e-06 (kg m^2)
% G3 = [ 0, -0.078456, 0 ] (N)
% m3*aC3 = [ 0, 0, 0 ] (N)
% IC3*alpha3 = [ 0, 0, -3.237519e-05 ] (N m)
%  link 4 
% m4 = 0.008 (kg)
% IC4 = 1.93333e-06 (kg m^2)
% G4 = [ 0, -0.078456, 0 ] (N)
% m4*aC4 = [ -0.0107454, 0.0724108, 0 ] (N)
% IC4*alpha4 = [ 0, 0, -1.270679e-05 ] (N m)
%  link 5  
% m5 =  0.048 (kg)
% IC5 =  0.0014404 (kg m^2)
% G5 = - m5 g = [ 0, -0.470736, 0] (N)
% m5*aC5 = [ -0.0503447, 0.0915653, 0] (N)
% IC5*alpha5 = [ 0, 0, -0.009467] (N m)
% Joint reactions and equilibrium moment 
% eom link 5 
% -.294911183*yP+.376819112+.404121755*xP = 0 (1)
% -.294911183*F45x-.404121755*F45y = 0 (2)
% F05x+F45x+.503446691e-1 = 0 (3)
% F05y+F45y-.562301255 = 0 (4)
% .176845230*F05y-.242333994*F05x+(xP+.926845230)*F45y-1.*(yP-.766600614e-2)*F45x+900.009467 = 0 (5)
% eom link 4 
% F24x-1.*F45x+.107454305e-1 = 0 (6)
% F24y-1.*F45y-.150866784 = 0 (7)
% -1.*(xP+1.04491118)*F45y+(yP+.154121755)*F45x+.127067901e-4 = 0 (8)
% Eqs(1)-(8) => F05x, F05y, F45x, F45y, F24x, F24y, xP, yP 
% F05 = [ 1453.32, -1060.04, 0] (N)
% F45 = [ -1453.37, 1060.61, 0] (N)
% F24 = [ -1453.38, 1060.76, 0] (N)
% rP = [ -1.04491, -0.154122, 0] (m)
% eom link 3 
% .500000000*yQ-.173205081*xQ-.103923049 = 0 (9)
% .500000000*F23x+.173205081*F23y = 0 (10)
% F03x+F23x = 0 (11)
% F03y+F23y-.784560000e-1 = 0 (12)
% (xQ+.600000000)*F23y-1.*yQ*F23x+.323751858e-4 = 0 (13)
% eom link 2 
% 1453.27221-1.*F23x+F12x = 0 (14)
% -1061.62953-1.*F23y+F12y = 0 (15)
% 739.136507+.472455592*F12y-.163663417*F12x-1.*(xQ+.572455591)*F23y+(yQ-.954166308e-2)*F23x = 0 (16)
% Eqs(9)-(16) => F03x, F03y, F23x, F23y, F12x, F12y, xQ, yQ 
% F03 = [ -914.62, 2640.36, 0] (N)
% F23 = [ 914.62, -2640.28, 0] (N)
% F12 = [ -538.652, -1578.65, 0] (N)
% rQ = [ -0.6, 3.79258e-09, 0] (m)
% Link 1 
% F01 = [ -538.621, -1578.55, 0] (N)
% Mm = [ 0, 0, 251.155] (N m)
%
%
%
%%%%%%%%%%%%%%%
% Problem 6.3 
%%%%%%%%%%%%%%%
% Dyad method
%%%%%%%%%%%%%%%
% Results 
% rA =  [ 0, 0, 0 ] (m)
% rD =  [ -1.04491, -0.154122, 0 ] (m)
% rB =  [ -0.1, 0.173205, 0 ] (m)
% rC =  [ -0.6, 0, 0 ] (m)
% rE =  [ -0.75, 0.25, 0 ] (m)
% rF =  [ -1.10369, -0.234668, 0 ] (m)
% phi2 = 19.1066 (degrees) 
% phi5 = 53.8796 (degrees) 
% rC1 = rB/2 = [ -0.05, 0.0866025, 0 ] (m)
% rC2 = (rB+rD)/2 = [ -0.572456, 0.00954166, 0 ] (m)
% rC3 = rC = [ -0.6, 0, 0 ] (m)
% rC4 = rD = [ -1.04491, -0.154122, 0 ] (m)
% rC5 = (rE+rF)/2 = [ -0.926845, 0.00766601, 0 ] (m)
% Velocity and acceleration analysis 
% omega1 =  [ 0, 0, 6.28319 ] (rad/s)
% alpha1 =  [ 0, 0, 0 ] (rad/s^2)
% vB = vB1 = vB2 =  [ -1.08828, -0.628319, 0 ] (m/s)
% aB = aB1 = aB2 =  [ 3.94784, -6.83786, 0 ] (m/s^2)
% vC2 = vB + omega2 x rBC = vC3 + vC23 (vC3=0)  => 
% x-axis: -1.08827962+.173205081*omega2z-.944911182*vC23 = 0 
% y-axis: -.628318530-.500000000*omega2z-.327326835*vC23 = 0 
% =>
% omega2z =  -0.448799 (rad/s)
% vC23 =  -1.23399 (m/s)
% omega2 = omega3 = [ 0, 0, -0.448799 ] (rad/s)
% vC2C3 = [ -1.16601, -0.403919, -0 ] (m/s)
% vD2 =  [ -1.23518, -0.204243, 0 ] (m/s)
% vD5 = vE + omega5 x rED = vD4 + vD54 (vD4=vD2)  => 
% x-axis: .404121755*omega5z+1.23518356-.589484100*vD54 = 0 
% y-axis: -.294911183*omega5z+.204243384-.807779980*vD54 = 0 
% =>
% omega5z =  -1.75371 (rad/s)
% vD23 =  0.893105 (m/s)
% omega5 = omega5 = [ 0, 0, -1.75371 ] (rad/s)
% vD2D3 = [ 0.526471, 0.721432, 0 ] (m/s)
% vF =  [ -0.849967, 0.620271, 0 ] (m/s)
% aC23cor =  [ -0.362557, 1.04661, 0 ] (m/s^2)
% aC2 = aB + alpha2 x rBC - (omega2.omega2)rBC 
% aC2 = aC3 + aC23 + aC23cor (aC3=0)  
% x-axis: 4.41110891+.173205081*alpha2z-.944911182*aC23 = 0 
% y-axis: -7.84958706-.500000000*alpha2z-.327326835*aC23 = 0 
% =>
% alpha2z =  -16.7458 (rad/s^2)
% aC23 =  1.59873 (m/s^2)
% alpha2 = [ 0, 0, -16.7458 ] (rad/s^2)
% aC2C3 = [ 1.51065, 0.523306, 0 ] (m/s^2)
% aD2 =  [ -1.34318, 9.05135, 0] (m/s^2)
% aD54cor =  [ 2.53037, -1.84656, 0 ] (m/s^2)
% aD5 = aE + alpha5 x rED - (omega4.omega4)rED (aE=0) 
% aD5 = aD4 + aD54 + aD54cor (aD4=aD2)  
% x-axis: .404121755*alpha5z-.280187945-.589484100*aD54 = 0 
% y-axis: -.294911183*alpha5z-5.96191614-.807779980*aD54 = 0 
% =>
% alpha5z =  -6.57248 (rad/s^2)
% aD54 =  -4.98108 (m/s^2)
% alpha5 = [ 0, 0, -6.57248 ] (rad/s^2)
% aD5D4 = [ -2.93627, -4.02362, -0 ] (m/s^2)
% aF =  [ -2.09769, 3.81522, 0] (m/s^2)
% alpha1 = [ 0, 0, 0 ] (rad/s^2)
% alpha2 = alpha3 = [ 0, 0, -16.7458 ] (rad/s^2)
% alpha4 = alpha5 = [ 0, 0, -6.57248 ] (rad/s^2)
% aC1 = [ 1.97392, -3.41893, 0 ] (m/s^2)
% aC2 = [ 1.30233, 1.10674, 0 ] (m/s^2)
% aC3 = [ 0, 0, 0 ] (m/s^2)
% aC4 = aD4 = aD2 = [ -1.34318, 9.05135, 0 ] (m/s^2)
% aC5 = [ -1.04885, 1.90761, 0 ] (m/s^2)
% external moment Me = [ 0, 0, 900 ] (N m)
% Dynamic force analysis  
% Newton-Euler method  
%  link 1 
% m1 = 0.016 (kg)
% IC1 = 5.34667e-05 (kg m^2)
% G1 = [ 0, -0.156912, 0 ] (N)
% m1*aC1 = [ 0.0315827, -0.0547029, 0 ] (N)
% IC1*alpha1 = [ 0, 0, 0 ] (N m)
%  link 2 
% m2 = 0.08 (kg)
% IC2 = 0.00666733 (kg m^2)
% G2 = [ 0, -0.78456, 0 ] (N)
% m1*aC2 = [ 0.104187, 0.0885394, 0 ] (N)
% IC2*alpha2 = [ 0, 0, -1.116497e-01 ] (N m)
%  link 3 
% m3 = 0.008 (kg)
% IC3 = 1.93333e-06 (kg m^2)
% G3 = [ 0, -0.078456, 0 ] (N)
% m3*aC3 = [ 0, 0, 0 ] (N)
% IC3*alpha3 = [ 0, 0, -3.237519e-05 ] (N m)
%  link 4 
% m4 = 0.008 (kg)
% IC4 = 1.93333e-06 (kg m^2)
% G4 = [ 0, -0.078456, 0 ] (N)
% m4*aC4 = [ -0.0107454, 0.0724108, 0 ] (N)
% IC4*alpha4 = [ 0, 0, -1.270679e-05 ] (N m)
%  link 5  
% m5 =  0.048 (kg)
% IC5 =  0.0014404 (kg m^2)
% G5 = - m5 g = [ 0, -0.470736, 0] (N)
% m5*aC5 = [ -0.0503447, 0.0915653, 0] (N)
% IC5*alpha5 = [ 0, 0, -0.009467] (N m)
% Joint reactions and equilibrium moment 
% eom links 4 and 5 dyad RTR 
% F05x+F24x+.610900996e-1 = 0 (1)
% F05y+F24y-.713168039 = 0 (2)
% 900.169955-.294911183*F24y+.404121755*F24x = 0 (3)
% .294911183*F24x-.577996019e-1+.404121755*F24y = 0 (4)
% Eqs(1)-(4) => F05x, F05y, F24x, F24y 
% F05 = [ 1453.32, -1060.04, 0] (N)
% F24 = [ -1453.38, 1060.76, 0] (N)
% F45 = [ -1453.37, 1060.61, 0] (N)
% verify: F45 perp to DE   F45.ED = 5.68434e-14 
% -.294911183*yP+.376819112+.404121755*xP = 0 (5)
% -.294911183*yP+.376819112+.404121755*xP = 0 (6)
% Eqs(5)-(6) => xP, yP 
% rP = [ -1.04491, -0.154122, 0] (m)
% rP - rD = [ 4.16319e-09, 5.70489e-09, 0] (m)
% because 
% -IC4*alpha4(3) =  1.27068e-05 is a very small number
% eom links 2 and 3 dyad RTR 
% F12x+1453.27221+F03x = 0 (7)
% F12y-1061.70799+F03y = 0 (8)
% 696.027948+.500000000*F12y-.173205081*F12x = 0 (9)
% -.500000000*F12x-542.756477-.173205081*F12y = 0 (10)
% Eqs(7)-(10) => F03x, F03y, F12x, F12y 
% F03 = [ -914.62, 2640.36, 0] (N)
% F12 = [ -538.652, -1578.65, 0] (N)
% F32 = [ -914.62, 2640.28, 0] (N)
% verify: F32 perp to BC   F32.BC = -1.13687e-13 
% -.500000000*yQ+.173205081*xQ+.103923049 = 0 (11)
% -2640.28008*xQ-1584.16802-914.619850*yQ = 0 (12)
% Eqs(11)-(12) => xQ, yQ 
% rQ = [ -0.6, 3.79258e-09, 0] (m)
% rQ - rC = [ 1.09482e-08, 3.79258e-09, 0] (m)
% because
% -IC2*alpha2(3) = 3.23752e-05 is a very small number 
% Link 1 
% F01 = [ -538.621, -1578.55, 0] (N)
% Mm = [ 0, 0, 251.155] (N m)
%
%
%
% %%%%%%%%%%%%
% Problem 6.4
% %%%%%%%%%%%%
% Results 
% rA =  [ 0, 0, 0 ] (m)
% rD =  [ -0.554223, -0.0964704, 0 ] (m)
% rB =  [ -0.075, 0.129904, 0 ] (m)
% rC =  [ -0.35, 0, 0 ] (m)
% rE =  [ -0.482421, 0.19481, 0 ] (m)
% rF =  [ -0.295, 0.125, 0 ] (m)
% phi2 = phi3 = 25.285 (degrees) 
% phi4 = 76.1523 (degrees) 
% phi5 = -20.4293 (degrees) 
% rC1 = [ -0.0375, 0.0649519, 0 ] (m)
% rC2 = [ -0.314612, 0.0167167, 0 ] (m)
% rC3 = [ -0.35, 0, 0 ] (m)
% rC4 = [ -0.518322, 0.04917, 0 ] (m)
% rC5 = [ -0.38871, 0.159905, 0 ] (m)
% Velocity and acceleration analysis 
% omega1 =  [ 0, 0, 3.14159 ] (rad/s)
% alpha1 =  [ 0, 0, 0 ] (rad/s^2)
% vB = vB1 = vB2 =  [ -0.408105, -0.235619, 0 ] (m/s)
% aB = aB1 = aB2 =  [ 0.74022, -1.2821, 0 ] (m/s^2)
% vC2 = vB + omega2 x rBC = vC3 + vC23 (vC3=0)  => 
% x-axis: -.408104857+.129903811*omega2z-.904194432*vC23 = 0 
% y-axis: -.235619449-.275000000*omega2z-.427121100*vC23 = 0 
% =>
% omega2z =  -0.127362 (rad/s)
% vC23 =  -0.469644 (m/s)
% omega2 = omega3 = [ 0, 0, -0.127362 ] (rad/s)
% vC2C3 = [ -0.42465, -0.200595, 0 ] (m/s)
% vD2 =  [ -0.436936, -0.174585, 0 ] (m/s)
% vE = vD + omega4 x rDE = vF + omega5 x rFE (vF=0) => 
% x-axis: -.436936295-.291280663*omega4z+.698102914e-1*omega5z = 0 
% y-axis: -.174584708+.718023362e-1*omega4z+.187420712*omega5z = 0 
% =>
% omega4z =  -1.16943 (rad/s)
% omega5z =  1.37953 (rad/s)
% omega4 = [ 0, 0, -1.16943 ] (rad/s)
% omega5 = [ 0, 0, 1.37953 ] (rad/s)
% vE =  [ -0.0963053, -0.258552, 0 ] (m/s)
% aC23cor =  [ -0.0510963, 0.108168, 0 ] (m/s^2)
% aC2 = aB + alpha2 x rBC - (omega2.omega2)rBC 
% aC2 = aC3 + aC23 + aC23cor (aC3=0)  
% x-axis: .795777407+.129903811*alpha2z-.904194432*aC23 = 0 
% y-axis: -1.38816039-.275000000*alpha2z-.427121100*aC23 = 0 
% =>
% alpha2z =  -5.24453 (rad/s^2)
% aC23 =  0.126625 (m/s^2)
% alpha2 = [ 0, 0, -5.24453 ] (rad/s^2)
% aC2C3 = [ 0.114494, 0.0540842, 0 ] (m/s^2)
% aD =  [ -0.439231, 1.23487, 0] (m/s^2)
% aE = aD + alpha4 x rDE - (omega4.omega4)rDE 
% aE = aF + alpha5 x rFE - (omega5.omega5)rFE  
% x-axis: -.894105159-.291280663*alpha4z+.698102914e-1*alpha5z = 0 
% y-axis: .969383660+.718023362e-1*alpha4z+.187420712*alpha5z = 0 
% =>
% alpha4z =  -3.94679 (rad/s^2)
% alpha5z =  -3.66019 (rad/s^2)
% alpha4 = [ 0, 0, -3.94679 ] (rad/s^2)
% alpha5 = [ 0, 0, -3.66019 ] (rad/s^2)
% aE =  [ 0.612199, 0.553139, 0] (m/s^2)
% alpha1 = [ 0, 0, 0 ] (rad/s^2)
% alpha2 = alpha3 = [ 0, 0, -5.24453 ] (rad/s^2)
% alpha4 = [ 0, 0, -3.94679 ] (rad/s^2)
% alpha5 = [ 0, 0, -3.66019 ] (rad/s^2)
% aC1 = [ 0.37011, -0.64105, 0 ] (m/s^2)
% aC2 = [ 0.150494, -0.0236144, 0 ] (m/s^2)
% aC3 = [ 0, 0, 0 ] (m/s^2)
% aC4 = aD4 = aD2 = [ 0.0864837, 0.894005, 0 ] (m/s^2)
% aC5 = [ 0.306099, 0.276569, 0 ] (m/s^2)
% external moment Me = [ 0, 0, -1500 ] (N m)
% Dynamic force analysis  
% Newton-Euler method  
%  link 1 
% m1 = 0.012 (kg)
% IC1 = 2.26e-05 (kg m^2)
% G1 = [ 0, -0.117684, 0 ] (N)
% m1*aC1 = [ 0.00444132, -0.0076926, 0 ] (N)
% IC1*alpha1 = [ 0, 0, 0 ] (N m)
%  link 2 
% m2 = 0.0424 (kg)
% IC2 = 0.000992867 (kg m^2)
% G2 = [ 0, -0.415817, 0 ] (N)
% m1*aC2 = [ 0.00638097, -0.00100125, 0 ] (N)
% IC2*alpha2 = [ 0, 0, -5.207115e-03 ] (N m)
%  link 3 
% m3 = 0.008 (kg)
% IC3 = 1.93333e-06 (kg m^2)
% G3 = [ 0, -0.078456, 0 ] (N)
% m3*aC3 = [ 0, 0, 0 ] (N)
% IC3*alpha3 = [ 0, 0, -1.013942e-05 ] (N m)
%  link 4 
% m4 = 0.024 (kg)
% IC4 = 0.0001802 (kg m^2)
% G4 = [ 0, -0.235368, 0 ] (N)
% m4*aC4 = [ 0.00207561, 0.0214561, 0 ] (N)
% IC4*alpha4 = [ 0, 0, -7.112117e-04 ] (N m)
%  link 5  
% m5 =  0.016 (kg)
% IC5 =  5.34667e-05 (kg m^2)
% G5 = - m5 g = [ 0, -0.156912, 0] (N)
% m5*aC5 = [ 0.00489759, 0.00442511, 0] (N)
% IC5*alpha5 = [ 0, 0, -0.000195698] (N m)
%
%
%
%%%%%%%%%%%%%%
% Problem 6.5
%%%%%%%%%%%%%%
% Results      
% phi = phi1 = 60 (degrees) 
% Position analysis 
% rA = [ 0, 0, 0 ] (m)
% rC = [ -0.3, 0, 0 ] (m)
% rB = [ 0.1, 0.173205, 0] (m)
% rD = [ -0.758831, -0.19868, 0 ] (m)
% phi2 = phi3 = 23.4132 (degrees) 
% rE = [ -0.7, 0.0442993, 0 ] (m)
% phi4 = 76.3892 (degrees) 
% rF = [ 0.158831, 0.19868, 0 ] (m)
% rC1 = [ 0.05, 0.0866025, 0 ] (m)
% rC2 = rB = [ 0.1, 0.173205, 0 ] (m)
% rC3 = [ -0.3, 1.38778e-17, 0 ] (m)
% rC4 = [ -0.729416, -0.0771903, 0 ] (m)
% rC5 = [ -0.7, 0.0442993, 0 ] (m)
% Velocity and acceleration analysis 
% vB1 = vB2 = [ -0.72552, 0.418879, 0 ] (m/s)
% aB1 = aB2 = [ -1.7546, -3.03905, 0 ] (m/s^2)
% vB32 =  0.499337 (m/s)
% omega2 = omega2 = [ 0, 0, 1.54324 ] (rad/s)
% vB3B2 = [ 0.458223, 0.198416, 0 ] (m/s)
% vD3 = vD4 = [ 0.30661, -0.708086, 0 ] (m/s)
% aB32 =  1.77962 (m/s^2)
% alpha2 = alpha3 =  [ 0, 0, -1.26276 ] (rad/s^2)
% aD3 = aD4 = [ 0.841861, 1.05257, 0 ] (m/s^2)
% omega4 = [ 0, 0, 1.26188 ] (rad/s)
% vE = [ 0, -0.633848, 0 ] (m/s)
% alpha4 =  [ 0, 0, 3.0792 ] (rad/s^2)
% aE = [ 0, 0.846817, 0 ] (m/s^2)
% aC1 = aB/2 = [ -0.877298, -1.51953, 0 ] (m/s^2)
% aC2 = aB = [ -1.7546, -3.03905, 0 ] (m/s^2)
% aC3 = [ -2.46885e-16, -1.73246e-16, 0 ] (m/s^2)
% aC4 = [ 0.42093, 0.949693, 0 ] (m/s^2)
% aC5 = aE = [ 0, 0.846817, 0 ] (m/s^2)
% Dynamic force analysis  
% Newton-Euler method  
% Fe = [ 0, 1000, 0] (N)
% Inertia forces and inertia moments  
% Link 1  
% m1 =  0.016 (kg)
% m1 aC1 = [ -0.0140368, -0.0243124, 0] (N)
% Fin1 = - m1 aC1 = [ 0.0140368, 0.0243124, 0] (N)
% G1 = - m1 g = [ 0, -0.156912, 0] (N)
% IC1 =  5.34667e-05 (kg m^2)
% IC1 alpha1 = [ 0, 0, 0] (N m)
% Min1 = - IC1 alpha1 = [ 0, 0, 0] (N m)
% Link 2  
% m2 =  0.008 (kg)
% m2 aC2 = [ -0.0140368, -0.0243124, 0] (N)
% Fin2 = - m2 aC2 = [ 0.0140368, 0.0243124, 0] (N)
% G2 = - m2 g = [ 0, -0.078456, 0] (N)
% IC2 =  1.93333e-06 (kg m^2)
% IC2 alpha2 = [ 0, 0, -2.44134e-06] (N m)
% Min2 = - IC2 alpha2 = [ 0, 0, 2.44134e-06] (N m)
% Link 3  
% m3 =  0.08 (kg)
% m3 aC3 = [ -1.97508e-17, -1.38597e-17, 0] (N)
% Fin3 = - m3 aC3 = [ 1.97508e-17, 1.38597e-17, 0] (N)
% G3 = - m3 g = [ 0, -0.78456, 0] (N)
% IC3 =  0.00666733 (kg m^2)
% IC3 alpha3 = [ 0, 0, -0.00841926] (N m)
% Min3 = - IC3 alpha3 = [ 0, 0, 0.00841926] (N m)
% Link 4  
% m4 =  0.02 (kg)
% m4 aC4 = [ 0.00841861, 0.0189939, 0] (N)
% Fin4 = - m4 aC4 = [ -0.00841861, -0.0189939, 0] (N)
% G4 = - m4 g = [ 0, -0.19614, 0] (N)
% IC4 =  0.000104333 (kg m^2)
% IC4 alpha4 = [ 0, 0, 0.000321263] (N m)
% Min4 = - IC4 alpha4 = [ 0, 0, -0.000321263] (N m)
% Link 5  
% m5 =  0.008 (kg)
% m5 aC5 = [ 0, 0.00677453, 0] (N)
% Fin5 = - m5 aC5 = [ 0, -0.00677453, 0] (N)
% G5 = - m5 g = [ 0, -0.078456, 0] (N)
% IC5 =  1.93333e-06 (kg m^2)
% IC5 alpha5 = [ 0, 0, 0] (N m)
% Min5 = - IC5 alpha5 = [ 0, 0, 0] (N m)
% Joint reactions and equilibrium moment 
% eom link 5 
% F05x+F45x = 0 (1)
% F45y+999.914769 = 0 (2)
% eom link 4 
% F34x-1.*F45x-.841860568e-2 = 0 (3)
% F34y-1.*F45y-.215133852 = 0 (4)
% -.294157339e-1*F45y+.121489566*F45x-.294157339e-1*F34y+.121489566*F34x-.321262996e-3 = 0 (5)
% Eqs(1)-(8) => F05x, F45x, F45y, F34x, F34y 
% F05 = [ 242.082, 0, 0] (N)
% F45 = [ -242.082, -999.915, 0] (N)
% F34 = [ -242.073, -999.7, 0] (N)
% eom ink 3 
% .400000000*yQ-.173205081*xQ-.519615243e-1 = 0 (6)
% .400000000*F23x+.173205081*F23y = 0 (7)
% 242.073386+F03x+F23x = 0 (8)
% 998.915076+F03y+F23y = 0 (9)
% -410.590127-.111022302e-15*F03y+.138777878e-16*F03x+(xQ+.300000000)*F23y-1.*(yQ-.138777878e-16)*F23x = 0 (10)
% eom link 2 
% -1.*F23x+F12x+.140367707e-1 = 0 (11)
% -1.*F23y+F12y-.541436000e-1 = 0 (12)
% -1.*(xQ-.100000000)*F23y+(yQ-.173205081)*F23x+.244134211e-5 = 0 (13)
% Eqs(6)-(13) => F03x, F03y, F23x, F23y, F12x, F12y, xQ, yQ 
% F03 = [ 132.223, -1863.32, 0] (N)
% F23 = [ -374.296, 864.4, 0] (N)
% F12 = [ -374.31, 864.454, 0] (N)
% rP = [ 0.1, 0.173205, 0] (m)
% eom link 1 
% F01 = [ -374.324, 864.587, 0] (N)
% Mm = [ 0, 0, 151.286] (N m)
%
%
%
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% Problem 6.6
%%%%%%%%%%%%%%
% Results
% phi = phi1 = 60 (degrees) 
% Position analysis 
% rA = [ 0, 0, 0 ] (m)
% rC = [ 0, 0.09, 0 ] (m)
% rB = [ 0.09, 0.155885, 0] (m)
% rD = [ -0.16138, -0.0281381, 0 ] (m)
% rF = [ 0.16138, 0.208138, 0 ] (m)
% rG = [ -0.28569, -0.0498128, 0 ]  (m)
% phi2 = phi3 = 36.206 (degrees) 
% phi4 = phi5 = 189.891 (degrees) 
% rC1 = [ 0.045, 0.0779423, 0 ] (m)
% rC2 = rB = [ 0.09, 0.155885, 0 ] (m)
% rC3 = [ 0, 0.09, 0 ] (m)
% rC4 = rD = [ -0.16138, -0.0281381, 0 ] (m)
% rC5 = [ -0.142845, -0.0249064, 0 ] (m)
% Velocity and acceleration analysis 
% vB1 = vB2 = [ -2.93835, 1.69646, 0 ] (m/s)
% aB1 = aB2 = [ -31.9775, -55.3867, 0 ] (m/s^2)
% vB32 =  1.36887 (m/s)
% omega2 = omega2 = [ 0, 0, 27.8338 ] (rad/s)
% vB3B2 = [ 1.10454, 0.808579, 0 ] (m/s)
% vD3 = vD4 = [ 3.28823, -4.4918, 0 ] (m/s)
% aB32 =  -27.8917 (m/s^2)
% alpha2 = alpha3 =  [ 0, 0, 451.854 ] (rad/s^2)
% aD3 = aD4 = [ 178.405, 18.6037, 0 ] (m/s^2)
% vD54 =  2.46781 (m/s)
% omega4 = omega5 = [ 0, 0, 30.4604 ] (rad/s)
% vD5D4 = [ -2.43113, -0.423891, 0 ] (m/s)
% aD54 =  26.9558 (m/s^2)
% alpha4 = alpha5 =  [ 0, 0, 992.942 ] (rad/s^2)
% aC1 = aB/2 = [ -15.9888, -27.6933, 0 ] (m/s^2)
% aC2 = aB = [ -31.9775, -55.3867, 0 ] (m/s^2)
% aC3 = aC = [ 0, 0, 0 ] (m/s^2)
% aC4 = aD4 = [ 178.405, 18.6037, 0 ] (m/s^2)
% aC5 = [ 157.268, -118.728, 0 ] (m/s^2)
% Dynamic force analysis  
% Newton-Euler method  
% Me = [ 0, 0, -1500] (N m)
% Inertia forces and inertia moments  
% Link 1  
% m1 =  0.0144 (kg)
% m1 aC1 = [ -0.230238, -0.398784, 0] (N)
% Fin1 = - m1 aC1 = [ 0.230238, 0.398784, 0] (N)
% G1 = - m1 g = [ 0, -0.141221, 0] (N)
% IC1 =  3.9e-05 (kg m^2)
% IC1 alpha1 = [ 0, 0, 0] (N m)
% Min1 = - IC1 alpha1 = [ 0, 0, 0] (N m)
% Link 2  
% m2 =  0.008 (kg)
% m2 aC2 = [ -0.25582, -0.443093, 0] (N)
% Fin2 = - m2 aC2 = [ 0.25582, 0.443093, 0] (N)
% G2 = - m2 g = [ 0, -0.078456, 0] (N)
% IC2 =  1.93333e-06 (kg m^2)
% IC2 alpha2 = [ 0, 0, 0.000873585] (N m)
% Min2 = - IC2 alpha2 = [ 0, 0, -0.000873585] (N m)
% Link 3  
% m3 =  0.032 (kg)
% m3 aC3 = [ 0, 0, 0] (N)
% Fin3 = - m3 aC3 = [ -0, -0, 0] (N)
% G3 = - m3 g = [ 0, -0.313824, 0] (N)
% IC3 =  0.000426933 (kg m^2)
% IC3 alpha3 = [ 0, 0, 0.192912] (N m)
% Min3 = - IC3 alpha3 = [ 0, 0, -0.192912] (N m)
% Link 4  
% m4 =  0.008 (kg)
% m4 aC4 = [ 1.42724, 0.148829, 0] (N)
% Fin4 = - m4 aC4 = [ -1.42724, -0.148829, 0] (N)
% G4 = - m4 g = [ 0, -0.078456, 0] (N)
% IC4 =  1.93333e-06 (kg m^2)
% IC4 alpha4 = [ 0, 0, 0.00191969] (N m)
% Min4 = - IC4 alpha4 = [ 0, 0, -0.00191969] (N m)
% Link 5  
% m5 =  0.0232 (kg)
% m5 aC5 = [ 3.64861, -2.75448, 0] (N)
% Fin5 = - m5 aC5 = [ -3.64861, 2.75448, 0] (N)
% G5 = - m5 g = [ 0, -0.227522, 0] (N)
% IC5 =  0.000162787 (kg m^2)
% IC5 alpha5 = [ 0, 0, 0.161638] (N m)
% Min5 = - IC5 alpha5 = [ 0, 0, -0.161638] (N m)