ex_cont.nb

# ex_cont.nb - ex_cont.nb 1 " DYNAMIC FORCE ANALYSIS VIA...

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" DYNAMIC FORCE ANALYSIS VIA CONTOUR METHOD " Apply [Clear, Names["Global`*"] ] ; Off[General::spell]; Off[General::spell1]; (* Input data *) n = 50 ; (* rpm *) omega = n N[Pi]/30 ; (* rad/s *) rule = {AB->0.14, AC->0.06, AE->0.25, CD->0.15, FD->0.4, EG->0.5, h->0.01, d->0.001, hSlider->0.02, wSlider->0.05, rho->8000, g->9.807, Me->-100., phi[t]->N[Pi]/6, phi'[t]- >omega, phi''[t]->0} ; (* Position analysis *) (* Position of joint A *) xA = yA = 0; rA = { xA, yA, 0}; Print["rA = ", rA, " [m]"] ; (* Position of joint C *) xC = 0 ; yC = AC ; rC = { xC, yC, 0} ; Print["rC = AC = ", rC/.rule, " [m]"] ; (* Position of joint E *) xE = 0 ; yE = -AE ; rE = { xE, yE, 0}; Print["rE = AE = ", rE/.rule, " [m]"] ; (* Position, velocity and acceleration of joint B *) xB = AB Cos [ phi[t] ] ; yB = AB Sin [ phi[t] ] ; rB = { xB, yB, 0} ; Print["rB = AB = ", rB/.rule, " [m]"] ; vB = D[rB,t] ; aB = D[D[rB,t],t] ; (* Position, velocity and acceleration of joint D *) (* Parameters m and n of line BC: y = m x + n *) mBC = ( yB - yC ) / ( xB - xC ) ; nBC = yB - mBC xB ; eqn41 = ( xDsol - xC )^2 + ( yDsol - yC )^2 - CD^2 == 0 ; eqn42 = yDsol - mBC xDsol - nBC == 0 ; solutionD = Solve [ { eqn41 , eqn42 } , { xDsol , yDsol } ]; (* Two solutions for D *) xD1 = xDsol /. solutionD[[1]]; yD1 = yDsol /. solutionD[[1]]; xD2 = xDsol /. solutionD[[2]]; yD2 = yDsol /. solutionD[[2]]; (* Select the correct position for D *) If[ (xD1/.rule)<=xC, xD=xD1; yD=yD1, xD=xD2; yD=yD2 ] ; rD = { xD, yD, 0} ; Print["rD = AD =", rD/.rule, " [m]"] ; vD = D[rD,t] ; aD = D[D[rD,t],t] ; ex_cont.nb 1

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(* Angular velocity and acceleration of the link 1 *) alpha1 = {0, 0, phi''[t]} ; (* Angular velocity and acceleration of the link 2 and link 3 *) phi2 = ArcTan[ mBC ] ; alpha2 = {0, 0, D[D[phi2,t],t]} ; phi3 = phi2 ; alpha3 = alpha2 ; (* Angular velocity and acceleration of the link 4 and link 5 *) phi4 = ArcTan[(yD-yE)/(xD-xE)] + N[Pi] ; alpha4 = {0, 0, D[D[phi4,t],t]} ; phi5 = phi4 ; alpha5 = alpha4 ; (* -------------------------- *) (* Inertia forces and moments *) (* -------------------------- *) (* Link 1 *) m1 = rho AB h d /.rule ; rC1 = rB/2 ; Print["rC1 = AC1 =", rC1/.rule, " [m]"] ; vC1 = vB/2 ; aC1 = aB/2 ; Fin1 = - m1 aC1 /.rule ; G1 = {0, -m1*g, 0} /.rule ; F1 = ( Fin1 + G1 ) /.rule ; IC1 = m1 (AB^2+h^2)/12 /.rule ; M1 = Min1 = - IC1 alpha1 /.rule ; Print["F1 = ", F1, " [N]"] ; Print["M1 = ", M1, " [Nm]"] ; (* Link 2 *) m2 = rho hSlider wSlider d /.rule ; rC2 = rB ; Print["rC2 = AC2 = AB = ", rC2/.rule, " [m]"] ; vC2 = vB ; aC2 = aB ; Fin2 = - m2 aC2 /.rule ; G2 = {0, -m2*g, 0} /.rule ; F2 = ( Fin2 + G2 ) /.rule ; IC2 = m2 (hSlider^2+wSlider^2)/12 /.rule ; M2 = Min2 = - IC2 alpha2 /.rule ; Print["F2 = ", F2, " [N]"] ; Print["M2 = ", M2, " [Nm]"] ; (* Link 3 *) m3 = rho FD h d /.rule ; xC3 = xC + (FD/2-CD) Cos [ phi3 ] ;
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## This note was uploaded on 08/29/2011 for the course MECH 6420 taught by Professor Marghitu during the Summer '11 term at University of Florida.

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ex_cont.nb - ex_cont.nb 1 " DYNAMIC FORCE ANALYSIS VIA...

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