def reactions(phi1,
omg1,
alp1,
ms,
Is,
M5_ext,
g=-9.807j,
AB=0.15,
AC=0.1,
CD=0.15,
DF=0.4,
AG=0.3):
rA, rB, rC, rD, rF, rG = pos(phi1, AB, AC, CD, DF, AG)
M5_ext = -np.sign(vel(phi1, omg1, AB, AC, CD, DF, AG)[-1]) * M5_ext
a2, a3_T, a5_T, a4, aF, aG, alp3, alp5 = acc(phi1, omg1, alp1, AB, AC, CD,
DF, AG)
aGs = np.array([a2 / 2, a2, (a4 + aF) / 2, a4, aG / 2])
Gs, FGs = ms * g, ms * aGs
# find F45, F05 with matrix solve AX=B
# moment equation, force equation, dot product of F45 and rD = 0
A = dA.mat([
dA.moment(rD - rG / 2),
dA.moment(rA - rG / 2), [1, 0, 1, 0], [0, 1, 0, 1],
[np.real(rD), np.imag(rD), 0, 0]
], (4, 4))
b = dA.mat([[Is[-1] * alp5 - M5_ext], kA.toList(FGs[-1] - Gs[-1]), [0]], 4)
F45, F05 = kA.toComplexes(np.linalg.solve(A, b))
# find F34
F34 = FGs[-2] - (Gs[-2] + (-F45))
# find F03, F23 with matrix solve AX=B
# moment equation, force equation, dot product of F23 and rF-rC = 0
rG3 = (rD + rF) / 2
A = dA.mat([
dA.moment(rC - rG3),
dA.moment(rB - rG3), [1, 0, 1, 0], [0, 1, 0, 1],
[0, 0, np.real(rB - rG3), np.imag(rB - rG3)]
], (4, 4))
b = dA.mat([[Is[2] * alp3 - dA.toCross(rD - rG3, -F34)],
kA.toList(FGs[2] - Gs[2] - (-F34)), [0]], 4)
F03, F23 = kA.toComplexes(np.linalg.solve(A, b))
# find F12, F01
F12 = FGs[1] - Gs[1] - (-F23)
F01 = FGs[0] - Gs[0] - (-F12)
M_eq = Is[0] * alp1 - dA.toCross(rB / 2, -F12) - dA.toCross(-rB / 2, F01)
return F05, F45, F34, F03, F23, F12, F01, M_eq
def reactions(theta1,
omg1,
alp1,
ms,
Is,
M_ext,
AB,
AD,
BC,
CD,
g=-9.807j,
variation=0):
rB, rC = pos(theta1, AB, AD, BC, CD)[variation]
aB, aC, alp2, alp3 = acc(theta1, omg1, alp1, AB, AD, BC, CD, variation)
aGs = np.array([aB / 2, (aB + aC) / 2, aC / 2])
M_ext *= -np.sign(vel(theta1, omg1, AB, AD, BC, CD, variation)[3])
Gs, FGs = ms * g, ms * aGs
# find F03, F12 using dyad method (link 2-3)
# equilibrium equations,
A = dA.mat([[1, 0, 1, 0], [0, 1, 0, 1],
dA.moment(AD - rC), [0, 0], [0, 0],
dA.moment(rB - rC)], (4, 4))
b = dA.mat([
kA.toList(FGs[1] + FGs[2] - Gs[1] - Gs[2]),
[
Is[2] * alp3 + dA.toCross((AD - rC) / 2, FGs[2] - Gs[2]) - M_ext,
Is[1] * alp2 + dA.toCross((rB - rC) / 2, FGs[1] - Gs[1])
]
], 4)
F03, F12 = kA.toComplexes(np.linalg.solve(A, b))
# find F23, F01
F23 = FGs[2] - Gs[2] - F03
F01 = FGs[0] - Gs[0] - (-F12)
# find drive moment
M_eq = Is[0] * alp1 - (dA.toCross(rB / 2, -F12) + dA.toCross(-rB / 2, F01))
return F03, F23, F12, F01, M_eq
a5_T, alp4 = kA.aCPA2(-aE, rF - rD, rF - rE, omg2=omg4, v1_T=v5_T)
aF = kA.acc(rF - rD, v_T=v5_T, a_T=a5_T)
return aB, aC, aE, aF, alp2, alp3, alp4
def reactions(phi1, case, ms, Is, F_ext, g=-9.807j):
rB, rC, rD, rE, rF = pos(phi1, case)
aB, aC, aE, aF, alp2, alp3, alp4 = acc(phi1, case)
F = F_ext * -np.sign(np.real(vel(phi1, case)[1]))
Gs, FGs = ms * g, ms * np.array(
[aB / 2, (aB + aC) / 2, (aC + aE) / 2, (aE + aF) / 2, aF])
# find F05, F34 using dyad method
A = dA.mat([[1, 0, 1, 0], [0, 1, 0, 1], [0, 0],
dA.moment(rE - rF), [1, 0, 0, 0]], (4, 4))
b = dA.mat([
kA.toList(FGs[3] + FGs[4] - Gs[3] - Gs[4] - F),
[Is[3] * alp4 + dA.toCross((rE - rF) / 2, FGs[3] - Gs[3]), 0]
], 4)
F05, F34 = kA.toComplexes(np.linalg.solve(A, b))
# find F45
F45 = FGs[4] - Gs[4] - F05 - F
# find F03, F12 using dyad method, moment at C
rG3, rG2 = (rE + rC) / 2, (rB + rC) / 2
A = dA.mat([[1, 0, 1, 0], [0, 1, 0, 1],
dA.moment(rD - rC), [0, 0], [0, 0],
dA.moment(rB - rC)], (4, 4))
b = dA.mat([
kA.toList(FGs[2] + FGs[1] - Gs[2] - Gs[1] - (-F34)),
aE = kA.acc(rE - rF, omg5, alp5)
return aB, aD, aE, alp2, alp4, alp5
def reactions(phi1, case, ms, Is, M_ext, g=-9.807j):
rB, rC, rD, rE, rF = pos(phi1, case)
aB, aD, aE, alp2, alp4, alp5 = acc(phi1, case)
M_ext *= -np.sign(vel(phi1, case)[-2])
aGs = np.array([aB / 2, (aB + aD) / 2, 0, (aE + aD) / 2, aE / 2])
Gs, FGs = ms * g, ms * aGs
# find F05, F34 using dyad method, moment at E
A = dA.mat([[1, 0, 1, 0], [0, 1, 0, 1],
dA.moment(rF - rE), [0, 0], [0, 0],
dA.moment(rD - rE)], (4, 4))
b = dA.mat([
kA.toList(FGs[3] + FGs[4] - Gs[3] - Gs[4]),
[
Is[4] * alp5 + dA.toCross((rF - rE) / 2, FGs[4] - Gs[4]) - M_ext,
Is[3] * alp4 + dA.toCross((rD - rE) / 2, FGs[3] - Gs[3])
]
], 4)
F05, F24 = kA.toComplexes(np.linalg.solve(A, b))
# find F45
F45 = FGs[4] - Gs[4] - F05
# find F03, F12 using dyad method, moment at C
rG2 = (rB + rD) / 2
a5 = kA.acc(r0F, v_T=v05, a_T=a05)
return aB, aC, aE, a5, a05, alp2, alp3, alp4
def reactions(theta1, case, ms, Is, F_ext, g=-9.807j, variation=0):
rB, rC, rD, rE, rCD, rED, r0F, rFE = pos(theta1, case)[variation]
aB, aC, aE, a5, a05, alp2, alp3, alp4 = acc(theta1, case, variation)
F = F_ext * -np.sign(vel(theta1, case, variation)[2])
aGs = np.array([aB / 2, (aB + aC) / 2, aE / 2, (aE + a5) / 2, a5])
Gs, FGs = ms * g, ms * aGs
# find F05, F34 using dyad method
A = dA.mat([[1, 0, 1, 0], [0, 1, 0, 1], [0, 0],
dA.moment(-rFE), [0, 1, 0, 0]], (4, 4))
b = dA.mat([
kA.toList(FGs[3] + FGs[4] - Gs[3] - Gs[4] - F),
[Is[3] * alp4 + dA.toCross(-rFE / 2, FGs[3] - Gs[3]), 0]
], 4)
F05, F34 = kA.toComplexes(np.linalg.solve(A, b))
# find F45
F45 = FGs[4] - Gs[4] - F05 - F_ext
# find F03, F12 using dyad method at C
rG3, rG2 = (rE + rD) / 2, (rB + rC) / 2
A = dA.mat([[1, 0, 1, 0], [0, 1, 0, 1],
dA.moment(rD - rC), [0, 0], [0, 0],
dA.moment(rB - rC)], (4, 4))
b = dA.mat([
aD_max = kA.acc(rD_max-rD, omg2, alp2, v2_T, a2_T)
return aB, aC, aE, aD_max, aC_max, alp2, a2_T
def reactions(phi1, case, ms, Is, F_ext, g=-9.807j):
rB, rC, rD, rD_max, rE, rC_max = pos(phi1, case)
aB, aC, aE, aD_max, aC_max, alp2, a2_T = acc(phi1, case)
F = F_ext*-np.sign(vel(phi1, case)[2])
aGs = np.array([aB/2, (aD_max+aC)/2, 0, aC, (aE+aC_max)/2])
Gs, FGs = ms*g, ms*aGs
# find F05, F24 using dyad method, moment at C
rG5 = (rE+rC_max)/2
A = dA.mat([[1, 0, 1, 0],
[0, 1, 0, 1],
dA.moment(rE-rC), [0, 0],
[0, 0, 1, 0]], (4, 4))
b = dA.mat([kA.toList(FGs[3]+FGs[4]-Gs[3]-Gs[4]-F),
[dA.toCross(rG5-rC, FGs[4]-Gs[4]), 0]], 4)
F05, F24 = kA.toComplexes(np.linalg.solve(A, b))
# find F45
F45 = FGs[4] - Gs[4] - F05 - F
# find F32, F12 using dyad method, moment at D
rG2 = (rC+rD_max)/2
A = dA.mat([[1, 0, 1, 0],
[0, 1, 0, 1],
kA.toList(rB-rD), [0, 0],
[0, 0], dA.moment(rB-rD)], (4, 4))
b = dA.mat([kA.toList(FGs[1]-Gs[1]-(-F24)),