def pos(phi1, AB=0.15, AC=0.1, CD=0.15, DF=0.4, AG=0.3):
rA = 0
rB = kA.toExp(AB, phi1)
rC = AC * 1j
rD = rC + kA.toExp(CD, np.angle(rC - rB))
rF = rC + kA.toExp(DF - CD, np.angle(rB - rC))
rG = kA.toExp(AG, np.angle(rD))
return rA, rB, rC, rD, rF, rG
def pos(theta1, AB, AD, BC, CD):
rB = kA.toExp(AB, theta1)
rDB = AD - rB
# find angle of rCB, rDC
res1, res2 = kA.CPA4(BC, CD, rDB)
CB_angle1 = res1[0]
CB_angle2 = res2[0]
rC1 = kA.toExp(BC, CB_angle1) + rB
rC2 = kA.toExp(BC, CB_angle2) + rB
return (rB, rC1), (rB, rC2)
def pos(phi1, case):
AB, AC, BD, DE, EF, a, b = case[:-2]
rB, rC, rF = kA.toExp(AB, phi1), -AC, (a - AC) + b * 1j
# find rBD
rBD = kA.toExp(BD, np.angle(rB - rC))
rD = rB - rBD
# find rDE and rE
angle_DE = kA.CPA4(EF, DE, rD - rF)[1][1]
rDE = kA.toExp(DE, angle_DE)
rE = rD - rDE
return rB, rC, rD, rE, rF
def pos(phi1, case):
AB, AD, BC, a = case[:-2]
CD_max = np.sqrt((AB/AD*(a+AD))**2 + (a+AD)**2)
rB, rD = kA.toExp(AB, phi1), AD
rBD = rB - rD
# rCD + rBC = rBD
rCD_max, rCD = kA.toExp([CD_max, np.abs(rBD)+BC], np.angle(rBD))
rD_max = rD - (rCD_max-rCD)
rC = rD + rCD
rE = -a + np.imag(rC)*1j
rC_max = rE + a
return rB, rC, rD, rD_max, rE, rC_max
def pos(phi, AC=.15, BC=.2, AD=0.35):
rC = AC
BA1, C_angle1 = kA.CPA2(phi, BC, rC)[0]
BA2, C_angle2 = kA.CPA2(phi, BC, rC)[1]
rB1, rB2 = kA.toExp(BA1, phi), kA.toExp(BA2, phi)
rBC1, rBC2 = -kA.toExp(BC, C_angle1), -kA.toExp(BC, C_angle2)
# BA must be positive and the angle ABC has to be smaller than 90 deg
if np.abs(np.angle(rBC1) - np.angle(rB1)) < np.pi / 2 and BA1 > 0:
rB, rBC = rB1, rBC1
else:
rB, rBC = rB2, rBC2
rD = kA.toExp(AD, np.angle(rB))
return rB, rD, rBC
def pos(phi1, case):
AB, BC, CE, CD, EF, a, b, c = case[:8]
rB, rD = kA.toExp(AB, phi1), a + b*1j
# rC-rD + rB-rC = rBD
CD_angle = kA.CPA4(CD, BC, rB-rD)[0][0]
rC = rD + kA.toExp(CD, CD_angle)
rE = rC + kA.toExp(CE, np.angle(rC-rB))
# find rFA', rE-rF
res1, res2 = kA.CPA2(0, EF, rE-c*1j)
# rF1 = rD + rFD1
rF = case[7]*1j + kA.toExp(res2[0], 0)
return rB, rC, rD, rE, rF
def pos(theta1, case):
rB = kA.toExp(case[0], theta1)
rD = case[5] + case[6] * 1j
rBD = rB - rD
# rCD + rBC = rBD
CD_angle = kA.CPA4(case[2], case[1], rBD)[0][1]
rCD = kA.toExp(case[2], CD_angle)
rED = kA.toExp(case[2] + case[3], CD_angle)
rC, rE = rD + rCD, rD + rED
res1, res2 = kA.CPA2(np.pi / 2, case[4], case[7] + rD + rED)
r0F_1, rFE_1 = kA.toExp(res1[0], np.pi / 2), kA.toExp(case[4], res1[1])
r0F_2, rFE_2 = kA.toExp(res2[0], np.pi / 2), kA.toExp(case[4], res2[1])
return (rB, rC, rD, rE, rCD, rED, r0F_1, rFE_1), \
(rB, rC, rD, rE, rCD, rED, r0F_2, rFE_2)
def pos(phi1, AB=1, BC=1):
"""
Calculate displacements
"""
rB = kA.toExp(AB, phi1)
B_angle1 = kA.CPA2(0, BC, rB)[0][1]
B_angle2 = kA.CPA2(0, BC, rB)[1][1]
rBC1 = kA.toExp(BC, B_angle1)
rBC2 = kA.toExp(BC, B_angle2)
rC1 = rB - rBC1
rC2 = rB - rBC2
if AB == BC:
if np.real(rB) > 0:
return rB, rC2, rBC2
if np.real(rB) < 0:
return rB, rC1, rBC1
return (rB, rC1, rBC1), (rB, rC2, rBC2)
def vel(phi, omg1, AC=0.15, BC=0.2, AD=0.35): # AC < BC
"find rB, rC, rD"
rA, rC = 0, AC
rB, rD, rBC = pos(phi, AC, BC, AD)
"find velocities"
# find vD
vD, vB1 = kA.toVel(rD, omg1), kA.toVel(rB, omg1)
# find vB2=vB3, omg2=omg3
# vB2 = vB1 + vB2B1
# _|_BC _|_AB //AB
# omg2? known |VB2B1|?
vB2_coeff = kA.toExp(rB - rC, np.pi / 2)
# using vB2 = vB1 + vB2B1 and the fact that vB2B1 only has 2 directions:
# one moving along rBC and the other is along rCB, we get the following
# code:
omg2, vB2B1 = kA.solve_w_angle(vB1, vB2_coeff, np.angle(rB))
vB2B1 = kA.toExp(vB2B1, np.angle(rB))
vB2 = vB3 = omg2 * vB2_coeff
return vD, vB1, vB2, vB2B1, omg2
def pos(phi1, case):
AB, BC, CD, DE, EF, a, b, c = case[:8]
rB, rD = kA.toExp(AB, phi1), -a + b * 1j
rBD = rB - rD
# rCD + rBC = rBD
CD_angle = kA.CPA4(CD, BC, rBD)[0][0]
rCD = kA.toExp(CD, CD_angle)
rED = -kA.toExp(DE, np.angle(rCD))
rC, rE = rD + rCD, rD + rED
# translate the origin b+c unit along y axis, find rE'
rEc = rE - (b + c) * 1j
# find rFA', rEF
res1, res2 = kA.CPA2(np.pi, EF, rEc)
rEF, rcF = kA.toExp(EF, res2[1]), kA.toExp(res2[0], 0)
# rF1 = rD + rFD1
rF = rE - rEF
return (rB, rC, rD, rE, rF, rcF)
def acc(phi1, omg1, alp1, AC=0.15, BC=0.2, AD=0.35):
"find accelerations"
# find aD
rA, rC = 0, AC
rB, rD, rBC = pos(phi1, AC, BC, AD)
vB2B1, omg2 = vel(phi1, omg1, AC, BC, AD)[-2:]
aD = -omg1**2 * rD
# find aB1, aB2=aB3, alp2=alp3
# aB2n + aB2t = aB1 + aB2B1c + aB2B1r
# //BC _|_BC known _|_vB2B1 //AB
# known alp2? known known |aB2B1r|?
aB1 = kA.totAcc(rB, omg1, alp1)
aB2n = -omg2**2 * (rB - rC)
aB2B1c = 2 * omg2 * kA.toExp(vB2B1, np.pi / 2)
# b = [np.real(aB1 + aB2B1c - aB2n), np.imag(aB1 + aB2B1c - aB2n)]
# print(aB2B1c)
aB2t_coeff = kA.toExp(rB - rC, np.pi / 2)
# aB2B1r_angle = phi1 + np.pi/2
# # print(aB2B1r_coeff)
# for i in range(2):
# A = [[np.real(aB2t_coeff), -np.cos(aB2B1r_angle)[i]],
# [np.imag(aB2t_coeff), -np.sin(aB2B1r_angle)[i]]]
# alp2, norm_aB2B1r = np.linalg.solve(A, b)
# # aB2_check = aB1 + aB2B1c + np.exp(1j*aB2B1r_angle[i])*norm_aB2B1r
# # print(aB2, aB2_check)
# # if aB2 == aB2_check: break
# if np.abs(np.linalg.solve(A, b)[0])>10e-4:
# alp2, norm_aB2B1r = np.linalg.solve(A, b)
# # print(norm_aB2B1r)
# break
alp2, aB2B1r = kA.solve_w_angle(aB1 + aB2B1c - aB2n, aB2t_coeff,
np.angle(rB))
aB2B1r = kA.toExp(aB2B1r, np.angle(rB))
aB2 = aB2n + alp2 * aB2t_coeff
# print(aB2)
return aB1, aD, aB2, alp2
def pos(phi1, case):
rB = kA.toExp(case[0], phi1)
rD = case[5] + case[6] * 1j
# rCD + rBC = rBD
CD_angle = kA.CPA4(case[2], case[1], rB - rD)[0][0]
rC = rD + kA.toExp(case[2], CD_angle)
rE = rD + kA.toExp(case[3], np.pi + CD_angle)
res1, res2 = kA.CPA2(0, case[4], rE - rD)
rFD = kA.toExp(res2[0], 0)
rF = rD + rFD
return rB, rC, rD, rE, rF