# ### Gravity # Again, like springs, the force of gravity is conservative and should be applied to all bodies. To globally apply the force of gravity to all particles and bodies, you can use the special ```addforcegravity``` method, by supplying the acceleration due to gravity as a vector. This will get applied to all bodies defined in your system. # In[20]: system.addforcegravity(-g * N.y) # ## Constraints # Constraints may be defined that prevent the motion of certain elements. Try uncommenting the commented out line to see what happens. # In[21]: eq = [] # eq.append(pCtip.dot(N.y)) eq_d = [(system.derivative(item)) for item in eq] eq_dd = [(system.derivative(item)) for item in eq_d] # ## F=ma # This is where the symbolic expressions for F and ma are calculated. This must be done after all parts of the system have been defined. The ```getdynamics``` function uses Kane's method to derive the equations of motion. # In[22]: f, ma = system.getdynamics() # In[23]: f # In[24]:
pNA2 = 2 * N.x pAB2 = pNA2 + x * N.x + y * N.y vAB2 = pAB2.time_derivative(N, system) ParticleA = Particle(pAB, mA, 'ParticleA', system) ParticleB = Particle(pAB2, mA, 'ParticleB', system) system.addforce(-b * vAB, vAB) system.addforce(-b * vAB2, vAB2) system.addforcegravity(-g * N.y) v = pAB2 - pNA2 u = (v.dot(v))**.5 eq1 = [(v.dot(v)) - lA**2] eq1_dd = system.derivative(system.derivative(eq1[0])) eq = [eq1_dd] f, ma = system.getdynamics() func = system.state_space_post_invert(f, ma, eq, constants=system.constant_values) states = pynamics.integration.integrate(func, ini, t, rtol=1e-12, atol=1e-12, hmin=1e-14) points = [pNA, pAB, pNA, pNA2, pAB2]
ParticleA = Particle(system, pAB, mA, 'ParticleA') system.addforce(-b * vAB, vAB) system.addforcegravity(-g * N.y) x1 = ParticleA.pCM.dot(N.x) y1 = ParticleA.pCM.dot(N.y) KE = system.KE PE = system.getPEGravity(pNA) - system.getPESprings() v = pAB - pNA u = (v.dot(v))**.5 eq1 = [(v.dot(v)) - lA**2] eq1_d = [system.derivative(item) for item in eq1] eq1_dd = [system.derivative(system.derivative(item)) for item in eq1] eq = eq1_dd # a = [(v.dot(v)) - lA**2] #a=[1] b = [(item + abs(item)) for item in a] pynamics.tic() print('solving dynamics...') f, ma = system.getdynamics() print('creating second order function...') func = system.state_space_post_invert2(f, ma, eq1_dd, eq1_d, eq1, eq_active=b) print('integrating...') states = scipy.integrate.odeint(func, ini, t, args=(1e4, 1e2)) pynamics.toc()
pAB2=pNA2+x*N.x+y*N.y vAB2=pAB2.time_derivative(N,system) ParticleA = Particle(pAB,mA,'ParticleA',system) ParticleB = Particle(pAB2,mA,'ParticleB',system) system.addforce(-b*vAB,vAB) system.addforce(-b*vAB2,vAB2) system.addforcegravity(-g*N.y) v = pAB2-pNA2 u = (v.dot(v))**.5 eq1 = v.dot(v) - lA**2 eq1_d=system.derivative(eq1) eq1_dd=system.derivative(eq1_d) eq = [eq1_dd] constraint = AccelerationConstraint([eq1_dd]) system.add_constraint(constraint) tol = 1e-4 tinitial = 0 tfinal = 5 tstep = 1/30 t = numpy.r_[tinitial:tfinal:tstep] f,ma = system.getdynamics() func = system.state_space_post_invert(f,ma,constants=system.constant_values)
import pynamics.variable_types from pynamics.frame import Frame from pynamics.system import System import pynamics from pynamics.frame import Frame from pynamics.variable_types import Differentiable,Constant from pynamics.system import System from pynamics.body import Body from pynamics.dyadic import Dyadic from pynamics.output import Output from pynamics.particle import Particle s = System() pynamics.set_system(__name__,s) x,x_d,x_dd=pynamics.variable_types.Differentiable('x',s) q1,q1_d,q1_dd=pynamics.variable_types.Differentiable('q1',s) eq = x**2+2*x eq_d = s.derivative(eq) N = Frame('N') A = Frame('A') s.set_newtonian(N) A.rotate_fixed_axis_directed(N,[0,0,1],q1,s) p1 = 3*A.x+2*N.y v1=p1.time_derivative(N,s)
def init_system(v, drag_direction, time_step): import pynamics from pynamics.frame import Frame from pynamics.variable_types import Differentiable, Constant from pynamics.system import System from pynamics.body import Body from pynamics.dyadic import Dyadic from pynamics.output import Output, PointsOutput from pynamics.particle import Particle import pynamics.integration import logging import sympy import numpy import matplotlib.pyplot as plt from math import pi from scipy import optimize from sympy import sin import pynamics.tanh as tanh from fit_qs import exp_fit import fit_qs # time_step = tstep x = numpy.zeros((7, 1)) friction_perp = x[0] friction_par = x[1] given_b = x[2] given_k = x[3] given_k1 = x[4] given_b1 = x[4] system = System() pynamics.set_system(__name__, system) global_q = True lO = Constant(7 / 1000, 'lO', system) lA = Constant(33 / 1000, 'lA', system) lB = Constant(33 / 1000, 'lB', system) lC = Constant(33 / 1000, 'lC', system) mO = Constant(10 / 1000, 'mA', system) mA = Constant(2.89 / 1000, 'mA', system) mB = Constant(2.89 / 1000, 'mB', system) mC = Constant(2.89 / 1000, 'mC', system) k = Constant(0.209, 'k', system) k1 = Constant(0.209, 'k1', system) friction_perp = Constant(1.2, 'f_perp', system) friction_par = Constant(-0.2, 'f_par', system) b_damping = Constant(given_b, 'b_damping', system) # time_step = 1/00 if v == 0: [ t, tinitial, tfinal, tstep, qAa1, qAb1, qAc1, qAa2, qAb2, qAc2, qAa3, qAb3, qAc3, qBa1, qBb1, qBc1, qBa2, qBb2, qBc2, qBa3, qBb3, qBc3, qCa1, qCb1, qCc1, qCa2, qCb2, qCc2, qCa3, qCb3, qCc3 ] = fit_qs.fit_0_amount(time_step) elif v == 10: [ t, tinitial, tfinal, tstep, qAa1, qAb1, qAc1, qAa2, qAb2, qAc2, qAa3, qAb3, qAc3, qBa1, qBb1, qBc1, qBa2, qBb2, qBc2, qBa3, qBb3, qBc3, qCa1, qCb1, qCc1, qCa2, qCb2, qCc2, qCa3, qCb3, qCc3 ] = fit_qs.fit_10_amount(time_step) elif v == 20: [ t, tinitial, tfinal, tstep, qAa1, qAb1, qAc1, qAa2, qAb2, qAc2, qAa3, qAb3, qAc3, qBa1, qBb1, qBc1, qBa2, qBb2, qBc2, qBa3, qBb3, qBc3, qCa1, qCb1, qCc1, qCa2, qCb2, qCc2, qCa3, qCb3, qCc3 ] = fit_qs.fit_20_amount(time_step) elif v == 30: [ t, tinitial, tfinal, tstep, qAa1, qAb1, qAc1, qAa2, qAb2, qAc2, qAa3, qAb3, qAc3, qBa1, qBb1, qBc1, qBa2, qBb2, qBc2, qBa3, qBb3, qBc3, qCa1, qCb1, qCc1, qCa2, qCb2, qCc2, qCa3, qCb3, qCc3 ] = fit_qs.fit_30_amount(time_step) elif v == 40: [ t, tinitial, tfinal, tstep, qAa1, qAb1, qAc1, qAa2, qAb2, qAc2, qAa3, qAb3, qAc3, qBa1, qBb1, qBc1, qBa2, qBb2, qBc2, qBa3, qBb3, qBc3, qCa1, qCb1, qCc1, qCa2, qCb2, qCc2, qCa3, qCb3, qCc3 ] = fit_qs.fit_40_amount(time_step) elif v == 50: [ t, tinitial, tfinal, tstep, qAa1, qAb1, qAc1, qAa2, qAb2, qAc2, qAa3, qAb3, qAc3, qBa1, qBb1, qBc1, qBa2, qBb2, qBc2, qBa3, qBb3, qBc3, qCa1, qCb1, qCc1, qCa2, qCb2, qCc2, qCa3, qCb3, qCc3 ] = fit_qs.fit_50_amount(time_step) distance = 200 / 1000 nums = int(tfinal / tstep) array_num = numpy.arange(0, nums) array_num1 = numpy.repeat(array_num, nums, axis=0) array_num1.shape = (nums, nums) error_k = array_num1 / 8000 + numpy.ones((nums, nums)) fit_t = t fit_qA = exp_fit(fit_t, qAa1, qAb1, qAc1, qAa2, qAb2, qAc2, qAa3, qAb3, qAc3) fit_qB = exp_fit(fit_t, qBa1, qBb1, qBc1, qBa2, qBb2, qBc2, qBa3, qBb3, qBc3) fit_qC = exp_fit(fit_t, qCa1, qCb1, qCc1, qCa2, qCb2, qCc2, qCa3, qCb3, qCc3) fit_qAd1 = numpy.diff(fit_qA) / numpy.diff(fit_t) fit_qAd = numpy.append(fit_qAd1[0], fit_qAd1) fit_qBd1 = numpy.diff(fit_qB) / numpy.diff(fit_t) fit_qBd = numpy.append(fit_qBd1[0], fit_qBd1) fit_qCd1 = numpy.diff(fit_qC) / numpy.diff(fit_t) fit_qCd = numpy.append(fit_qCd1[0], fit_qCd1) fit_states1 = numpy.stack( (fit_qA, fit_qB, fit_qC, fit_qAd, fit_qBd, fit_qCd), axis=1) fit_states1[:, 0:3] = fit_states1[:, 0:3] - fit_states1[0, 0:3] fit_states = -drag_direction * numpy.deg2rad(fit_states1) # plt.plot(t,fit_states) if drag_direction == -1: zero_shape = fit_states.shape fit_states = numpy.zeros(zero_shape) fit_vel = drag_direction * distance / (tfinal) if qAa1 == 0: fit_vel = 0 fit_v = numpy.ones(t.shape) * fit_vel if qAa1 == 0: fit_d = numpy.ones(t.shape) * fit_vel else: fit_d = drag_direction * numpy.r_[tinitial:distance:tstep * abs(fit_vel)] preload0 = Constant(0 * pi / 180, 'preload0', system) preload1 = Constant(0 * pi / 180, 'preload1', system) preload2 = Constant(0 * pi / 180, 'preload2', system) preload3 = Constant(0 * pi / 180, 'preload3', system) Ixx_O = Constant(1, 'Ixx_O', system) Iyy_O = Constant(1, 'Iyy_O', system) Izz_O = Constant(1, 'Izz_O', system) Ixx_A = Constant(1, 'Ixx_A', system) Iyy_A = Constant(1, 'Iyy_A', system) Izz_A = Constant(1, 'Izz_A', system) Ixx_B = Constant(1, 'Ixx_B', system) Iyy_B = Constant(1, 'Iyy_B', system) Izz_B = Constant(1, 'Izz_B', system) Ixx_C = Constant(1, 'Ixx_C', system) Iyy_C = Constant(1, 'Iyy_C', system) Izz_C = Constant(1, 'Izz_C', system) y, y_d, y_dd = Differentiable('y', system) qO, qO_d, qO_dd = Differentiable('qO', system) qA, qA_d, qA_dd = Differentiable('qA', system) qB, qB_d, qB_dd = Differentiable('qB', system) qC, qC_d, qC_dd = Differentiable('qC', system) initialvalues = {} initialvalues[y] = 0 + 1e-14 initialvalues[y_d] = fit_vel + 1e-14 initialvalues[qO] = 0 + 1e-14 initialvalues[qO_d] = 0 + 1e-14 initialvalues[qA] = fit_states[0, 0] + 1e-14 initialvalues[qA_d] = fit_states[0, 3] + 1e-14 initialvalues[qB] = fit_states[0, 1] + 1e-14 initialvalues[qB_d] = fit_states[0, 4] + 1e-14 initialvalues[qC] = fit_states[0, 2] + 1e-14 initialvalues[qC_d] = fit_states[0, 5] + 1e-14 statevariables = system.get_state_variables() ini = [initialvalues[item] for item in statevariables] N = Frame('N') O = Frame('O') A = Frame('A') B = Frame('B') C = Frame('C') drag_direction = drag_direction velocity = 200 / tfinal / 1000 vSoil = drag_direction * velocity * N.y nSoil = 1 / vSoil.length() * vSoil system.set_newtonian(N) if not global_q: O.rotate_fixed_axis_directed(N, [0, 0, 1], qO, system) A.rotate_fixed_axis_directed(O, [0, 0, 1], qA, system) B.rotate_fixed_axis_directed(A, [0, 0, 1], qB, system) C.rotate_fixed_axis_directed(B, [0, 0, 1], qC, system) else: O.rotate_fixed_axis_directed(N, [0, 0, 1], qO, system) A.rotate_fixed_axis_directed(N, [0, 0, 1], qA, system) B.rotate_fixed_axis_directed(N, [0, 0, 1], qB, system) C.rotate_fixed_axis_directed(N, [0, 0, 1], qC, system) pNO = 0 * N.x + y * N.y pOA = lO * N.x + y * N.y pAB = pOA + lA * A.x pBC = pAB + lB * B.x pCtip = pBC + lC * C.x pOcm = pNO + lO / 2 * N.x pAcm = pOA + lA / 2 * A.x pBcm = pAB + lB / 2 * B.x pCcm = pBC + lC / 2 * C.x wNO = N.getw_(O) wOA = N.getw_(A) wAB = A.getw_(B) wBC = B.getw_(C) IO = Dyadic.build(O, Ixx_O, Iyy_O, Izz_O) IA = Dyadic.build(A, Ixx_A, Iyy_A, Izz_A) IB = Dyadic.build(B, Ixx_B, Iyy_B, Izz_B) IC = Dyadic.build(C, Ixx_C, Iyy_C, Izz_C) BodyO = Body('BodyO', O, pOcm, mO, IO, system) BodyA = Body('BodyA', A, pAcm, mA, IA, system) BodyB = Body('BodyB', B, pBcm, mB, IB, system) BodyC = Body('BodyC', C, pCcm, mC, IC, system) # BodyC = Particle(pCcm,mC,'ParticleC',system) vOcm = pOcm.time_derivative() vAcm = pAcm.time_derivative() vBcm = pBcm.time_derivative() vCcm = pCcm.time_derivative() system.add_spring_force1(k1 + 10000 * (qA + abs(qA)), (qA - qO - preload1) * N.z, wOA) system.add_spring_force1(k + 10000 * (qB + abs(qB)), (qB - qA - preload2) * N.z, wAB) system.add_spring_force1(k + 10000 * (qC + abs(qC)), (qC - qB - preload3) * N.z, wBC) #new Method use nJoint nvAcm = 1 / vAcm.length() * vAcm nvBcm = 1 / vBcm.length() * vBcm nvCcm = 1 / vCcm.length() * vCcm faperp = friction_perp * nvAcm.dot(A.y) * A.y fapar = friction_par * nvAcm.dot(A.x) * A.x system.addforce(-(faperp + fapar), vAcm) fbperp = friction_perp * nvBcm.dot(B.y) * B.y fbpar = friction_par * nvBcm.dot(B.x) * B.x system.addforce(-(fbperp + fbpar), vBcm) fcperp = friction_perp * nvCcm.dot(C.y) * C.y fcpar = friction_par * nvCcm.dot(C.x) * C.x system.addforce(-(fcperp + fcpar), vCcm) system.addforce(-b_damping * wOA, wOA) system.addforce(-b_damping * wAB, wAB) system.addforce(-b_damping * wBC, wBC) eq = [] eq_d = [(system.derivative(item)) for item in eq] eq_d.append(y_d - fit_vel) eq_dd = [(system.derivative(item)) for item in eq_d] f, ma = system.getdynamics() func1 = system.state_space_post_invert(f, ma, eq_dd) points = [pNO, pOA, pAB, pBC, pCtip] constants = system.constant_values return system, f, ma, func1, points, t, ini, constants, b_damping, k, k1, tstep, fit_states
import pynamics.variable_types from pynamics.frame import Frame from pynamics.system import System import pynamics from pynamics.frame import Frame from pynamics.variable_types import Differentiable,Constant from pynamics.system import System from pynamics.body import Body from pynamics.dyadic import Dyadic from pynamics.output import Output from pynamics.particle import Particle system = System() pynamics.set_system(__name__,system) x,x_d,x_dd=pynamics.variable_types.Differentiable('x',system) q1,q1_d,q1_dd=pynamics.variable_types.Differentiable('q1',system) eq = x**2+2*x eq_d = system.derivative(eq) N = Frame('N',system) A = Frame('A',system) system.set_newtonian(N) A.rotate_fixed_axis(N,[0,0,1],q1,system) p1 = 3*A.x+2*N.y v1=p1.time_derivative(N,system)
def Cal_system(initial_states, drag_direction, tinitial, tstep, tfinal, fit_vel, f1, f2): g_k, g_b_damping, g_b_damping1 = [0.30867935, 1.42946955, 1.08464536] system = System() pynamics.set_system(__name__, system) global_q = True lO = Constant(7 / 1000, 'lO', system) lA = Constant(33 / 1000, 'lA', system) lB = Constant(33 / 1000, 'lB', system) lC = Constant(33 / 1000, 'lC', system) mO = Constant(10 / 1000, 'mA', system) mA = Constant(2.89 / 1000, 'mA', system) mB = Constant(2.89 / 1000, 'mB', system) mC = Constant(2.89 / 1000, 'mC', system) k = Constant(g_k, 'k', system) k1 = Constant(0.4, 'k1', system) friction_perp = Constant(f1, 'f_perp', system) friction_par = Constant(f2, 'f_par', system) b_damping = Constant(g_b_damping, 'b_damping', system) b_damping1 = Constant(g_b_damping1, 'b_damping1', system) preload0 = Constant(0 * pi / 180, 'preload0', system) preload1 = Constant(0 * pi / 180, 'preload1', system) preload2 = Constant(0 * pi / 180, 'preload2', system) preload3 = Constant(0 * pi / 180, 'preload3', system) Ixx_O = Constant(1, 'Ixx_O', system) Iyy_O = Constant(1, 'Iyy_O', system) Izz_O = Constant(1, 'Izz_O', system) Ixx_A = Constant(1, 'Ixx_A', system) Iyy_A = Constant(1, 'Iyy_A', system) Izz_A = Constant(1, 'Izz_A', system) Ixx_B = Constant(1, 'Ixx_B', system) Iyy_B = Constant(1, 'Iyy_B', system) Izz_B = Constant(1, 'Izz_B', system) Ixx_C = Constant(1, 'Ixx_C', system) Iyy_C = Constant(1, 'Iyy_C', system) Izz_C = Constant(1, 'Izz_C', system) y, y_d, y_dd = Differentiable('y', system) qO, qO_d, qO_dd = Differentiable('qO', system) qA, qA_d, qA_dd = Differentiable('qA', system) qB, qB_d, qB_dd = Differentiable('qB', system) qC, qC_d, qC_dd = Differentiable('qC', system) fit_states = initial_states initialvalues = {} initialvalues[y] = fit_states[0] initialvalues[y_d] = fit_states[5] initialvalues[qO] = 0 initialvalues[qO_d] = 0 initialvalues[qA] = fit_states[2] initialvalues[qA_d] = fit_states[7] initialvalues[qB] = fit_states[3] initialvalues[qB_d] = fit_states[8] initialvalues[qC] = fit_states[4] initialvalues[qC_d] = fit_states[9] statevariables = system.get_state_variables() ini = [initialvalues[item] for item in statevariables] N = Frame('N') O = Frame('O') A = Frame('A') B = Frame('B') C = Frame('C') system.set_newtonian(N) if not global_q: O.rotate_fixed_axis_directed(N, [0, 0, 1], qO, system) A.rotate_fixed_axis_directed(O, [0, 0, 1], qA, system) B.rotate_fixed_axis_directed(A, [0, 0, 1], qB, system) C.rotate_fixed_axis_directed(B, [0, 0, 1], qC, system) else: O.rotate_fixed_axis_directed(N, [0, 0, 1], qO, system) A.rotate_fixed_axis_directed(N, [0, 0, 1], qA, system) B.rotate_fixed_axis_directed(N, [0, 0, 1], qB, system) C.rotate_fixed_axis_directed(N, [0, 0, 1], qC, system) pNO = 0 * N.x + y * N.y pOA = lO * N.x + y * N.y pAB = pOA + lA * A.x pBC = pAB + lB * B.x pCtip = pBC + lC * C.x pOcm = pNO + lO / 2 * N.x pAcm = pOA + lA / 2 * A.x pBcm = pAB + lB / 2 * B.x pCcm = pBC + lC / 2 * C.x wNO = N.getw_(O) wOA = N.getw_(A) wAB = A.getw_(B) wBC = B.getw_(C) IO = Dyadic.build(O, Ixx_O, Iyy_O, Izz_O) IA = Dyadic.build(A, Ixx_A, Iyy_A, Izz_A) IB = Dyadic.build(B, Ixx_B, Iyy_B, Izz_B) IC = Dyadic.build(C, Ixx_C, Iyy_C, Izz_C) BodyO = Body('BodyO', O, pOcm, mO, IO, system) BodyA = Body('BodyA', A, pAcm, mA, IA, system) BodyB = Body('BodyB', B, pBcm, mB, IB, system) BodyC = Body('BodyC', C, pCcm, mC, IC, system) # vOcm = pOcm.time_derivative() vAcm = pAcm.time_derivative() vBcm = pBcm.time_derivative() vCcm = pCcm.time_derivative() # system.add_spring_force1(k1+10000*(qA+abs(qA)),(qA-qO-preload1)*N.z,wOA) # system.add_spring_force1(k+10000*(qB+abs(qB)),(qB-qA-preload2)*N.z,wAB) # system.add_spring_force1(k+10000*(qC+abs(qC)),(qC-qB-preload3)*N.z,wBC) system.add_spring_force1(k1, (qA - qO - preload1) * N.z, wOA) system.add_spring_force1(k, (qB - qA - preload2) * N.z, wAB) system.add_spring_force1(k, (qC - qB - preload3) * N.z, wBC) #new Method use nJoint nvAcm = 1 / vAcm.length() * vAcm nvBcm = 1 / vBcm.length() * vBcm nvCcm = 1 / vCcm.length() * vCcm vSoil = drag_direction * 1 * N.y nSoil = 1 / vSoil.length() * vSoil if fit_vel == 0: vSoil = 1 * 1 * N.y nSoil = 1 / vSoil.length() * vSoil faperp = friction_perp * nSoil.dot(A.y) * A.y fapar = friction_par * nSoil.dot(A.x) * A.x system.addforce(-(faperp + fapar), vAcm) fbperp = friction_perp * nSoil.dot(B.y) * B.y fbpar = friction_par * nSoil.dot(B.x) * B.x system.addforce(-(fbperp + fbpar), vBcm) fcperp = friction_perp * nSoil.dot(C.y) * C.y fcpar = friction_par * nSoil.dot(C.x) * C.x system.addforce(-(fcperp + fcpar), vCcm) else: faperp = friction_perp * nvAcm.dot(A.y) * A.y fapar = friction_par * nvAcm.dot(A.x) * A.x system.addforce(-(faperp + fapar), vAcm) fbperp = friction_perp * nvBcm.dot(B.y) * B.y fbpar = friction_par * nvBcm.dot(B.x) * B.x system.addforce(-(fbperp + fbpar), vBcm) fcperp = friction_perp * nvCcm.dot(C.y) * C.y fcpar = friction_par * nvCcm.dot(C.x) * C.x system.addforce(-(fcperp + fcpar), vCcm) system.addforce(-b_damping1 * wOA, wOA) system.addforce(-b_damping * wAB, wAB) system.addforce(-b_damping * wBC, wBC) eq = [] eq_d = [(system.derivative(item)) for item in eq] eq_d.append(y_d - fit_vel) eq_dd = [(system.derivative(item)) for item in eq_d] f, ma = system.getdynamics() func1 = system.state_space_post_invert(f, ma, eq_dd) points = [pNO, pOA, pAB, pBC, pCtip] constants = system.constant_values states = pynamics.integration.integrate_odeint(func1, ini, t, args=({ 'constants': constants }, )) points_output = PointsOutput(points, system, constant_values=constants) y = points_output.calc(states) final = numpy.asarray(states[-1, :]) time1 = time.time() points_output.animate(fps=30, movie_name=str(time1) + 'video_1.mp4', lw=2, marker='o', color=(1, 0, 0, 1), linestyle='-') return final, states, y, system
vCM=i * M.x, aCM=i_d * M.x) #Load = Body('Load',B,pO,0,I_load,system,wNBody = wNB,alNBody = aNB) Load = Body('Load', B, pO, m, I_load, system) #T = kt*(V/R)-kv*G*qB_d T = kt * i system.addforce(T * N.z, wNA) system.addforce(-b * wNA, wNA) system.addforce(-Tl * B.z, wNB) system.addforce((V - i * R - kv * G * qB_d) * M.x, i * M.x) eq_d = [] #eq_d = [N.getw_(A).dot(N.z) - G*wB] #eq_d = [N.getw_(A).dot(N.z) - G*N.getw_(B).dot(N.z)] eq_dd = [system.derivative(item) for item in eq_d] #import sympy #ind = sympy.Matrix([wB]) #dep = sympy.Matrix([qA_d]) # #EQ = sympy.Matrix(eq_d) #A = EQ.jacobian(ind) #B = EQ.jacobian(dep) #dep2 = sympy.simplify(B.solve(-(A),method = 'LU')) f, ma = system.getdynamics() #f,ma = system.getdynamics([qB_d]) #f,ma = system.getdynamics([qA_d,wB]) #f.append(V-i*R - kv*G*qB_d) #ma.append(L*i_d )
def Cal_robot(direction, given_l, given_arm_l, omega1, t1, t2, ini_states, name1, video_on, x1, x2): system1 = System() time_a = time.time() pynamics.set_system(__name__, system1) given_k, given_b = x1 f1, f2, f3 = x2 global_q = True damping_r = 0 tinitial = 0 tfinal = (t1 - t2) / omega1 tstep = 1 / 50 t = numpy.r_[tinitial:tfinal:tstep] tol_1 = 1e-6 tol_2 = 1e-6 lO = Constant(27.5 / 1000, 'lO', system1) # given_arm_l = 65 lR = Constant(given_arm_l / 1000, 'lR', system1) # lR = Constant(40.5/1000,'lR',system11) lA = Constant(given_l / 1000, 'lA', system1) lB = Constant(given_l / 1000, 'lB', system1) lC = Constant(given_l / 1000, 'lC', system1) mO = Constant(1e0 * 154.5 / 1000, 'mO', system1) # mR = Constant(9.282/1000 ,'mR',system1) mR = Constant((1.158 + 0.1445 * given_arm_l) / 1000, 'mR', system1) mA = Constant(given_l * 2.75 * 0.14450000000000002 / 1000, 'mA', system1) mB = Constant(given_l * 2.75 * 0.14450000000000002 / 1000, 'mB', system1) mC = Constant(given_l * 2.75 * 0.14450000000000002 / 1000, 'mC', system1) k = Constant(given_k, 'k', system1) friction_perp = Constant(f1, 'f_perp', system1) friction_par = Constant(-1, 'f_par', system1) friction_arm_perp = Constant(2 + given_arm_l * f3, 'fr_perp', system1) friction_arm_par = Constant(-0.3, 'fr_par', system1) b_damping = Constant(given_b, 'b_damping', system1) preload0 = Constant(0 * pi / 180, 'preload0', system1) preload1 = Constant(0 * pi / 180, 'preload1', system1) preload2 = Constant(0 * pi / 180, 'preload2', system1) preload3 = Constant(0 * pi / 180, 'preload3', system1) Ixx_O = Constant(1, 'Ixx_O', system1) Iyy_O = Constant(1, 'Iyy_O', system1) Izz_O = Constant(1, 'Izz_O', system1) Ixx_R = Constant(1, 'Ixx_R', system1) Iyy_R = Constant(1, 'Iyy_R', system1) Izz_R = Constant(1, 'Izz_R', system1) Ixx_A = Constant(1, 'Ixx_A', system1) Iyy_A = Constant(1, 'Iyy_A', system1) Izz_A = Constant(1, 'Izz_A', system1) Ixx_B = Constant(1, 'Ixx_B', system1) Iyy_B = Constant(1, 'Iyy_B', system1) Izz_B = Constant(1, 'Izz_B', system1) Ixx_C = Constant(1, 'Ixx_C', system1) Iyy_C = Constant(1, 'Iyy_C', system1) Izz_C = Constant(1, 'Izz_C', system1) y, y_d, y_dd = Differentiable('y', system1) qO, qO_d, qO_dd = Differentiable('qO', system1) qR, qR_d, qR_dd = Differentiable('qR', system1) qA, qA_d, qA_dd = Differentiable('qA', system1) qB, qB_d, qB_dd = Differentiable('qB', system1) qC, qC_d, qC_dd = Differentiable('qC', system1) initialvalues = {} initialvalues[y] = ini_states[0] + tol_1 initialvalues[qO] = ini_states[1] + tol_1 initialvalues[qR] = ini_states[2] + tol_1 initialvalues[qA] = ini_states[3] + tol_1 initialvalues[qB] = ini_states[4] + tol_1 initialvalues[qC] = ini_states[5] + tol_1 initialvalues[y_d] = ini_states[6] + tol_1 initialvalues[qO_d] = ini_states[7] + tol_1 initialvalues[qR_d] = ini_states[8] + tol_1 initialvalues[qA_d] = ini_states[9] + tol_1 initialvalues[qB_d] = ini_states[10] + tol_1 initialvalues[qC_d] = ini_states[11] + tol_1 statevariables = system1.get_state_variables() ini = [initialvalues[item] for item in statevariables] N = Frame('N') O = Frame('O') R = Frame('R') A = Frame('A') B = Frame('B') C = Frame('C') system1.set_newtonian(N) if not global_q: O.rotate_fixed_axis_directed(N, [0, 0, 1], qO, system1) R.rotate_fixed_axis_directed(O, [0, 0, 1], qR, system1) A.rotate_fixed_axis_directed(O, [0, 0, 1], qA, system1) B.rotate_fixed_axis_directed(A, [0, 0, 1], qB, system1) C.rotate_fixed_axis_directed(B, [0, 0, 1], qC, system1) else: O.rotate_fixed_axis_directed(N, [0, 0, 1], qO, system1) R.rotate_fixed_axis_directed(N, [0, 0, 1], qR, system1) A.rotate_fixed_axis_directed(N, [0, 0, 1], qA, system1) B.rotate_fixed_axis_directed(N, [0, 0, 1], qB, system1) C.rotate_fixed_axis_directed(N, [0, 0, 1], qC, system1) pNO = 0 * N.x + y * N.y pOR = pNO + lO * N.x # pOR= pNO +lO*N.x pRA = pOR + lR * R.x pAB = pRA + lA * A.x pBC = pAB + lB * B.x pCtip = pBC + lC * C.x # pOcm=pNO +lO/2*N.x pOcm = pNO pRcm = pOR + lR / 2 * R.x pAcm = pRA + lA / 2 * A.x pBcm = pAB + lB / 2 * B.x pCcm = pBC + lC / 2 * C.x wNO = N.getw_(O) wOR = N.getw_(R) wRA = R.getw_(A) wAB = A.getw_(B) wBC = B.getw_(C) IO = Dyadic.build(O, Ixx_O, Iyy_O, Izz_O) IR = Dyadic.build(R, Ixx_R, Iyy_R, Izz_R) IA = Dyadic.build(A, Ixx_A, Iyy_A, Izz_A) IB = Dyadic.build(B, Ixx_B, Iyy_B, Izz_B) IC = Dyadic.build(C, Ixx_C, Iyy_C, Izz_C) BodyO = Body('BodyO', O, pOcm, mO, IO, system1) BodyR = Body('BodyR', R, pRcm, mR, IR, system1) BodyA = Body('BodyA', A, pAcm, mA, IA, system1) BodyB = Body('BodyB', B, pBcm, mB, IB, system1) BodyC = Body('BodyC', C, pCcm, mC, IC, system1) j_tol = 0 * pi / 180 inv_k = 1e2 alw = 1 system1.add_spring_force1( k + inv_k * (qA - qR + alw * abs(qA - qR - j_tol)), (qA - qR - preload1) * N.z, wRA) system1.add_spring_force1( k + inv_k * (qB - qA + alw * abs(qB - qA - j_tol)), (qB - qA - preload2) * N.z, wAB) system1.add_spring_force1( k + inv_k * (qC - qB + alw * abs(qC - qB - j_tol)), (qC - qB - preload3) * N.z, wBC) # system1.add_spring_force1(k,(qA-qR-preload1)*N.z,wRA) # system1.add_spring_force1(k,(qB-qA-preload2)*N.z,wAB) # system1.add_spring_force1(k,(qC-qB-preload3)*N.z,wBC) vOcm = y_d * N.y # vOcm = pOcm.time_derivative() vRcm = pRcm.time_derivative() vAcm = pAcm.time_derivative() vBcm = pBcm.time_derivative() vCcm = pCcm.time_derivative() nvRcm = 1 / (vRcm.length() + tol_1) * vRcm nvAcm = 1 / (vAcm.length() + tol_1) * vAcm nvBcm = 1 / (vBcm.length() + tol_1) * vBcm nvCcm = 1 / (vCcm.length() + tol_1) * vCcm vSoil = -direction * 1 * N.y nSoil = 1 / vSoil.length() * vSoil # reff = abs( abs(y_d+0.01)-abs(y_d-0.01))*1/0.02*9.75 # foperp = reff*nSoil foperp = f2 * nSoil system1.addforce(foperp, vOcm) # system1.addforce(9.75*1*nSoil,vOcm) # system1.addforce(9.75*1*nSoil*y_d,vOcm) # system1.addforce(-100*N.x, y_d*N.x) frperp = friction_arm_perp * nvRcm.dot(R.y) * R.y frpar = friction_arm_par * nvRcm.dot(R.x) * R.x system1.addforce(-(frperp + frpar), vRcm) faperp = friction_perp * nvAcm.dot(A.y) * A.y fapar = friction_par * nvAcm.dot(A.x) * A.x system1.addforce(-(faperp + fapar), vAcm) fbperp = friction_perp * nvBcm.dot(B.y) * B.y fbpar = friction_par * nvBcm.dot(B.x) * B.x system1.addforce(-(fbperp + fbpar), vBcm) fcperp = friction_perp * nvCcm.dot(C.y) * C.y fcpar = friction_par * nvCcm.dot(C.x) * C.x system1.addforce(-(fcperp + fcpar), vCcm) system1.addforce(-b_damping * 1 * wRA, wRA) system1.addforce(-b_damping * 1 * wAB, wAB) system1.addforce(-b_damping * 1 * wBC, wBC) eq = [] eq_d = [(system1.derivative(item)) for item in eq] eq_d.append(qR_d - omega1) # eq_dd= [(system1.derivative(item)) for item in eq_d] eq_dd = [system1.derivative(eq_d[0])] f, ma = system1.getdynamics() func1 = system1.state_space_post_invert(f, ma, eq_dd) points = [pNO, pOR, pRA, pAB, pBC, pCtip] constants = system1.constant_values states = pynamics.integration.integrate_odeint(func1, ini, t, args=({ 'constants': constants }, )) final = numpy.asarray(states[-1, :]) logger1 = logging.getLogger('pynamics.system1') logger2 = logging.getLogger('pynamics.integration') logger3 = logging.getLogger('pynamics.output') logger1.disabled = True logger2.disabled = True logger3.disabled = True points_output = PointsOutput(points, system1, constant_values=constants) y1 = points_output.calc(states) if video_on == 1: plt.figure() plt.plot(*(y1[::int(len(y1) / 20)].T) * 1000) plt.axis('equal') plt.axis('equal') plt.title("Plate Configuration vs Distance") plt.xlabel("Configuration") plt.ylabel("Distance (mm)") plt.figure() plt.plot(t, numpy.rad2deg(states[:, 2])) plt.plot(t, numpy.rad2deg(states[:, 8])) plt.legend(["qR", "qR_d"]) plt.hlines(numpy.rad2deg(t1), tinitial, tfinal) plt.hlines(numpy.rad2deg(t2), tinitial, tfinal) plt.title("Robot Arm angle and velocitues (qR and qR_d) over Time") plt.xlabel("Time (s)") plt.ylabel("Angles,Velocities (deg, deg/s)") plt.figure() q_states = numpy.c_[(states[:, 2], states[:, 3], states[:, 4], states[:, 5])] plt.plot(t, numpy.rad2deg(q_states)) plt.title("Joint Angule over Time") plt.xlabel("Time (s)") plt.ylabel("Joint Angles (deg)") plt.legend(["Arm", "Joint 1", "Joint 2", "Joint 3"]) plt.figure() qd_states = numpy.c_[(states[:, 8], states[:, 9], states[:, 10], states[:, 11])] plt.plot(t, numpy.rad2deg(qd_states)) plt.legend(["qR_d", "qA_d", "qB_d", "qC_d"]) plt.title("Joint Angular Velocities over Time") plt.xlabel("Time (s)") plt.ylabel("Joint Angular Velocities (deg/s)") plt.legend(["Arm", "Joint 1", "Joint 2", "Joint 3"]) plt.figure() plt.plot(t, states[:, 0], '--') plt.plot(t, states[:, 6]) y_d1 = states[:, 6] # force1 = abs( abs(y_d1+0.1)-abs(y_d1-0.1))*40 # plt.plot(t,force1) plt.title("Robot Distance and Velocity over time") plt.xlabel("Time (s)") plt.ylabel("Distance (mm)") plt.legend(["Distance", "Velocity of the robot"]) points_output.animate(fps=1 / tstep, movie_name=name1, lw=2, marker='o', color=(1, 0, 0, 1), linestyle='-') else: pass return final, states, y1