You can view and download this file on Github: PARTS_ATEs_moving.py
#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
# This is an EXUDYN example
#
# Details: example to simulate moving ATEs of PARTS
#
# Author: Michael Pieber and Johannes Gerstmayr
# Date: 2020-01-14
#
# Copyright:This file is part of Exudyn. Exudyn is free software. You can redistribute it and/or modify it under the terms of the Exudyn license. See 'LICENSE.txt' for more details.
#
#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
import exudyn as exu
from exudyn.itemInterface import *
import numpy as np
useGraphics = True #without test
#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
#you can erase the following lines and all exudynTestGlobals related operations if this is not intended to be used as TestModel:
try: #only if called from test suite
from modelUnitTests import exudynTestGlobals #for globally storing test results
useGraphics = exudynTestGlobals.useGraphics
except:
class ExudynTestGlobals:
pass
exudynTestGlobals = ExudynTestGlobals()
#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
#plots
if useGraphics:
import matplotlib.pyplot as plt
import matplotlib.ticker as ticker
SC = exu.SystemContainer()
mbs = SC.AddSystem()
computeDynamic=True
displaySimulation=True
#Options, if False RevoluteJoint2D are used
CartesianSpringDamperActive = False
#Options for visualization
frameList = True
#Dimensions
L1 = 38e-3 #mm
L2 = 29e-3 #mm
L3 = 8e-3 #mm
L4 = 10e-3 #mm
psi = np.arctan(L3/L1) #11.9°
CE = L3/np.sin(psi) #38.8e-3 mm
## Visualization
if frameList:
fL = 0.01 #frame length
else:
fL = 0
graphicsX = {'type':'Line', 'color':[0.8,0.1,0.1,1], 'data':[0,0,0, fL,0,0]}
graphicsY = {'type':'Line', 'color':[0.1,0.8,0.1,1], 'data':[0,0,0, 0,fL,0]}
graphicsZ = {'type':'Line', 'color':[0.1,0.1,0.8,1], 'data':[0,0,0, 0,0,fL]}
frameList = [] #no frames
#frameList = [graphicsX,graphicsY,graphicsZ]
class CSixBarLinkage:
def __init__(self, name = ''):
self.name = name #needed?
## USER defined functions
def To3D(p): #convert numpy 2D vector to 3D list
return [p[0],p[1],0]
def RotZVec(angleRad,vec):
Rz=np.array([ [np.cos(angleRad),-np.sin(angleRad)],
[np.sin(angleRad), np.cos(angleRad)] ])
return np.dot(Rz,np.array(vec));
def centreM(vec1, vec2): #Centre M of a line AB
return (vec1+vec2)/2
def userLoadDriveAle(t, load): #Add drive via ALE:
if t < 1:
return [-t*0.1,t*0.1,0 ]
return [-1,1,0]
def SixBarLinkage(P00,theta,alphaMean): #compute one six-bar linkage (P00: idealized rotation point, theta: rotaton of the six-bar linkage, angleMean: angle of the six-bar linkage (alpha, beta, gamma))
#Parameters for RigidBody2D
massRigid = 1e0
inertiaRigid = 3.3e1
#Parameters for CartesianSpringDamper
if CartesianSpringDamperActive:
k=[1e6,1e6,0]
d=[1e2,1e2,0]
#define the points/coordinates one six-bar linkage
P01=[0,0]
P1=[L1,0]
P2=[L1+L2,0]
P3=[L1,L3]
P4=[L1+L2,L3]
P5=[L1+CE*np.cos(alphaMean-psi),L3+CE*np.sin(alphaMean-psi)]
P6=[L1+L2+CE*np.cos(alphaMean-psi),L3+CE*np.sin(alphaMean-psi)]
P7=[L1+CE*np.cos(alphaMean-psi)+L2*np.cos(alphaMean),L3+CE*np.sin(alphaMean-psi)+L2*np.sin(alphaMean)]
P8=[CE*np.cos(alphaMean-psi),CE*np.sin(alphaMean-psi)]
P9=[CE*np.cos(alphaMean-psi)+L2*np.cos(alphaMean),CE*np.sin(alphaMean-psi)+L2*np.sin(alphaMean)]
P10=[L1*np.cos(alphaMean),L1*np.sin(alphaMean)]
P11=[(L1+L2)*np.cos(alphaMean),(L1+L2)*np.sin(alphaMean)]
PList=[P01,P1,P2,P3,P4,P5,P6,P7,P8,P9,P10,P11]
#calculate vectors of the two long arms
P53=list(np.array(PList[3])-np.array(PList[5]))
P56=list(np.array(PList[6])-np.array(PList[5]))
P57=list(np.array(PList[7])-np.array(PList[5]))
P58=list(np.array(PList[8])-np.array(PList[5]))
#displacement and rotation of all points P01-P11
pT=[]
for x in range(len(PList)):
pT+=[list(RotZVec(theta,np.array(PList[x]))+P00)]
#calculate centrers of mass of the rigid bodies
M0=list(centreM(np.array(pT[4]), np.array(pT[3])))
M2=list(centreM(np.array(pT[6]), np.array(pT[4])))
M5=list(centreM(np.array(pT[7]), np.array(pT[9])))
M7=list(centreM(np.array(pT[9]), np.array(pT[8])))
#Draw++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
bLength = 0.5e-3 #y-dim of pendulum
graphicsCE = {'type':'Line', 'color':[0.1,0.1,0.8,1], 'data':[-CE/2,-bLength,0, CE/2,-bLength,0, CE/2,bLength,0, -CE/2,bLength,0, -CE/2,-bLength,0]}
graphicsL2 = {'type':'Line', 'color':[0.1,0.1,0.8,1], 'data':[-L2/2,-bLength,0, L2/2,-bLength,0, L2/2,bLength,0, -L2/2,bLength,0, -L2/2,-bLength,0]}
ad=list(RotZVec((alphaMean-psi),[-CE,-bLength]))
bd=list(RotZVec((alphaMean-psi),[0,-bLength]))
cd=list(RotZVec((alphaMean-psi),[0,bLength]))
dd=list(RotZVec((alphaMean-psi),[-CE,bLength]))
ed=list(RotZVec((alphaMean-psi),[-CE,-bLength]))
graphicsCE1 = {'type':'Line', 'color':[0.1,0.1,0.8,1], 'data':ad+[0]+ bd+[0]+ cd+[0]+ dd+[0]+ ed+[0]} #background
ad=list(RotZVec((alphaMean-psi),[0,-bLength]))
bd=list(RotZVec((alphaMean-psi),[L2*np.cos(psi),L2*np.sin(psi)-bLength]))
cd=list(RotZVec((alphaMean-psi),[L2*np.cos(psi),L2*np.sin(psi)+bLength]))
dd=list(RotZVec((alphaMean-psi),[0,bLength]))
ed=list(RotZVec((alphaMean-psi),[0,-bLength]))
graphicsL21 = {'type':'Line', 'color':[0.1,0.1,0.8,1], 'data':ad+[0]+ bd+[0]+ cd+[0]+ dd+[0]+ ed+[0]} #background
ad=list(RotZVec(0,[-CE*np.cos(psi),-CE*np.sin(psi)-bLength]))
bd=list(RotZVec(0,[0,-bLength]))
cd=list(RotZVec(0,[0,bLength]))
dd=list(RotZVec(0,[-CE*np.cos(psi),-CE*np.sin(psi)+bLength]))
ed=list(RotZVec(0,[-CE*np.cos(psi),-CE*np.sin(psi)-bLength]))
graphicsCE2 = {'type':'Line', 'color':[0.1,0.1,0.8,1],'data':ad+[0]+ bd+[0]+ cd+[0]+ dd+[0]+ ed+[0]}
ad=list(RotZVec(0,[0,-bLength]))
bd=list(RotZVec(0,[L2,-bLength]))
cd=list(RotZVec(0,[L2,bLength]))
dd=list(RotZVec(0,[0,bLength]))
ed=list(RotZVec(0,[0,-bLength]))
graphicsL22 = {'type':'Line', 'color':[0.1,0.1,0.8,1], 'data':ad+[0]+ bd+[0]+ cd+[0]+ dd+[0]+ ed+[0]} #background
#Define rigid bodies and markers+++++++++++++++++++++++++++++++++++++++++++
#rigid body M0 with markers mR01,mR02
nRigid0 = mbs.AddNode(Rigid2D(referenceCoordinates=M0+[theta], initialVelocities=[0.,0.,0.]));
oRigid0 = mbs.AddObject(RigidBody2D(physicsMass=massRigid, physicsInertia=inertiaRigid,nodeNumber=nRigid0,visualization=VObjectRigidBody2D(graphicsData= [graphicsL2]+frameList)))
mR01 = mbs.AddMarker(MarkerBodyPosition(bodyNumber=oRigid0, localPosition=[-L2/2,0.,0.]))
mR02 = mbs.AddMarker(MarkerBodyPosition(bodyNumber=oRigid0, localPosition=[L2/2,0.,0.]))
#rigid body M1 with markers mR1,mR2,mR15
nRigid1 = mbs.AddNode(Rigid2D(referenceCoordinates=pT[5]+[0.+theta], initialVelocities=[0.,0.,0.]));
oRigid1 = mbs.AddObject(RigidBody2D(physicsMass=massRigid, physicsInertia=inertiaRigid,nodeNumber=nRigid1,visualization=VObjectRigidBody2D(graphicsData= [graphicsCE1,graphicsL21]+frameList)))
mR1 = mbs.AddMarker(MarkerBodyPosition(bodyNumber=oRigid1, localPosition=P53+[0.]))
mR2 = mbs.AddMarker(MarkerBodyPosition(bodyNumber=oRigid1, localPosition=P57+[0.]))
mR15 = mbs.AddMarker(MarkerBodyPosition(bodyNumber=oRigid1, localPosition=[0.,0.,0.]))
#rigid body M2 with markers mR3,mR4
nRigid2 = mbs.AddNode(Rigid2D(referenceCoordinates=M2+[alphaMean-psi+theta], initialVelocities=[0.,0.,0.]));
oRigid2 = mbs.AddObject(RigidBody2D(physicsMass=massRigid, physicsInertia=inertiaRigid,nodeNumber=nRigid2,visualization=VObjectRigidBody2D(graphicsData= [graphicsCE]+frameList)))
mR3 = mbs.AddMarker(MarkerBodyPosition(bodyNumber=oRigid2, localPosition=[-CE/2,0.,0]))
mR4 = mbs.AddMarker(MarkerBodyPosition(bodyNumber=oRigid2, localPosition=[CE/2,0.,0]))
#rigid body M5 with markers mR9,mR10
nRigid5 = mbs.AddNode(Rigid2D(referenceCoordinates=M5+[psi+theta], initialVelocities=[0.,0.,0.]));
oRigid5 = mbs.AddObject(RigidBody2D(physicsMass=massRigid, physicsInertia=inertiaRigid,nodeNumber=nRigid5,visualization=VObjectRigidBody2D(graphicsData= [graphicsCE]+frameList)))
mR9 = mbs.AddMarker(MarkerBodyPosition(bodyNumber=oRigid5, localPosition=[-CE/2,0.,0]))
mR10 = mbs.AddMarker(MarkerBodyPosition(bodyNumber=oRigid5, localPosition=[CE/2,0.,0]))
#rigid body M6 with markers mR11,mR12,mR65
nRigid6 = mbs.AddNode(Rigid2D(referenceCoordinates=pT[5]+[0.+theta], initialVelocities=[0.,0.,0.]));
oRigid6 = mbs.AddObject(RigidBody2D(physicsMass=massRigid, physicsInertia=inertiaRigid,nodeNumber=nRigid6,visualization=VObjectRigidBody2D(graphicsData= [graphicsCE2,graphicsL22]+frameList)))
mR11 = mbs.AddMarker(MarkerBodyPosition(bodyNumber=oRigid6, localPosition=P58+[0.]))
mR12 = mbs.AddMarker(MarkerBodyPosition(bodyNumber=oRigid6, localPosition=P56+[0.]))
mR65 = mbs.AddMarker(MarkerBodyPosition(bodyNumber=oRigid6, localPosition=[0.,0.,0.]))
#rigid body M7 with markers mR13,mR14
nRigid7 = mbs.AddNode(Rigid2D(referenceCoordinates=M7+[alphaMean+theta], initialVelocities=[0.,0.,0.]));
oRigid7 = mbs.AddObject(RigidBody2D(physicsMass=massRigid, physicsInertia=inertiaRigid,nodeNumber=nRigid7,visualization=VObjectRigidBody2D(graphicsData= [graphicsL2]+frameList)))
mR13 = mbs.AddMarker(MarkerBodyPosition(bodyNumber=oRigid7, localPosition=[-L2/2,0.,0.]))
mR14 = mbs.AddMarker(MarkerBodyPosition(bodyNumber=oRigid7, localPosition=[L2/2,0.,0.]))
#plug and socket for connection
mC1 = mbs.AddMarker(MarkerBodyPosition(bodyNumber=oRigid0, localPosition=[-L2/2-L4,-L3,0.]))
mC2 = mbs.AddMarker(MarkerBodyPosition(bodyNumber=oRigid7, localPosition=[-L2/2-L4,L3,0.]))
#markers for prismatic joints
mP02 = mbs.AddMarker(MarkerBodyRigid(bodyNumber=oRigid0, localPosition=[L2/2,0.,0.]))
mP14 = mbs.AddMarker(MarkerBodyRigid(bodyNumber=oRigid7, localPosition=[L2/2,0.,0.]))
#Define joints+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
if CartesianSpringDamperActive:
mbs.AddObject(CartesianSpringDamper(markerNumbers=[mR01,mR1],stiffness=k,damping=d))
mbs.AddObject(CartesianSpringDamper(markerNumbers=[mR02,mR3],stiffness=k,damping=d))
mbs.AddObject(CartesianSpringDamper(markerNumbers=[mR10,mR2],stiffness=k,damping=d))
mbs.AddObject(CartesianSpringDamper(markerNumbers=[mR14,mR9],stiffness=k,damping=d))
mbs.AddObject(CartesianSpringDamper(markerNumbers=[mR13,mR11],stiffness=k,damping=d))
mbs.AddObject(CartesianSpringDamper(markerNumbers=[mR15,mR65],stiffness=k,damping=d))
mbs.AddObject(CartesianSpringDamper(markerNumbers=[mR4,mR12],stiffness=k,damping=d))
else:
mbs.AddObject(RevoluteJoint2D(markerNumbers=[mR01,mR1]))
mbs.AddObject(RevoluteJoint2D(markerNumbers=[mR02,mR3]))
mbs.AddObject(RevoluteJoint2D(markerNumbers=[mR10,mR2]))
mbs.AddObject(RevoluteJoint2D(markerNumbers=[mR14,mR9]))
mbs.AddObject(RevoluteJoint2D(markerNumbers=[mR13,mR11]))
mbs.AddObject(RevoluteJoint2D(markerNumbers=[mR15,mR65]))
mbs.AddObject(RevoluteJoint2D(markerNumbers=[mR4,mR12]))
dictSixBarLinkages = {"markersForPrismaticJoints":[mP02,mP14],"markersForConnectors":[mC1,mC2],"markers":[mR1,mR3,mR9,mR01,mR02],"coordinatePoints":pT,"objects":[oRigid0,oRigid7],"nodes":[nRigid0,nRigid7]}
return dictSixBarLinkages
def ATC(A,B,C):
AB=(np.array(B)-np.array(A))
BC=(np.array(C)-np.array(B))
AC=(np.array(C)-np.array(A))
# offsetAngle=np.arcsin( np.dot(np.array(e1),AB)/(np.linalg.norm(np.array(e1)*np.linalg.norm(AB))))
offsetAngle=np.arctan2(AB[1],AB[0])
a=np.linalg.norm(np.array(C)-np.array(B))
b=np.linalg.norm(np.array(C)-np.array(A))
c=np.linalg.norm(np.array(B)-np.array(A))
alpha=np.arccos((np.square(b)+np.square(c)-np.square(a))/(2*b*c))
beta=np.arccos((np.square(a)+np.square(c)-np.square(b))/(2*a*c))
gamma=np.arccos((np.square(a)+np.square(b)-np.square(c))/(2*a*b))
s1=SixBarLinkage(A,offsetAngle,alpha)
s2=SixBarLinkage(B,np.pi-beta+offsetAngle,beta)
s3=SixBarLinkage(C,-(beta+gamma)+offsetAngle,gamma)
#markersForConnectors
mFC=[s1["markersForConnectors"][0],s2["markersForConnectors"][1],s2["markersForConnectors"][0],s3["markersForConnectors"][1],s3["markersForConnectors"][0],s1["markersForConnectors"][1]]
#markersForPismaticJoints
mFPJ=[s1["markersForPrismaticJoints"][0],s2["markersForPrismaticJoints"][1],s2["markersForPrismaticJoints"][0],s3["markersForPrismaticJoints"][1],s3["markersForPrismaticJoints"][0],s1["markersForPrismaticJoints"][1]]
mbs.AddObject(PrismaticJoint2D(markerNumbers=[mFPJ[0],mFPJ[1]],axisMarker0=[1.,0.,0.],normalMarker1=[0.,-1.,0.], constrainRotation=True))
mbs.AddObject(PrismaticJoint2D(markerNumbers=[mFPJ[2],mFPJ[3]],axisMarker0=[1.,0.,0.],normalMarker1=[0.,-1.,0.], constrainRotation=True))
mbs.AddObject(PrismaticJoint2D(markerNumbers=[mFPJ[5],mFPJ[4]],axisMarker0=[1.,0.,0.],normalMarker1=[0.,-1.,0.], constrainRotation=True))
La=a-2*L1-2*L2
Lb=b-2*L1-2*L2
Lc=c-2*L1-2*L2
mbs.AddObject(SpringDamper(markerNumbers = [mFPJ[0],mFPJ[1]], stiffness = 1e5, damping=10e2, referenceLength=Lc))
mbs.AddObject(SpringDamper(markerNumbers = [mFPJ[2],mFPJ[3]], stiffness = 1e5, damping=10e2, referenceLength=La))
mbs.AddObject(SpringDamper(markerNumbers = [mFPJ[4],mFPJ[5]], stiffness = 1e5, damping=10e2, referenceLength=Lb))
points=[s1["coordinatePoints"][0],s1["coordinatePoints"][3],s1["coordinatePoints"][4]]
nodes=[s1["nodes"][0],s1["nodes"][1],s2["nodes"][1],s3["nodes"][1]]
objects=[s1["objects"][0],s1["objects"][1]]
markers=[s1["markers"][0],s1["markers"][1],s1["markers"][2],s1["markers"][3],s1["markers"][4]]
dictATE = {"markersForConnectors":mFC,"markersForPrismaticJoints":mFPJ,"coordinatePoints":points,"nodes":nodes,"objects":objects,"markers":markers}
return dictATE
## START main program
#define start mesh
nx = 4
ny = 2
endTime = 0.05
###connection of ATCs
kk=[1e8,1e8,0]
dd=[1e2,1e2,0]
topCon=[]
bottomCon=[]
for y in range(ny):
for x in range(nx):
A=[0.229*(x),0.229*(y)]
B=[0.229*(x+1),0.229*(y)]
C=[0.229*(x+1),0.229*(y+1)]
D=[0.229*(x),0.229*(y+1)]
#create ATCs
n1=ATC(A,B,C)
n2=ATC(A,C,D)
#n3=ATC(C,D,E)
mbs.AddObject(CartesianSpringDamper(markerNumbers=[n1["markersForConnectors"][5],n2["markersForConnectors"][0]],stiffness=kk,damping=dd))
mbs.AddObject(CartesianSpringDamper(markerNumbers=[n1["markersForConnectors"][4],n2["markersForConnectors"][1]],stiffness=kk,damping=dd))
if x == 0 and y == 0:
nFirstATE=n1 #used only now first ATC for visualization purpose/boundary/force
if x == 0:
topCon+=[n2["markersForConnectors"][3]]
topCon+=[n2["markersForConnectors"][2]]
bottomCon+=[n1["markersForConnectors"][0]]
bottomCon+=[n1["markersForConnectors"][1]]
if x > 0 and x < nx:
c21=n2["markersForConnectors"][5]
c22=n2["markersForConnectors"][4]
mbs.AddObject(CartesianSpringDamper(markerNumbers=[c11alt,c21],stiffness=kk,damping=dd))
mbs.AddObject(CartesianSpringDamper(markerNumbers=[c12alt,c22],stiffness=kk,damping=dd))
topCon+=[n2["markersForConnectors"][3]]
topCon+=[n2["markersForConnectors"][2]]
bottomCon+=[n1["markersForConnectors"][0]]
bottomCon+=[n1["markersForConnectors"][1]]
c11alt=n1["markersForConnectors"][2]
c12alt=n1["markersForConnectors"][3]
if y > 0 and y < ny:
for i in range(len(topCon)-(nx*2)):
mbs.AddObject(CartesianSpringDamper(markerNumbers=[topCon[i],bottomCon[i+(nx*2)]],stiffness=kk,damping=dd))
n1=nFirstATE
P0=n1["coordinatePoints"][0]
#
#
###connection of ATCs
#kk=[1e4,1e4,0]
#dd=[1e2,1e2,0]
#
#mbs.AddObject(CartesianSpringDamper(markerNumbers=[n2["markersForConnectors"][0],n1["markersForConnectors"][5]],stiffness=kk,damping=dd))
#mbs.AddObject(CartesianSpringDamper(markerNumbers=[n2["markersForConnectors"][1],n1["markersForConnectors"][4]],stiffness=kk,damping=dd))
##
##loads
#mbs.AddLoad(Force(markerNumber = n1["markersForConnectors"][4], loadVector=[1e2,1e2,0]))
#Michael
#mbs.AddLoad(Force(markerNumber = topCon[15], loadVector=[1e3,-1e3,0]))
#mbs.AddLoad(Force(markerNumber = bottomCon[7], loadVector=[-1e3,-1e3,0]))
#Johannes:
def userLoad(mbs, t, loadVector):
f=0.01+0.99*(1-np.cos((t/0.05)*np.pi)) #use small initial value for solver
if t>8:
f = 1
return [f*loadVector[0], f*loadVector[1], f*loadVector[2]]
fL = 1e3*10
mbs.AddLoad(Force(markerNumber = topCon[15], loadVector=[fL,-fL,0], loadVectorUserFunction = userLoad))
mbs.AddLoad(Force(markerNumber = bottomCon[7], loadVector=[-fL,-fL,0], loadVectorUserFunction = userLoad))
#for i in range (8):
# mbs.AddLoad(Force(markerNumber = topCon[15-i], loadVector=[1e2,-1e2*0,0]))
#for i in range (8):
# mbs.AddLoad(Force(markerNumber = bottomCon[i], loadVector=[-1e2,-1e2*0,0]))
#
#
#
#mbs.AddLoad(Force(markerNumber = bottomCon[7], loadVector=[1e2,1e2,0]))
#mbs.AddLoad(Force(markerNumber = topCon[15], loadVector=[1e2,1e2,0]))
#boundaries
nGround=mbs.AddNode(PointGround(referenceCoordinates=P0+[0], visualization=VNodePointGround(show=False)))
nRidgid0=n1["nodes"][0]
##prescribe rotation of link
mCoordinateGround = mbs.AddMarker(MarkerNodeCoordinate(nodeNumber=nGround, coordinate=0)) #gives always 0 displacement
mCoordinateRigid7x = mbs.AddMarker(MarkerNodeCoordinate(nodeNumber=nRidgid0, coordinate=0)) #angle of node of Rigid7
mCoordinateRigid7y = mbs.AddMarker(MarkerNodeCoordinate(nodeNumber=nRidgid0, coordinate=1)) #angle of node of Rigid7
mCoordinateRigid7phi = mbs.AddMarker(MarkerNodeCoordinate(nodeNumber=nRidgid0, coordinate=2)) #angle of node of Rigid7
#
#
#JOH: oCoordAlphax = mbs.AddObject(CoordinateConstraint(markerNumbers=[mCoordinateGround,mCoordinateRigid7x], offset = 0))
oCoordAlphay = mbs.AddObject(CoordinateConstraint(markerNumbers=[mCoordinateGround,mCoordinateRigid7y], offset = 0))
#JOH: oCoordAlpha = mbs.AddObject(CoordinateConstraint(markerNumbers=[mCoordinateGround,mCoordinateRigid7phi], offset = 0))
nRidgid7=n1["nodes"][1]
mCoordinateRigid7x = mbs.AddMarker(MarkerNodeCoordinate(nodeNumber=nRidgid7, coordinate=0)) #angle of node of Rigid7
mCoordinateRigid7y = mbs.AddMarker(MarkerNodeCoordinate(nodeNumber=nRidgid7, coordinate=1)) #angle of node of Rigid7
mCoordinateRigid7phi = mbs.AddMarker(MarkerNodeCoordinate(nodeNumber=nRidgid7, coordinate=2)) #angle of node of Rigid7
#oCoordAlphax = mbs.AddObject(CoordinateConstraint(markerNumbers=[mCoordinateGround,mCoordinateRigid7x], offset = 0))
#JOH: oCoordAlphay = mbs.AddObject(CoordinateConstraint(markerNumbers=[mCoordinateGround,mCoordinateRigid7y], offset = 0))
#oCoordAlpha = mbs.AddObject(CoordinateConstraint(markerNumbers=[mCoordinateGround,mCoordinateRigid7phi], offset = 0))
#hack to add additional coordinate constraints:
constrainLeftSide = True
if constrainLeftSide:
nn = mbs.systemData.NumberOfNodes()
for i in range(nn):
n0 = mbs.GetNode(i)
if n0['nodeType'] == 'RigidBody2D':
if np.round(n0['referenceCoordinates'][0],3) == 0.008: #constrain all rigidbody nodes with xref=0.008
mCC = mbs.AddMarker(MarkerNodeCoordinate(nodeNumber=i, coordinate=0)) #x-displacement
mbs.AddObject(CoordinateConstraint(markerNumbers=[mCoordinateGround,mCC]))
mCC = mbs.AddMarker(MarkerNodeCoordinate(nodeNumber=i, coordinate=1)) #y-displacement
mbs.AddObject(CoordinateConstraint(markerNumbers=[mCoordinateGround,mCC]))
#mbs.AddObject(DistanceConstraint(markerNumbers=[n1["markersForPrismaticJoints"][0],n1["markersForPrismaticJoints"][1]], distance = 0.))
#mbs.AddObject(DistanceConstraint(markerNumbers=[n1["markersForPrismaticJoints"][2],n1["markersForPrismaticJoints"][3]], distance = 0.))
#mbs.AddObject(DistanceConstraint(markerNumbers=[n1["markersForPrismaticJoints"][4],n1["markersForPrismaticJoints"][5]], distance = 0.))
mbs.Assemble() #creates initial configuration
#exu.Print(mbs)
simulationSettings = exu.SimulationSettings() #takes currently set values or default values
uList=[]
phiList=[]
T=0.002
SC.visualizationSettings.connectors.defaultSize = T
SC.visualizationSettings.bodies.defaultSize = [T, T, T]
SC.visualizationSettings.nodes.defaultSize = 0.0025
SC.visualizationSettings.markers.defaultSize = 0.005
SC.visualizationSettings.loads.defaultSize = 0.005
SC.visualizationSettings.nodes.show= False
SC.visualizationSettings.markers.show= False
SC.visualizationSettings.openGL.lineWidth=2 #maximum
SC.visualizationSettings.openGL.lineSmooth=True
SC.visualizationSettings.general.drawCoordinateSystem = False
SC.visualizationSettings.window.renderWindowSize=[1600,1024]
##++++++++++++++++++++++++++++++
##ANIMATIONS
##make images for animations (requires FFMPEG):
##requires a subfolder 'images'
#simulationSettings.solutionSettings.recordImagesInterval=endTime/200
if useGraphics: #only start graphics once, but after background is set
exu.StartRenderer()
if displaySimulation:
mbs.WaitForUserToContinue()
#SC.visualizationSettings.nodes.show = False
simulationSettings.solutionSettings.solutionInformation = "PARTS_1Joint"
if computeDynamic:
simulationSettings.timeIntegration.numberOfSteps = 50
simulationSettings.timeIntegration.endTime = endTime
simulationSettings.timeIntegration.newton.relativeTolerance = 1e-8 #10000
simulationSettings.timeIntegration.newton.absoluteTolerance = 1e-8
simulationSettings.timeIntegration.verboseMode = 1
#simulationSettings.timeIntegration.verboseModeFile = 1
simulationSettings.timeIntegration.generalizedAlpha.useNewmark = True
simulationSettings.timeIntegration.generalizedAlpha.useIndex2Constraints = simulationSettings.timeIntegration.generalizedAlpha.useNewmark
simulationSettings.timeIntegration.newton.useModifiedNewton = False
simulationSettings.timeIntegration.newton.numericalDifferentiation.minimumCoordinateSize = 1
simulationSettings.timeIntegration.generalizedAlpha.spectralRadius = 0.8
simulationSettings.timeIntegration.adaptiveStep = False #disable adaptive step reduction
##############################################################
# IMPORTANT!!!!!!!!!
simulationSettings.linearSolverType = exu.LinearSolverType.EigenSparse #sparse solver !!!!!!!!!!!!!!!
##############################################################
simulationSettings.displayStatistics = True
mbs.SolveDynamic(simulationSettings)
if useGraphics: #only start graphics once, but after background is set
if displaySimulation:
SC.WaitForRenderEngineStopFlag()
exu.StopRenderer() #safely close rendering window!
nLast = mbs.systemData.NumberOfNodes()-1#just take last node-1 (last node is ground)
uy=mbs.GetNodeOutput(nLast-1,exu.OutputVariableType.Position)[1] #y-coordinate of last node
exu.Print("uy=", uy)
exudynTestGlobals.testError = uy - (0.44656762760262225) #2020-01-16: 0.44656762760262225
exudynTestGlobals.testResult = uy