scissorPrismaticRevolute2D.py
You can view and download this file on Github: scissorPrismaticRevolute2D.py
1#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
2# This is an EXUDYN example
3#
4# Details: Create scissor-like chain of bodies and prismatic joints to test functionality
5#
6# Author: Johannes Gerstmayr
7# Date: 2020-01-14
8#
9# 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.
10#
11#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
12
13import exudyn as exu
14from exudyn.utilities import *
15
16useGraphics = True #without test
17#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
18#you can erase the following lines and all exudynTestGlobals related operations if this is not intended to be used as TestModel:
19try: #only if called from test suite
20 from modelUnitTests import exudynTestGlobals #for globally storing test results
21 useGraphics = exudynTestGlobals.useGraphics
22except:
23 class ExudynTestGlobals:
24 pass
25 exudynTestGlobals = ExudynTestGlobals()
26#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
27
28SC = exu.SystemContainer()
29mbs = SC.AddSystem()
30
31L = 0.8 #distance
32b=L*0.1
33mass = 1
34g = 9.81*0.1
35
36#number of scissors:
37n=3 #run test with n=3
38
39r = 0.05 #just for graphics
40nL = (n+0.5)*L
41graphicsBackground = GraphicsDataRectangle(-L*1.5,-L*1.5, 1.5*nL, nL, color4lightgrey) #for appropriate zoom
42graphicscube = GraphicsDataRectangle(-L,-0.5*b, L, 0.5*b, color4steelblue) #GraphicsDataSphere(point=[0,0,0], radius=r, color=[1.,0.2,0.2,1], nTiles = 8)
43graphicscube2 = GraphicsDataRectangle(-L,-0.5*b, n*L*2**0.5, 0.5*b, color4steelblue) #GraphicsDataSphere(point=[0,0,0], radius=r, color=[1.,0.2,0.2,1], nTiles = 8)
44#add ground object and mass point:
45
46pi = 3.1415926535897932384626
47
48#prescribed driving function:
49def springForceUF(mbs, t, itemIndex, u, v, k, d, offset): #changed 2023-01-21:, mu, muPropZone):
50 f=k*(u+offset)+v*d
51 return f
52
53addPrismaticJoint = True
54useCartesianSD = True
55
56simulationSettings = exu.SimulationSettings()
57
58f = 500
59simulationSettings.timeIntegration.numberOfSteps = int(1*f)
60simulationSettings.timeIntegration.endTime = 0.02*f #make small steps to see something during simulation
61simulationSettings.solutionSettings.solutionWritePeriod = simulationSettings.timeIntegration.endTime/5000
62
63simulationSettings.solutionSettings.writeSolutionToFile = True
64simulationSettings.displayComputationTime = True
65simulationSettings.timeIntegration.verboseMode = 1
66#simulationSettings.timeIntegration.verboseModeFile = 0
67
68simulationSettings.timeIntegration.newton.useModifiedNewton = False
69simulationSettings.timeIntegration.newton.modifiedNewtonJacUpdatePerStep = True
70
71#added JacobianODE2, but example computed with numDiff forODE2connectors, 2022-01-18: 27.202556489044145 :
72simulationSettings.timeIntegration.newton.numericalDifferentiation.forODE2connectors=True
73
74simulationSettings.timeIntegration.generalizedAlpha.useNewmark = True
75simulationSettings.timeIntegration.generalizedAlpha.useIndex2Constraints = simulationSettings.timeIntegration.generalizedAlpha.useNewmark
76simulationSettings.timeIntegration.generalizedAlpha.spectralRadius = 0.6 #0.61
77simulationSettings.timeIntegration.adaptiveStep = False
78simulationSettings.linearSolverType = exu.LinearSolverType.EigenSparse
79
80simulationSettings.timeIntegration.generalizedAlpha.computeInitialAccelerations = True
81simulationSettings.solutionSettings.coordinatesSolutionFileName= "coordinatesSolution.txt"
82
83
84simulationSettings.displayComputationTime = False
85simulationSettings.displayStatistics = True
86
87
88if useGraphics: #only start graphics once, but after background is set
89# SC.visualizationSettings.window.alwaysOnTop = True #must be done before exu.StartRenderer() called
90# SC.visualizationSettings.window.maximize = True
91# SC.visualizationSettings.window.showWindow = False
92 exu.StartRenderer()
93
94
95
96resUy = 0 #add up displacements of selected node
97resIt = 0 #total iterations
98nMeasure = 0 #selected node
99#treat two cases: 0=revolute, 1=ObjectConnectorCartesianSpringDamper
100for case in range(2):
101 mbs.Reset()
102 oGround = mbs.AddObject(ObjectGround(referencePosition = [0,0,0], visualization = VObjectGround(graphicsData = [graphicsBackground])))
103 mGround = mbs.AddMarker(MarkerBodyPosition(bodyNumber=oGround, localPosition = [0,0,0]))
104 #start 3D visualization
105
106 lastMarkerV = mGround
107 lastMarkerH = mGround
108
109 useCartesianSD = True
110 if case == 0: useCartesianSD = False
111 oBodyD = 0
112 mBodyDCOM = 0
113
114 #create several scissor elements if wanted
115 for i in range(n):
116 #stiffness and damping for CartesianSpringDamper
117 k=1e4
118 d=1e-2*k
119
120 #horizontal body:
121 nBodyH = mbs.AddNode(NodeRigidBody2D(referenceCoordinates=[L*i,L*i,0]))
122 oBodyH = mbs.AddObject(RigidBody2D(physicsMass = mass, physicsInertia=mass, nodeNumber = nBodyH, visualization = VObjectRigidBody2D(graphicsData = [graphicscube])))
123
124 mBodyH0 = mbs.AddMarker(MarkerBodyPosition(bodyNumber=oBodyH, localPosition=[-L,0,0]))
125 mBodyH1 = mbs.AddMarker(MarkerBodyPosition(bodyNumber=oBodyH, localPosition=[ L,0,0]))
126 mBodyHCOM = mbs.AddMarker(MarkerBodyPosition(bodyNumber=oBodyH, localPosition=[ 0,0,0]))
127
128 #vertical body:
129 nBodyV = mbs.AddNode(NodeRigidBody2D(referenceCoordinates=[L*i,L*i,0.5*pi]))
130 oBodyV = mbs.AddObject(RigidBody2D(physicsMass = mass, physicsInertia=mass, nodeNumber = nBodyV, visualization = VObjectRigidBody2D(graphicsData = [graphicscube])))
131 nMeasure = nBodyV
132
133 mBodyV0 = mbs.AddMarker(MarkerBodyPosition(bodyNumber=oBodyV, localPosition=[-L,0,0]))
134 mBodyV1 = mbs.AddMarker(MarkerBodyPosition(bodyNumber=oBodyV, localPosition=[ L,0,0]))
135 mBodyVCOM = mbs.AddMarker(MarkerBodyRigid(bodyNumber=oBodyV, localPosition=[ 0,0,0]))
136
137 #diagonal body:
138 if i==0 and addPrismaticJoint:
139 nBodyD = mbs.AddNode(NodeRigidBody2D(referenceCoordinates=[0,0,0.25*pi]))
140 oBodyD = mbs.AddObject(RigidBody2D(physicsMass = mass, physicsInertia=mass, nodeNumber = nBodyD, visualization = VObjectRigidBody2D(graphicsData = [graphicscube2])))
141
142 #mBodyD0 = mbs.AddMarker(MarkerBodyPosition(bodyNumber=oBodyD, localPosition=[-L,0,0]))
143 #mBodyD1 = mbs.AddMarker(MarkerBodyPosition(bodyNumber=oBodyD, localPosition=[ L,0,0]))
144 mBodyDCOM = mbs.AddMarker(MarkerBodyRigid(bodyNumber=oBodyD, localPosition=[ 0,0,0]))
145 mbs.AddLoad(Force(markerNumber = mBodyDCOM, loadVector = [0, -mass*g, 0]))
146 #keep this as Cartesian spring damper, as revolute joint may overconstrain system?
147 mbs.AddObject(ObjectConnectorCartesianSpringDamper(markerNumbers=[mBodyDCOM, mGround], stiffness = [k, k, k], damping=[d,d,d]))
148
149 if addPrismaticJoint and i>0:
150 mBodyDact = mbs.AddMarker(MarkerBodyRigid(bodyNumber=oBodyD, localPosition=[ i*L*2**0.5,0,0]))
151 mbs.AddObject(PrismaticJoint2D(markerNumbers=[mBodyVCOM, mBodyDact], axisMarker0=[1,0,0], normalMarker1=[0,1,0], constrainRotation=False))
152
153
154 if i==0:
155 if useCartesianSD:
156 mbs.AddObject(ObjectConnectorCartesianSpringDamper(markerNumbers=[mBodyHCOM, mGround], stiffness = [k, k, k], damping=[d,d,d]))
157 mbs.AddObject(ObjectConnectorCartesianSpringDamper(markerNumbers=[mBodyVCOM, mGround], stiffness = [k, k, k], damping=[d,d,d]))
158 else:
159 mbs.AddObject(RevoluteJoint2D(markerNumbers=[mBodyHCOM, mGround]))
160 mbs.AddObject(RevoluteJoint2D(markerNumbers=[mBodyVCOM, mGround]))
161
162 #fix rotation of H-body
163 nGround = mbs.AddNode(NodePointGround(referenceCoordinates=[L,0,0]))
164 mCoordGround = mbs.AddMarker(MarkerNodeCoordinate(nodeNumber=nGround, coordinate=0)) #ref node
165 mCoordPhiH = mbs.AddMarker(MarkerNodeCoordinate(nodeNumber=nBodyH, coordinate=2)) #rotation
166 mbs.AddObject(CoordinateConstraint(markerNumbers=[mCoordGround, mCoordPhiH]))
167
168 #activate rotation of V-body
169 mCoordPhiV = mbs.AddMarker(MarkerNodeCoordinate(nodeNumber=nBodyV, coordinate=2)) #rotation
170 mbs.AddObject(ObjectConnectorCoordinateSpringDamper(markerNumbers=[mCoordGround, mCoordPhiV], stiffness=1e4, damping=10e3,
171 offset=0.25*pi,springForceUserFunction=springForceUF))
172
173 else:
174 if useCartesianSD:
175 mbs.AddObject(ObjectConnectorCartesianSpringDamper(markerNumbers=[mBodyHCOM, mBodyVCOM], stiffness = [k, k, k], damping=[d,d,d]))
176 mbs.AddObject(ObjectConnectorCartesianSpringDamper(markerNumbers=[mBodyH0, lastMarkerV], stiffness = [k, k, k], damping=[d,d,d]))
177 mbs.AddObject(ObjectConnectorCartesianSpringDamper(markerNumbers=[mBodyV0, lastMarkerH], stiffness = [k, k, k], damping=[d,d,d]))
178 else:
179 mbs.AddObject(RevoluteJoint2D(markerNumbers=[mBodyHCOM, mBodyVCOM]))
180 mbs.AddObject(RevoluteJoint2D(markerNumbers=[mBodyH0, lastMarkerV]))
181 mbs.AddObject(RevoluteJoint2D(markerNumbers=[mBodyV0, lastMarkerH]))
182
183 lastMarkerH = mBodyH1
184 lastMarkerV = mBodyV1
185
186 mbs.AddLoad(Force(markerNumber = mBodyHCOM, loadVector = [0, -mass*g, 0]))
187 mbs.AddLoad(Force(markerNumber = mBodyVCOM, loadVector = [0, -mass*g, 0]))
188
189 #exu.Print(mbs)
190 mbs.Assemble()
191 SC.RenderEngineZoomAll()
192
193 if useGraphics:
194 mbs.WaitForUserToContinue()
195 #solve
196 #exu.InfoStat()
197 solver = exu.MainSolverImplicitSecondOrder()
198 solver.SolveSystem(mbs, simulationSettings)
199 #exu.Print("jac=",solver.GetSystemJacobian())
200 #exu.Print(solver.conv)
201 #exu.Print(solver.it)
202 #exu.InfoStat()
203 uy=mbs.GetNodeOutput(nMeasure,exu.OutputVariableType.Position)[1] #y-coordinate of node point
204 exu.Print("uy=",uy)
205 nit = solver.it.newtonStepsCount
206 exu.Print("solver.it.newtonStepsCount=",nit)
207 resUy += uy #add up displacements of selected node
208 resIt += nit #total iterations
209# mbs.WaitForUserToContinue()
210
211 #alternative solver command
212 #mbs.SolveDynamic(simulationSettings)
213
214
215
216#stop 3D visualization
217if useGraphics:
218 SC.WaitForRenderEngineStopFlag()
219 exu.StopRenderer() #safely close rendering window!
220
221#factor 1e-2: 32bit version shows larger differences ...
222exudynTestGlobals.testError = 1e-2*(resUy + resIt - (1.131033204186729+1.1246157002409096 + 1501+1217)) #2020-01-16: (1.131033204186729+1.1246157002409096 + 1501+1217)
223exudynTestGlobals.testResult = 1e-2*(resUy + resIt)
224#+++++++++++++++++++++++++++++++++++
225#plot data:
226
227#if simulationSettings.solutionSettings.writeSolutionToFile:
228# import matplotlib.pyplot as plt
229# import matplotlib.ticker as ticker
230
231# data = np.loadtxt('coordinatesSolution.txt', comments='#', delimiter=',')
232# plt.plot(data[:,0], data[:,1+2*nODE2+1], 'b-')
233# #plt.plot(data[:,0], data[:,1+1], 'r-') #y-coordinate
234
235# ax=plt.gca() # get current axes
236# ax.grid(True, 'major', 'both')
237# ax.xaxis.set_major_locator(ticker.MaxNLocator(10))
238# ax.yaxis.set_major_locator(ticker.MaxNLocator(10))
239# plt.tight_layout()
240# plt.show()