fourBarMechanism3D.py

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  1#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
  2# This is an EXUDYN example
  3#
  4# Details:  A simple 3D four bar mechanism #read full text output!
  5#           1) regular case does not work (redundant constraints/overconstrained joints; jacobian singluar)
  6#           2) use simulationSettings.linearSolverSettings.ignoreSingularJacobian = True
  7#           3) remove redundant constraints: change flags for GenericJoint at last joint [1,1,0,0,0,0] to obtain well defined mbs
  8#
  9# Author:   Johannes Gerstmayr
 10# Date:     2021-08-05
 11#
 12# 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.
 13#
 14#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 15
 16import exudyn as exu
 17from exudyn.itemInterface import *
 18from exudyn.utilities import * #includes itemInterface and rigidBodyUtilities
 19import exudyn.graphics as graphics #only import if it does not conflict
 20import numpy as np
 21from math import pi, sin, cos
 22
 23
 24useGraphics = True
 25
 26casesText = ['redundant constraints', 'redundant constraints with improved solver', 'non-redundant constraints']
 27cases = [0,1,2]
 28
 29for case in cases:
 30    caseText = casesText[case]
 31    print('\n\n************************************************')
 32    print('run four bar mechanism with case:\n  '+caseText)
 33    print('************************************************')
 34
 35    SC = exu.SystemContainer()
 36    mbs = SC.AddSystem()
 37
 38
 39    #%%++++++++++++++++++++++++++++++++++++++++++++++++++++
 40    #physical parameters
 41    g =     [0.1,-9.81,0] #gravity + disturbance
 42    L = 1               #length
 43    w = 0.1             #width
 44    bodyDim=[L,w,w]     #body dimensions
 45    # p0 =    [0,0,0]
 46    pMid0 = np.array([0,L*0.5,0]) #center of mass, body0
 47    pMid1 = np.array([L*0.5,L,0]) #center of mass, body1
 48    pMid2 = np.array([L,L*0.5,0]) #center of mass, body2
 49
 50    #ground body
 51    graphicsCOM0 = graphics.Basis(origin=[0,0,0], length=4*w)
 52    oGround = mbs.AddObject(ObjectGround(visualization=VObjectGround(graphicsData=[graphicsCOM0])))
 53    markerGround0 = mbs.AddMarker(MarkerBodyRigid(bodyNumber=oGround, localPosition=[0,0,0]))
 54    markerGround1 = mbs.AddMarker(MarkerBodyRigid(bodyNumber=oGround, localPosition=[L,0,0]))
 55
 56    #%%++++++++++++++++++++++++++++++++++++++++++++++++++++
 57    #first link:
 58    iCube0 = InertiaCuboid(density=5000, sideLengths=bodyDim)
 59
 60    #graphics for body
 61    graphicsBody0 = graphics.RigidLink(p0=[-0.5*L,0,0],p1=[0.5*L,0,0],
 62                                         axis0=[0,0,1], axis1=[0,0,1], radius=[0.5*w,0.5*w],
 63                                         thickness = w, width = [1.2*w,1.2*w], color=graphics.color.red)
 64    graphicsBody1 = graphics.RigidLink(p0=[-0.5*L,0,0],p1=[0.5*L,0,0],
 65                                         axis0=[0,0,1], axis1=[0,0,1], radius=[0.5*w,0.5*w],
 66                                         thickness = w, width = [1.2*w,1.2*w], color=graphics.color.green)
 67    graphicsBody2 = graphics.RigidLink(p0=[-0.5*L,0,0],p1=[0.5*L,0,0],
 68                                         axis0=[0,0,1], axis1=[0,0,1], radius=[0.5*w,0.5*w],
 69                                         thickness = w, width = [1.2*w,1.2*w], color=graphics.color.steelblue)
 70
 71    [n0,b0]=AddRigidBody(mainSys = mbs,
 72                         inertia = iCube0, #includes COM
 73                         nodeType = exu.NodeType.RotationEulerParameters,
 74                         position = pMid0,
 75                         rotationMatrix = RotationMatrixZ( 0.5*pi),
 76                         gravity = g,
 77                         graphicsDataList = [graphicsBody0])
 78
 79    markerBody0J0 = mbs.AddMarker(MarkerBodyRigid(bodyNumber=b0, localPosition=[-0.5*L,0,0]))
 80    markerBody0J1 = mbs.AddMarker(MarkerBodyRigid(bodyNumber=b0, localPosition=[ 0.5*L,0,0]))
 81
 82    [n1,b1]=AddRigidBody(mainSys = mbs,
 83                         inertia = iCube0, #includes COM
 84                         nodeType = exu.NodeType.RotationEulerParameters,
 85                         position = pMid1,
 86                         rotationMatrix = RotationMatrixZ(0.),
 87                         gravity = g,
 88                         graphicsDataList = [graphicsBody1])
 89    markerBody1J0 = mbs.AddMarker(MarkerBodyRigid(bodyNumber=b1, localPosition=[-0.5*L,0,0]))
 90    markerBody1J1 = mbs.AddMarker(MarkerBodyRigid(bodyNumber=b1, localPosition=[ 0.5*L,0,0]))
 91
 92    [n2,b2]=AddRigidBody(mainSys = mbs,
 93                         inertia = iCube0, #includes COM
 94                         nodeType = exu.NodeType.RotationEulerParameters,
 95                         position = pMid2,
 96                         rotationMatrix = RotationMatrixZ(-0.5*pi),
 97                         gravity = g,
 98                         graphicsDataList = [graphicsBody2])
 99
100    markerBody2J0 = mbs.AddMarker(MarkerBodyRigid(bodyNumber=b2, localPosition=[-0.5*L,0,0]))
101    markerBody2J1 = mbs.AddMarker(MarkerBodyRigid(bodyNumber=b2, localPosition=[ 0.5*L,0,0]))
102
103
104    #revolute joint option 1:
105    mbs.AddObject(GenericJoint(markerNumbers=[markerGround0, markerBody0J0],
106                                constrainedAxes=[1,1,1,1,1,0],
107                                visualization=VObjectJointGeneric(axesRadius=0.2*w, axesLength=1.4*w)))
108
109    mbs.AddObject(GenericJoint(markerNumbers=[markerBody0J1, markerBody1J0],
110                                constrainedAxes=[1,1,1,1,1,0],
111                                visualization=VObjectJointGeneric(axesRadius=0.2*w, axesLength=1.4*w)))
112
113    mbs.AddObject(GenericJoint(markerNumbers=[markerBody1J1, markerBody2J0],
114                                constrainedAxes=[1,1,1,1,1,0],
115                                visualization=VObjectJointGeneric(axesRadius=0.2*w, axesLength=1.4*w)))
116
117    constrainedAxes3 = [1,1,1,1,1,0]
118    if case == 2:
119        constrainedAxes3 = [1,1,0,0,0,0] #only these constraints are needed for closing loop!
120        print('use non-redundant constraints for last joint:', constrainedAxes3)
121
122    mbs.AddObject(GenericJoint(markerNumbers=[markerBody2J1, markerGround1],
123                                constrainedAxes=constrainedAxes3,
124                                visualization=VObjectJointGeneric(axesRadius=0.2*w, axesLength=1.4*w)))
125
126    #position sensor at tip of body1
127    sens1=mbs.AddSensor(SensorBody(bodyNumber=b1, localPosition=[0,0,0.5*L],
128                                   fileName='solution/sensorPos.txt',
129                                   outputVariableType = exu.OutputVariableType.Position))
130
131    #%%++++++++++++++++++++++++++++++++++++++++++++++++++++++
132    #assemble system before solving
133    mbs.Assemble()
134    if False:
135        mbs.systemData.Info() #show detailed information
136    if False:
137        #from exudyn.utilities import DrawSystemGraph
138        mbs.DrawSystemGraph(useItemTypes=True) #draw nice graph of system
139
140    simulationSettings = exu.SimulationSettings() #takes currently set values or default values
141
142    tEnd = 10 #simulation time
143    h = 2e-3 #step size
144    simulationSettings.timeIntegration.numberOfSteps = int(tEnd/h)
145    simulationSettings.timeIntegration.endTime = tEnd
146    simulationSettings.timeIntegration.verboseMode = 1
147    #simulationSettings.timeIntegration.simulateInRealtime = True
148    #simulationSettings.timeIntegration.realtimeFactor = 4
149
150    if case == 1:
151        simulationSettings.linearSolverSettings.ignoreSingularJacobian = True #for redundant constraints
152
153    simulationSettings.timeIntegration.newton.useModifiedNewton = True
154    simulationSettings.solutionSettings.writeSolutionToFile = False
155    #simulationSettings.solutionSettings.solutionWritePeriod = 0.005 #store every 5 ms
156
157    SC.visualizationSettings.window.renderWindowSize=[1200,1024]
158    SC.visualizationSettings.openGL.multiSampling = 4
159    SC.visualizationSettings.general.autoFitScene = False
160
161    SC.visualizationSettings.nodes.drawNodesAsPoint=False
162    SC.visualizationSettings.nodes.showBasis=True
163
164    if useGraphics:
165        exu.StartRenderer()
166        if 'renderState' in exu.sys: #reload old view
167            SC.SetRenderState(exu.sys['renderState'])
168
169        mbs.WaitForUserToContinue() #stop before simulating
170
171    try: #solver will raise exception in case 1
172        mbs.SolveDynamic(simulationSettings = simulationSettings)
173    except:
174        pass
175
176    # mbs.SolveDynamic(simulationSettings = simulationSettings,
177    #                  solverType=exu.DynamicSolverType.TrapezoidalIndex2)
178    if useGraphics:
179        SC.WaitForRenderEngineStopFlag() #stop before closing
180        exu.StopRenderer() #safely close rendering window!
181
182    #check redundant constraints and DOF:
183    mbs.ComputeSystemDegreeOfFreedom(verbose=useGraphics)
184
185
186if False:
187    sol = LoadSolutionFile('coordinatesSolution.txt')
188
189    mbs.SolutionViewer(sol)
190
191if False:
192
193    mbs.PlotSensor([sens1],[1])