<!-- GENERATED by tools/generators/examplesDocsEmitter.py from python/ - do not edit -->
(testmodels-sphericaljointtest)=
# sphericalJointTest.py

You can view and download this file on Github: [sphericalJointTest.py](https://github.com/jgerstmayr/EXUDYN/tree/master/python/TestModels/sphericalJointTest.py)

```{code-block} python
:linenos:

#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
# This is an EXUDYN example
#
# Details:  Simulate Chain with 3D rigid bodies and SphericalJoint;
#           Also test MarkerNodePosition
#
# Author:   Johannes Gerstmayr
# Date:     2020-04-09
#
# 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.utilities import * #includes itemInterface and rigidBodyUtilities
import exudyn.graphics as graphics

testIsActive = exu.sys.get('testIsActive', False)

SC = exu.SystemContainer()
mbs = SC.AddSystem()

nBodies = 4
color = [0.1,0.1,0.8,1]
s = 0.1 #width of cube
sx = 3*s #lengt of cube/body
cPosZ = 0.1 #offset of constraint in z-direction
zz = sx * (nBodies+1)*2 #max size of background

background0 = graphics.Lines([[-zz,-zz,0], [zz,-zz,0], [zz,sx,0], [-zz,sx,0], [-zz,-zz,0]], color=color)
oGround=mbs.AddObject(ObjectGround(referencePosition= [0,0,0], 
                                   visualization=VObjectGround(graphicsData= [background0])))
mPosLast = mbs.AddMarker(MarkerBodyPosition(bodyNumber = oGround, 
                                            localPosition=[-sx,0,cPosZ*0]))

#create a chain of bodies:
for i in range(nBodies):
    f = 0 #factor for initial velocities
    omega0 = [0,50.*f,20*f] #arbitrary initial angular velocity
    ep0 = eulerParameters0 #no rotation
    ep_t0 = AngularVelocity2EulerParameters_t(omega0, ep0)

    p0 = [-sx+i*2*sx,0.,0] #reference position
    v0 = [0.2*f,0.,0.] #initial translational velocity

    nRB = mbs.AddNode(NodeRigidBodyEP(referenceCoordinates=p0+ep0, 
                                      initialVelocities=v0+list(ep_t0)))
    #nRB = mbs.AddNode(NodeRigidBodyEP(referenceCoordinates=[0,0,0,1,0,0,0], initialVelocities=[0,0,0,0,0,0,0]))
    oGraphics = graphics.Brick(centerPoint=[0, 0, 0], size=[2*sx, 2*s, 2*s], addFaces=False, addEdges=True, edgeColor=[0.8,0.1,0.1,1])
    oRB = mbs.AddObject(ObjectRigidBody(mass=2, 
                                        inertia=[6,1,6,0,0,0], 
                                        nodeNumber=nRB, 
                                        visualization=VObjectRigidBody(graphicsData=[oGraphics])))

    mMassRB = mbs.AddMarker(MarkerBodyMass(bodyNumber = oRB))
    mbs.AddLoad(Gravity(markerNumber = mMassRB, loadVector=[0.,-9.81,0.])) #gravity in negative z-direction

    if i==0:
        #mPos = mbs.AddMarker(MarkerBodyPosition(bodyNumber = oRB, localPosition = [-sx*0,0.,cPosZ*0]))
        mPos = mbs.AddMarker(MarkerNodePosition(nodeNumber=nRB))
    else:
        mPos = mbs.AddMarker(MarkerBodyPosition(bodyNumber = oRB, localPosition = [-sx,0.,cPosZ]))

    #alternative with spring-damper:    
    #mbs.AddObject(ObjectConnectorCartesianSpringDamper(markerNumbers = [mPosLast, mPos], 
    #                                                   stiffness=[k,k,k], damping=[d,d,d])) #gravity in negative z-direction
    axes = [1,1,1]
    if (i==0):
        axes = [0,1,1]

    mbs.AddObject(SphericalJoint(markerNumbers = [mPosLast, mPos], constrainedAxes=axes))

    #marker for next chain body
    mPosLast = mbs.AddMarker(MarkerBodyPosition(bodyNumber = oRB, localPosition = [sx,0.,cPosZ]))


mbs.Assemble()
#exu.Print(mbs)

simulationSettings = exu.SimulationSettings() #takes currently set values or default values

fact = 1000
simulationSettings.timeIntegration.numberOfSteps = 1*fact
simulationSettings.timeIntegration.endTime = 0.001*fact
simulationSettings.solution.file.writePeriod = simulationSettings.timeIntegration.endTime/fact*10
simulationSettings.timeIntegration.verboseMode = 1

simulationSettings.timeIntegration.newton.useModifiedNewton = True
simulationSettings.timeIntegration.generalizedAlpha.useIndex2Constraints = False
simulationSettings.timeIntegration.generalizedAlpha.useNewmark = False
simulationSettings.timeIntegration.generalizedAlpha.spectralRadius = 0.6 #0.6 works well 

simulationSettings.solution.file.information = "rigid body tests"
SC.visualizationSettings.nodes.defaultSize = 0.05
#simulationSettings.show.computationTime = True
#simulationSettings.show.statistics = True

if not testIsActive:
    SC.renderer.Start()
    SC.renderer.DoIdleTasks()

mbs.SolveDynamic(simulationSettings)

#+++++++++++++++++++++++++++++++++++++++++++++
sol = mbs.systemData.GetODE2Coordinates(); 
solref = mbs.systemData.GetODE2Coordinates(configuration=exu.ConfigurationType.Reference); 
#exu.Print('sol=',sol)
u = 0
for i in range(14): #take coordinates of first two bodies
    u += abs(sol[i]+solref[i])

exu.Print('solution of sphericalJointTest=',u)

exu.sys['testResult'] = u


if not testIsActive:
    #SC.renderer.DoIdleTasks()
    SC.renderer.Stop() #safely close rendering window!
```