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(testmodels-reevingsystemspringstest)=
# reevingSystemSpringsTest.py

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

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

#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
# This is an EXUDYN example
#
# Details:  A simple 3D reeving system;
#
# Author:   Johannes Gerstmayr
# Date:     2022-06-16
#
# 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)

import numpy as np
from math import sin, cos, sqrt,pi

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

gGround = graphics.CheckerBoard(point=[8,-8,-2], size=32, nTiles=10)
oGround = mbs.AddObject(ObjectGround(visualization=VObjectGround(graphicsData=[gGround])))

t = 0.1
r0 = 0.5
g = [0,-9.81,0]

posList = [[0,0,0], 
           [7,-20,1], 
           [12,0,2],
           ]
rList = [r0*1.,4*r0,r0,5.9*r0,r0,r0,r0]

# posList = [[0,0,0], 
#            [5,-20,1], 
#            [8,0,2],
#            [12,-10,0], 
#            [16,0,0] 
#            ]
# rList = [r0*0.,6*r0,r0,5.9*r0,r0,r0,r0]
dirList = [-1,1,-1,1,-1,1,1]


n = len(posList)
nodeList = []
bodyList = []
markerList = []
sheavesRadii = []
sheavesAxes = exu.Vector3DList()
Lref = 0
pLast = [0,0,0]

for i, pos in enumerate(posList):
    r = rList[i]

    graphicsRoll = graphics.Cylinder(pAxis=[0,0,-0.5*t], vAxis=[0,0,t], nTiles=32, radius=r, color=graphics.color.dodgerblue, alternatingColor=graphics.color.darkgrey)
    
    inertiaRoll = InertiaCylinder(density=1000,length=t,outerRadius=r, axis=2)
    inertiaRoll = inertiaRoll.Translated([0,-r,0])

    dictR = mbs.CreateRigidBody(referencePosition=pos,  
                                inertia=inertiaRoll,  
                                gravity=g,  
                                graphicsDataList=[graphicsRoll, graphics.Basis(inertiaRoll.COM(), length=0.5)],  
                                returnDict=True)  
    nR = dictR['nodeNumber']  
    bR = dictR['bodyNumber']

    mR = mbs.AddMarker(MarkerNodeRigid(nodeNumber=nR))
    nodeList += [nR]
    bodyList += [bR]
    markerList += [mR]

    sheavesAxes.Append([0,0,dirList[i]*1])
    sheavesRadii += [r]

    if i != 0:
        Lref += np.linalg.norm(np.array(pos)-pLast)
    if i > 0 and i < len(posList)-1:
        #note that in this test example, Lref is slightly too long, leading to negative spring forces (compression) if not treated nonlinearly with default settings in ReevingSystemSprings
        Lref += r*pi #0.8*r*pi would always lead to tension

    #mR = mbs.AddMarker(MarkerBodyRigid(bodyNumber=bR, localPosition=[0,-r,0]))
    #mbs.AddLoad(Force(markerNumber=mR, loadVector=[0,-inertiaRoll.mass*9.81,0]))
        
    pLast = pos


markerGround0 = mbs.AddMarker(MarkerBodyRigid(bodyNumber=oGround, localPosition=posList[0]))
markerGroundMid = mbs.AddMarker(MarkerBodyRigid(bodyNumber=oGround, localPosition=posList[2]))
markerGroundLast = mbs.AddMarker(MarkerBodyRigid(bodyNumber=oGround, localPosition=posList[-1]))

#sMarkerR = mbs.AddSensor(SensorMarker(markerNumber=markerR, outputVariableType=exu.OutputVariableType.Position))

#%%++++++++++++++++++++++++++++++++++++++++++++++++
#add joints:
oJoint0 = mbs.AddObject(GenericJoint(markerNumbers=[markerGround0, markerList[0]],
                                    constrainedAxes=[1,1,1,1,1,1],
                                    visualization=VGenericJoint(axesRadius=0.5*t, axesLength=1.5*t)))
oJointLast = mbs.AddObject(GenericJoint(markerNumbers=[markerGroundLast, markerList[-1]],
                                    constrainedAxes=[1,1,1,1,1,1],
                                    visualization=VGenericJoint(axesRadius=0.5*t, axesLength=1.5*t)))

if len(posList) > 3:
    mbs.AddObject(GenericJoint(markerNumbers=[markerGroundMid, markerList[2]],
                                        constrainedAxes=[1,1,1,1,1,1],
                                        visualization=VGenericJoint(axesRadius=0.5*t, axesLength=1.5*t)))

#%%++++++++++++++++++++++++++++++++++++++++++++++++
#add reeving system spring
stiffness = 1e5 #stiffness per length
damping = 0.5*stiffness #dampiung per length
oRS=mbs.AddObject(ReevingSystemSprings(markerNumbers=markerList, hasCoordinateMarkers=False, 
                                   stiffnessPerLength=stiffness, dampingPerLength=damping, 
                                   referenceLength = Lref,
                                   dampingTorsional = 0.01*damping, dampingShear = 0.1*damping,
                                   sheavesAxes=sheavesAxes, sheavesRadii=sheavesRadii,
                                   #regularizationForce = -1, #purely linear system
                                   visualization=VReevingSystemSprings(ropeRadius=0.05, color=graphics.color.dodgerblue)))

#%%++++++++++++++++++++++++++++++++++++++++++++++++
#add sensors 
if True:
    sPos1 = mbs.AddSensor(SensorNode(nodeNumber=nodeList[1], storeInternal=True,
                                          outputVariableType=exu.OutputVariableType.Position))
    sOmega1 = mbs.AddSensor(SensorNode(nodeNumber=nodeList[1], storeInternal=True,
                                          outputVariableType=exu.OutputVariableType.AngularVelocity))
    sLength= mbs.AddSensor(SensorObject(objectNumber=oRS, storeInternal=True,
                                          outputVariableType=exu.OutputVariableType.Distance))
    sLength_t= mbs.AddSensor(SensorObject(objectNumber=oRS, storeInternal=True,
                                          outputVariableType=exu.OutputVariableType.VelocityLocal))
    sForce= mbs.AddSensor(SensorObject(objectNumber=oRS, storeInternal=True,
                                          outputVariableType=exu.OutputVariableType.ForceLocal))

#%%++++++++++++++++++++++++++++++++++++++++++++++++
#simulate:
mbs.Assemble()

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

tEnd = 2
if not testIsActive:
    tEnd = 2 #200
h=0.01  #use small step size to detext contact switching

simulationSettings.timeIntegration.numberOfSteps = int(tEnd/h)
simulationSettings.timeIntegration.endTime = tEnd
#simulationSettings.solution.file.write= True #set False for CPU performance measurement
simulationSettings.solution.sensors.writePeriod = 0.01

simulationSettings.timeIntegration.verboseMode = 1

simulationSettings.timeIntegration.newton.useModifiedNewton = True

SC.visualizationSettings.nodes.show = True
SC.visualizationSettings.nodes.drawNodesAsPoint  = False
SC.visualizationSettings.nodes.showBasis = True
SC.visualizationSettings.nodes.basisSize = 0.2

SC.visualizationSettings.openGL.multiSampling = 4

#SC.visualizationSettings.general.autoFitScene = False #use loaded render state
# testIsActive = False
if not testIsActive:
    SC.renderer.Start()
    SC.renderer.RestoreSavedState()
    SC.renderer.DoIdleTasks()


mbs.SolveDynamic(simulationSettings, 
                 #solverType=exu.DynamicSolverType.TrapezoidalIndex2 #in this case, drift shows up significantly!
                 )

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

if True:
    

    mbs.PlotSensor(sPos1, components=[0,1,2], labels=['pos X','pos Y','pos Z'], closeAll=True)
    mbs.PlotSensor(sOmega1, components=[0,1,2], labels=['omega X','omega Y','omega Z'])
    mbs.PlotSensor(sLength, components=[0], labels=['length'])
    mbs.PlotSensor(sLength_t, components=[0], labels=['vel'])
    mbs.PlotSensor(sForce, components=[0], labels=['force'])


#compute error for test suite:
sol2 = mbs.systemData.GetODE2Coordinates(); 
u = np.linalg.norm(sol2); 
exu.Print('solution of ReevingSystemSprings=',u)

exu.sys['testResult'] = u
```