ObjectConnectorDistance

Connector which enforces constant or prescribed distance between two bodies/nodes.

Additional information for ObjectConnectorDistance:

• This Object has/provides the following types = Connector, Constraint
• Requested Marker type = Position
• Short name for Python = DistanceConstraint
• Short name for Python visualization object = VDistanceConstraint

The item ObjectConnectorDistance with type = ‘ConnectorDistance’ has the following parameters:

• name [type = String, default = ‘’]:

  constraints’s unique name
• markerNumbers [\([m0,m1]\tp\), type = ArrayMarkerIndex, default = [ invalid [-1], invalid [-1] ]]:

  list of markers used in connector
• distance [\(d_0\), type = PReal, default = 0.]:

  prescribed distance [SI:m] of the used markers; must by greater than zero
• activeConnector [type = Bool, default = True]:

  flag, which determines, if the connector is active; used to deactivate (temporarily) a connector or constraint
• visualization [type = VObjectConnectorDistance]:

  parameters for visualization of item

The item VObjectConnectorDistance has the following parameters:

• show [type = Bool, default = True]:

  set true, if item is shown in visualization and false if it is not shown
• drawSize [type = float, default = -1.]:

  drawing size = link size; size == -1.f means that default connector size is used
• color [type = Float4, default = [-1.,-1.,-1.,-1.]]:

  RGBA connector color; if R==-1, use default color

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DESCRIPTION of ObjectConnectorDistance

The following output variables are available as OutputVariableType in sensors, Get…Output() and other functions:

• Displacement: \(\LU{0}{\Delta{\mathbf{p}}}\)

  relative displacement in global coordinates
• Velocity: \(\LU{0}{\Delta{\mathbf{v}}}\)

  relative translational velocity in global coordinates
• Distance: \(|\LU{0}{\Delta{\mathbf{p}}}|\)

  distance between markers (should stay constant; shows constraint deviation)
• Force: \(\lambda_0\)

  joint force (=scalar Lagrange multiplier)

Definition of quantities

intermediate variables	symbol	description
marker m0 position	\(\LU{0}{{\mathbf{p}}}_{m0}\)	current global position which is provided by marker m0
marker m1 position	\(\LU{0}{{\mathbf{p}}}_{m1}\)	accordingly
marker m0 velocity	\(\LU{0}{{\mathbf{v}}}_{m0}\)	current global velocity which is provided by marker m0
marker m1 velocity	\(\LU{0}{{\mathbf{v}}}_{m1}\)	accordingly
relative displacement	\(\LU{0}{\Delta{\mathbf{p}}}\)	\(\LU{0}{{\mathbf{p}}}_{m1} - \LU{0}{{\mathbf{p}}}_{m0}\)
relative velocity	\(\LU{0}{\Delta{\mathbf{v}}}\)	\(\LU{0}{{\mathbf{v}}}_{m1} - \LU{0}{{\mathbf{v}}}_{m0}\)
algebraicVariable	\(\lambda_0\)	Lagrange multiplier = force in constraint

Connector forces constraint equations

If activeConnector = True, the index 3 algebraic equation reads

\[\left|\LU{0}{\Delta{\mathbf{p}}}\right| - d_0 = 0\]

Due to the fact that the force direction is given by

\[\frac{1}{|\LU{0}{\Delta{\mathbf{p}}}|}\LU{0}{\Delta{\mathbf{p}}} ,\]

the prescribed distance \(d_0\) may not be zero. This would, otherwise, result in a change of the number of constraints. The index 2 (velocity level) algebraic equation reads

\[\left(\frac{\LU{0}{\Delta{\mathbf{p}}}}{\left|\LU{0}{\Delta{\mathbf{p}}}\right|}\right)\tp \Delta{\mathbf{v}} = 0\]

if activeConnector = False, the algebraic equation reads

\[\lambda_0 = 0\]

MINI EXAMPLE for ObjectConnectorDistance

#example with 1m pendulum, 50kg under gravity
nMass = mbs.AddNode(NodePoint2D(referenceCoordinates=[1,0]))
oMass = mbs.AddObject(MassPoint2D(physicsMass = 50, nodeNumber = nMass))

mMass = mbs.AddMarker(MarkerNodePosition(nodeNumber=nMass))
mGround = mbs.AddMarker(MarkerBodyPosition(bodyNumber=oGround, localPosition = [0,0,0]))
oDistance = mbs.AddObject(DistanceConstraint(markerNumbers = [mGround, mMass], distance = 1))

mbs.AddLoad(Force(markerNumber = mMass, loadVector = [0, -50*9.81, 0]))

#assemble and solve system for default parameters
mbs.Assemble()

sims=exu.SimulationSettings()
sims.timeIntegration.generalizedAlpha.spectralRadius=0.7
mbs.SolveDynamic(sims)

#check result at default integration time
exudynTestGlobals.testResult = mbs.GetNodeOutput(nMass, exu.OutputVariableType.Position)[0]

Relevant Examples and TestModels with weblink:

HydraulicActuatorStaticInitialization.py (Examples/), pendulum2Dconstraint.py (Examples/), pendulumIftommBenchmark.py (Examples/), fourBarMechanismTest.py (TestModels/), coordinateVectorConstraint.py (TestModels/), coordinateVectorConstraintGenericODE2.py (TestModels/), modelUnitTests.py (TestModels/), PARTS_ATEs_moving.py (TestModels/)

The web version may not be complete. For details, consider also the Exudyn PDF documentation : theDoc.pdf