ObjectConnectorDistance

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

Simpler: mbs.CreateDistanceConstraint adds this item, with what it needs, in one call.

Interface

Python names: ObjectConnectorDistance or DistanceConstraint, and VDistanceConstraint for its visualization
Markers it acts on: those providing Position: MarkerBodyPosition, MarkerBodyRigid, MarkerNodePosition, MarkerNodeRigid, MarkerSuperElementPosition, MarkerSuperElementRigid, MarkerKinematicTreeRigid

Parameters

The parameters of the item; in a dictionary, its type is ‘ConnectorDistance’:

name	type	default	description
name	String	‘’	constraints’s unique name
markerNumbers	ArrayMarkerIndex	[ invalid (-1), invalid (-1) ]	(symbol: \([m0,m1]\tp\)) list of markers used in connector
distance	PReal	0.	(symbol: \(d_0\)) prescribed distance [SI:m] of the used markers; must by greater than zero; must be given: the default is only a placeholder
activeConnector	Bool	True	flag, which determines, if the connector is active; used to deactivate (temporarily) a connector or constraint
visualization	VObjectConnectorDistance		parameters for visualization of item

Visualization parameters

The parameters of VObjectConnectorDistance, given as visualization:

name	type	size	default	description
show	Bool		True	set true, if item is shown in visualization and false if it is not shown
drawSize	float		-1.	the diameter of the rod drawn between the markers if visualizationSettings.connectors.drawSimplified is False; -1 means a tenth of connectors.defaultSize; with drawSimplified, the connector is a line
color	Float4	4	[-1.,-1.,-1.,-1.]	RGBA connector color; if R==-1, use default color

Drawing

Drawn as all constraints; a line between the markers with connectors.drawSimplified, otherwise a rod of diameter drawSize.

Settings beyond those of all constraints: connectors.drawSimplified, general.cylinderTiling.

Output variables

Available as OutputVariableType in sensors, Get...Output() and other functions:

output variable	symbol	description
Displacement	\(\LU{0}{\Delta\pv}\)	relative displacement in global coordinates
Velocity	\(\LU{0}{\Delta\vv}\)	relative translational velocity in global coordinates
Distance	\(\vert \LU{0}{\Delta\pv}\vert \)	distance between markers (should stay constant; shows constraint deviation)
Force	\(\lambda_0\)	joint force (=scalar Lagrange multiplier)

Detailed description

Definition of quantities

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

Connector constraint equations

If activeConnector = True, the index 3 algebraic equation reads

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

Due to the fact that the force direction is given by

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

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

\[ \left(\frac{\LU{0}{\Delta\pv}}{\left|\LU{0}{\Delta\pv}\right|}\right)\tp \Delta\vv = 0 \]

if activeConnector = False, the algebraic equation reads

\[ \lambda_0 = 0 \]

Mini example

#example with 1m pendulum, 50kg under gravity
nMass = mbs.AddNode(NodePoint2D(referenceCoordinates=[1,0]))
oMass = mbs.AddObject(MassPoint2D(mass = 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
exu.sys['testResult'] = mbs.GetNodeOutput(nMass, exu.OutputVariableType.Position)[0]

Examples (Ex) and TestModels (TM) that show this item, with weblink to github: pendulum2Dconstraint.py (Ex), MathematicalPendulumTest.py (TM), fourBarMechanismTest.py (TM)