MarkerBodyPosition

A position body-marker attached to a local (body-fixed) position \(\pLocB = [b_0,\; b_1,\; b_2]\) (\(x\), \(y\), and \(z\) coordinates) of the body. It provides position information as well as the according derivatives (=velocity and derivative of position w.r.t. body coordinates). It can be used for connectors, joints or loads where position is required. If connectors also require orientation information, use a MarkerBodyRigid.

Interface

Provides: Position
Bodies it can be placed on: ObjectGround, ObjectMassPoint, ObjectMassPoint2D, ObjectMass1D, ObjectRotationalMass1D, ObjectRigidBody, ObjectRigidBody2D, ObjectFFRF, ObjectFFRFreducedOrder, ObjectANCFCable, ObjectANCFCable2D, ObjectALEANCFCable2D, ObjectANCFBeam, ObjectBeamGeometricallyExact2D, ObjectBeamGeometricallyExact, ObjectANCFThinPlate
Connectors, constraints and loads that can use it: ObjectConnectorSpringDamper, ObjectConnectorCartesianSpringDamper, ObjectConnectorGravity, ObjectConnectorHydraulicActuatorSimple, ObjectConnectorDistance, ObjectContactSphereSphere, ObjectContactSphereTriangle, ObjectJointSpherical, ObjectJointRevolute2D, LoadForceVector

Parameters

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

name	type	size	default	description
name	String		‘’	marker’s unique name
bodyNumber	ObjectIndex		invalid (-1)	body number to which marker is attached to
localPosition	Vector3D	3	[0.,0.,0.]	(symbol: \(\pLocB\)) local body position of marker; e.g. local (body-fixed) position where force is applied to
visualization	VMarkerBodyPosition			parameters for visualization of item

Visualization parameters

The parameters of VMarkerBodyPosition, 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

Drawing

Drawn as all markers.

Detailed description

Marker quantities

quantity	symbol	as computed
position	\(\LU{0}{\pv}_m\)	the output variable `Position` of the body at the local position \(\pLocB\)
velocity	\(\LU{0}{\vv}_m\)	the output variable `Velocity` of the body at \(\pLocB\)

Both are global. \(\pLocB\) is given in the body frame, from the reference point of the body.

Jacobians

The position Jacobian is the derivative of the velocity of the point with respect to the velocity coordinates of the body,

\[ \LU{0}{\Jm_{pos}} = \frac{\partial \LU{0}{\vv}_m}{\partial \dot\qv} , \]

which the body computes (its access function TranslationalVelocity_qt). For a rigid body it contains the rotation of the local position, see the page of the body.

Mini example

#a point of a body - here of the ground, at a local position - connected to a mass point by a spring
node = mbs.AddNode(NodePoint(referenceCoordinates=[1,0,0]))
body = mbs.AddObject(ObjectMassPoint(nodeNumber=node, mass=1))
mBody = mbs.AddMarker(MarkerBodyPosition(bodyNumber=body, localPosition=[0,0,0]))
mGround = mbs.AddMarker(MarkerBodyPosition(bodyNumber=oGround, localPosition=[1,0,0]))
mbs.AddObject(ObjectConnectorCartesianSpringDamper(markerNumbers=[mGround, mBody], stiffness=[100,100,100]))
mbs.AddLoad(LoadForceVector(markerNumber=mBody, loadVector=[0,0,-10]))

mbs.Assemble()
mbs.SolveStatic()

#the spring is stretched by F/k
exu.sys['testResult'] = mbs.GetNodeOutput(node, exu.OutputVariableType.Displacement)[2] #-0.1

Examples (Ex) and TestModels (TM) that show this item, with weblink to github: tutorialSpringDamperCreate.py (Ex), tutorialRigidBodyCreate.py (Ex), rigidPendulum.py (Ex), pendulum2Dconstraint.py (Ex), cartesianSpringDamper.py (Ex)