MarkerNodeRigid

A rigid-body (position+orientation) node-marker attached to a rigid-body node. It provides position and orientation (rotation), as well as the according derivatives. It can be used for most connectors, joints or loads where either position, position and orientation, or orientation are required.

Interface

Provides: Position, Orientation
Nodes it can be attached to: NodeRigidBodyEP, NodeRigidBodyRxyz, NodeRigidBodyRotVecLG, NodeRigidBody2D, NodePoint2DSlope1, NodePointSlope12, NodePointSlope23, NodePointGround
Connectors, constraints and loads that can use it: ObjectConnectorSpringDamper, ObjectConnectorCartesianSpringDamper, ObjectConnectorRigidBodySpringDamper, ObjectConnectorLinearSpringDamper, ObjectConnectorTorsionalSpringDamper, ObjectConnectorGravity, ObjectConnectorHydraulicActuatorSimple, ObjectConnectorDistance, ObjectConnectorRollingDiscPenalty, ObjectContactConvexRoll, ObjectContactSphereSphere, ObjectContactSphereTorus, ObjectContactSphereTriangle, ObjectContactCurveCircles, ObjectJointGeneric, ObjectJointRevoluteZ, ObjectJointPrismaticX, ObjectJointSpherical, ObjectJointRollingDisc, ObjectJointRevolute2D, ObjectJointPrismatic2D, LoadForceVector, LoadTorqueVector

Parameters

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

name	type	default	description
name	String	‘’	marker’s unique name
nodeNumber	NodeIndex	invalid (-1)	node number to which marker is attached to
localHT	HomogeneousTransformation	None (identity)	(symbol: \(\LU{n}{\Hm}_{m}\)) the frame of the marker in the node frame, as homogeneous transformation: its rotation turns the marker frame against the node; its translation must be zero for now; a 4x4 matrix, its 16 values row by row or an exu.HT; None: the node frame
visualization	VMarkerNodeRigid		parameters for visualization of item

Visualization parameters

The parameters of VMarkerNodeRigid, 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 position of the node
velocity	\(\LU{0}{\vv}_m\)	the velocity of the node
rotation matrix	\(\LU{0m}{\Rot} = \LU{0n}{\Rot} \LU{nm}{\Rot}\)	the rotation matrix of the node, turned by the rotation \(\LU{nm}{\Rot}\) of `localHT`
angular velocity	\(\LU{m}{\tomega} = \LU{nm}{\Rot}\tp \LU{n}{\tomega}\)	the angular velocity of the node, in the marker frame

The translation of localHT must be zero: the marker is at the node.

Jacobians

\[ \LU{0}{\Jm_{pos}} = \frac{\partial \LU{0}{\pv}}{\partial \qv} , \quad \LU{0}{\Jm_{rot}} = \frac{\partial \LU{0}{\tomega}}{\partial \dot\qv} , \]

with respect to the coordinates of the node; for a rigid body node \(\LU{0}{\Jm_{rot}}\) is the velocity transformation \(\LU{0}{\Gm}\) of its rotation parameters in the rotation columns, see the page of the node. For a slope node the orientation is that of its slope vector(s).

Mini example

#position and orientation of a rigid body node: a torque spins the body up
inertia = InertiaCuboid(density=1000, sideLengths=[0.4,0.2,0.1])
node = mbs.AddNode(NodeRigidBodyRxyz(referenceCoordinates=[0.5,0.2,0.1, 0,0,0]))
mbs.AddObject(ObjectRigidBody(nodeNumber=node, mass=inertia.Mass(),
                              inertia=inertia.GetInertia6D()))
mNode = mbs.AddMarker(MarkerNodeRigid(nodeNumber=node))
mbs.AddLoad(LoadTorqueVector(markerNumber=mNode, loadVector=[0,0,1]))

mbs.Assemble()
mbs.SolveDynamic()

#angle = M/(2*J_zz)*t^2 at t=1
Jzz = inertia.GetInertia6D()[2]
exu.sys['testResult'] = mbs.GetNodeOutput(node, exu.OutputVariableType.Rotation)[2]*2*Jzz #1

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