LoadTorqueVector

Load with (3D) torque vector; attached to rigidbody-based marker.

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

Interface

Python names: LoadTorqueVector or Torque, and VTorque for its visualization
Markers it acts on: those providing Orientation: MarkerBodyRigid, MarkerNodeRigid, MarkerSuperElementRigid, MarkerKinematicTreeRigid

Parameters

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

name	type	size	default	description
name	String		‘’	load’s unique name
markerNumber	MarkerIndex		invalid (-1)	marker’s number to which load is applied
loadVector	Vector3D	3	[0.,0.,0.]	(symbol: \(\ttau\)) vector-valued load [SI:N]; in case of a user function, this vector is ignored
bodyFixed	Bool		False	if bodyFixed is true, the load is defined in body-fixed (local) coordinates, leading to a follower torque; if false: global coordinates are used
loadVectorUserFunction	LoadTorqueVectorLoadVectorUserFunction		0	(symbol: \(\mathrm{UF} \in \Rcal^3\)) A Python function which defines the time-dependent load and replaces loadVector; see description below; see also notes on loadFactor and drawing in LoadForceVector! Example for Python function: def f(mbs, t, loadVector): return [loadVector[0]np.sin(t1023.1415),0,0]
visualization	VLoadTorqueVector			parameters for visualization of item

Visualization parameters

The parameters of VLoadTorqueVector, 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 loads; a double arrow.

Detailed description

Load and its frame

The torque \(\ttau\) = loadVector, or the return value of loadVectorUserFunction, acts on the body or node of the marker, which must provide an orientation (MarkerBodyRigid, MarkerNodeRigid). With bodyFixed = False it is given in the global frame, \(\LU{0}{\ttau} = \ttau\); with bodyFixed = True in the frame of the marker, turning with it, and transformed into the global frame with the rotation matrix of the marker,

\[ \LU{0}{\ttau} = \LU{0m}{\Rot}\, \LU{m}{\ttau} . \]

Generalized forces

The global torque enters the equations through the rotation Jacobian of the marker, the derivative of the global angular velocity with respect to the velocity coordinates, \(\LU{0}{\Jm_{rot}} = \partial \LU{0}{\tomega}_m / \partial \dot\qv\),

\[ \Qm = \LU{0}{\Jm_{rot}}\tp\, \LU{0}{\ttau} . \]

For a rigid body node, \(\LU{0}{\Jm_{rot}}\) contains the velocity transformation \(\LU{0}{\Gm}\) of its rotation parameters, which is how a torque reaches Euler parameters or angles, see the page of the node. The load factor applies as for a force.

Userfunction: loadVectorUserFunction(mbs, t, loadVector) A user function, which computes the torque vector depending on time and object parameters, which is hereafter applied to object or node.

arguments / return	type or size	description
`mbs`	MainSystem	provides MainSystem mbs to which load belongs
`t`	Real	current time in mbs
`loadVector`	Vector3D	\(\ttau\) copied from object; WARNING: this parameter does not work in combination with static computation, as it is changed by the solver over step time
return value	Vector3D	computed torque vector

Example:

from math import sin, cos, pi
def UFforce(mbs, t, loadVector):
    return [loadVector[0]*sin(t*10*2*pi),0,0]

Mini example

#a torque about z spins a rigid body up
inertia = InertiaCuboid(density=1000, sideLengths=[0.4,0.2,0.1])
node = mbs.AddNode(NodeRigidBodyEP(referenceCoordinates=[0.5,0.2,0.1]+eulerParameters0))
body = mbs.AddObject(ObjectRigidBody(nodeNumber=node, mass=inertia.Mass(),
                                     inertia=inertia.GetInertia6D()))
mBody = mbs.AddMarker(MarkerBodyRigid(bodyNumber=body, localPosition=[0,0,0]))
mbs.AddLoad(LoadTorqueVector(markerNumber=mBody, loadVector=[0,0,1]))

mbs.Assemble()
mbs.SolveDynamic()

#angular velocity = M/J_zz*t at t=1
Jzz = inertia.GetInertia6D()[2]
exu.sys['testResult'] = mbs.GetNodeOutput(node, exu.OutputVariableType.AngularVelocity)[2]*Jzz #1, to the accuracy of the time integration

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