ObjectJointRevolute2D

A revolute joint in 2D; constrains the absolute 2D position of two points given by PointMarkers or RigidMarkers

Interface

Python names: ObjectJointRevolute2D or RevoluteJoint2D, and VRevoluteJoint2D 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 ‘JointRevolute2D’:

name	type	default	description
name	String	‘’	constraints’s unique name
markerNumbers	ArrayMarkerIndex	[ invalid (-1), invalid (-1) ]	list of markers used in connector
activeConnector	Bool	True	flag, which determines, if the connector is active; used to deactivate (temporarily) a connector or constraint
visualization	VObjectJointRevolute2D		parameters for visualization of item

Visualization parameters

The parameters of VObjectJointRevolute2D, 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.	drawing size = radius of revolute joint; size == -1.f means that default connector size is used
color	Float4	4	[-1.,-1.,-1.,-1.]	RGBA connector color; if R==-1, use default color

Drawing

Drawn as all joints; a circle of diameter drawSize at each marker, the one of marker 0 red.

Output variables

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

output variable	symbol	description
Displacement	\(\LU{0}{\pv}_{m1} - \LU{0}{\pv}_{m0}\)	global vector from marker m0 to marker m1, zero up to the drift of the position on the velocity level
Position	\(\LU{0}{\pv}_{m0}\)	current global position of position marker \(m0\)
Velocity	\(\LU{0}{\vv}_{m0}\)	current global velocity of position marker \(m0\)
Force	\(\LU{0}{\fv} = [\lambda_0,\,\lambda_1,\,0]\tp\)	global joint force; as for the other joints the force on marker m0

Detailed description

Definition of quantities

intermediate variables	symbol	description
marker m0 position	\(\LU{0}{\pv}_{m0}\)	global position provided by marker m0
marker m1 position	\(\LU{0}{\pv}_{m1}\)	global position provided by marker m1
marker velocities	\(\LU{0}{\vv}_{m0}\), \(\LU{0}{\vv}_{m1}\)	global velocities of the two markers
Lagrange multipliers	\(\tlambda = [\lambda_0,\,\lambda_1]\tp\)	the joint force in \(x\) and \(y\)

Connector constraint equations

The two points coincide in the \(x\)-\(y\) plane; the rotation about \(z\) is free. On the position level (index 3)

\[ \vp{p_{m1,x} - p_{m0,x}}{p_{m1,y} - p_{m0,y}} = \Null , \]

and on the velocity level (index 2) the same with the velocities. The multipliers act on the markers with the \(x\) and \(y\) rows of the position Jacobians, \(\pm\LU{0}{\Jm_{pos}}\tp\tlambda\). With activeConnector = False the equations become \(\tlambda = \Null\).

Mini example

#a planar rigid body pendulum held at its end by a planar revolute joint
node = mbs.AddNode(NodeRigidBody2D(referenceCoordinates=[0.5,0,0]))
body = mbs.AddObject(ObjectRigidBody2D(nodeNumber=node, mass=1, inertia=1/12))
mbs.AddLoad(LoadForceVector(markerNumber=mbs.AddMarker(MarkerBodyPosition(bodyNumber=body)), loadVector=[0,-9.81,0]))
mGround = mbs.AddMarker(MarkerBodyPosition(bodyNumber=oGround, localPosition=[0,0,0]))
mBody = mbs.AddMarker(MarkerBodyPosition(bodyNumber=body, localPosition=[-0.5,0,0]))
mbs.AddObject(ObjectJointRevolute2D(markerNumbers=[mGround, mBody]))

mbs.Assemble()
simulationSettings = exu.SimulationSettings()
simulationSettings.timeIntegration.numberOfSteps = 1000
mbs.SolveDynamic(simulationSettings)

#the pendulum falls from horizontal; the angle after 1 second (numerical)
exu.sys['testResult'] = mbs.GetNodeOutput(node, exu.OutputVariableType.Coordinates)[2]

Examples (Ex) and TestModels (TM) that show this item, with weblink to github: rigidPendulum.py (Ex), doublePendulum2D.py (Ex), SliderCrank.py (Ex), simple4linkPendulumBing.py (Ex), slidercrankWithMassSpring.py (Ex)