<!-- GENERATED by tools/generators/itemDocsEmitter.py from definitions/ - do not edit -->
```{raw} latex
\clearpage
```

(sec-item-objectjointrevolute2d)=
# ObjectJointRevolute2D

A revolute joint in 2D; constrains the absolute 2D position of two points given by PointMarkers or RigidMarkers
```{image} /docs/figures/itemImages/ObjectJointRevolute2D.png
:width: 500
```

## Interface

- Python names: `ObjectJointRevolute2D` or `RevoluteJoint2D`, and `VRevoluteJoint2D` for its visualization
- Markers it acts on: those providing `Position`: [](#sec-item-markerbodyposition), [](#sec-item-markerbodyrigid), [](#sec-item-markernodeposition), [](#sec-item-markernoderigid), [](#sec-item-markersuperelementposition), [](#sec-item-markersuperelementrigid), [](#sec-item-markerkinematictreerigid)

## Parameters

The parameters of the item; in a dictionary, its type is 'JointRevolute2D':

| name | type | size | 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](#sec-drawing-objectsjoint); 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:

```{tabularcolumns} \Y{0.25}\Y{0.25}\Y{0.5}
```

| 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 |

(description-objectjointrevolute2d)=
## 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 $\tlambda = \Null$.

(miniexample-objectjointrevolute2d)=
## Mini example


```python
#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`](https://github.com/jgerstmayr/EXUDYN/blob/master/python/Examples/rigidPendulum.py) (Ex), [`doublePendulum2D.py`](https://github.com/jgerstmayr/EXUDYN/blob/master/python/Examples/doublePendulum2D.py) (Ex), [`SliderCrank.py`](https://github.com/jgerstmayr/EXUDYN/blob/master/python/Examples/SliderCrank.py) (Ex), [`simple4linkPendulumBing.py`](https://github.com/jgerstmayr/EXUDYN/blob/master/python/Examples/simple4linkPendulumBing.py) (Ex), [`slidercrankWithMassSpring.py`](https://github.com/jgerstmayr/EXUDYN/blob/master/python/Examples/slidercrankWithMassSpring.py) (Ex)