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ObjectRigidBody2D.rst

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ObjectRigidBody2D

A 2D rigid body which is attached to a rigid body 2D node. The body obtains coordinates, position, velocity, etc. from the underlying 2D node

Additional information for ObjectRigidBody2D:

  • This Object has/provides the following types = Body, SingleNoded
  • Requested Node type = Position2D + Orientation2D + Position + Orientation
  • Short name for Python = RigidBody2D
  • Short name for Python visualization object = VRigidBody2D

The item ObjectRigidBody2D with type = 'RigidBody2D' has the following parameters:

  • name [type = String, default = '']:
    objects's unique name
  • physicsMass [m, type = UReal, default = 0.]:
    mass [SI:kg] of rigid body
  • physicsInertia [J, type = UReal, default = 0.]:
    inertia [SI:kgm^2] of rigid body w.r.t. center of mass
  • nodeNumber [n_0, type = NodeIndex, default = invalid (-1)]:
    node number (type NodeIndex) for 2D rigid body node
  • visualization [type = VObjectRigidBody2D]:
    parameters for visualization of item

The item VObjectRigidBody2D has the following parameters:

  • show [type = Bool, default = True]:
    set true, if item is shown in visualization and false if it is not shown
  • graphicsDataUserFunction [type = PyFunctionGraphicsData, default = 0]:
    A Python function which returns a bodyGraphicsData object, which is a list of graphics data in a dictionary computed by the user function; the graphics elements need to be defined in the local body coordinates and are transformed by mbs to global coordinates
  • graphicsData [type = BodyGraphicsData]:
    Structure contains data for body visualization; data is defined in special list / dictionary structure

DESCRIPTION of ObjectRigidBody2D

The following output variables are available as OutputVariableType in sensors, Get...Output() and other functions:

  • Position: \LU{0}{{\mathbf{p}}}\cConfig(\pLocB) = \LU{0}{\pRef}\cConfig + \LU{0}{\pRef}\cRef + \LU{0b}{\Rot}\pLocB
    global position vector of body-fixed point given by local position vector \pLocB
  • Displacement: \LU{0}{{\mathbf{u}}}\cConfig + \LU{0b}{\Rot}\pLocB
    global displacement vector of body-fixed point given by local position vector \pLocB
  • Velocity: \LU{0}{{\mathbf{v}}}\cConfig(\pLocB) = \LU{0}{\dot{\mathbf{u}}}\cConfig + \LU{0b}{\Rot}(\LU{b}{\tomega} \times \pLocB\cConfig)
    global velocity vector of body-fixed point given by local position vector \pLocB
  • VelocityLocal: \LU{b}{{\mathbf{v}}}\cConfig(\pLocB) = \LU{b0}{\Rot} \LU{0}{{\mathbf{v}}}\cConfig(\pLocB)
    local (body-fixed) velocity vector of body-fixed point given by local position vector \pLocB
  • RotationMatrix: \mathrm{vec}(\LU{0b}{\Rot})=[A_{00},\,A_{01},\,A_{02},\,A_{10},\,\ldots,\,A_{21},\,A_{22}]\cConfig\tp
    vector with 9 components of the rotation matrix (row-major format)
  • Rotation: \theta_{0\mathrm{config}}
    scalar rotation angle of body
  • AngularVelocity: \LU{0}{\tomega}\cConfig
    angular velocity of body
  • AngularVelocityLocal: \LU{b}{\tomega}\cConfig
    local (body-fixed) 3D velocity vector of node
  • Acceleration: \LU{0}{{\mathbf{a}}}\cConfig(\pLocB) = \LU{0}{\ddot{\mathbf{u}}} + \LU{0}{\talpha} \times (\LU{0b}{\Rot} \pLocB) + \LU{0}{\tomega} \times ( \LU{0}{\tomega} \times(\LU{0b}{\Rot} \pLocB))
    global acceleration vector of body-fixed point given by local position vector \pLocB
  • AccelerationLocal: \LU{b}{{\mathbf{a}}}\cConfig(\pLocB) = \LU{b0}{\Rot} \LU{0}{{\mathbf{a}}}\cConfig(\pLocB)
    local (body-fixed) acceleration vector of body-fixed point given by local position vector \pLocB
  • AngularAcceleration: \LU{0}{\talpha}\cConfig
    angular acceleration vector of body
  • AngularAccelerationLocal: \LU{b}{\talpha}\cConfig = \LU{b0}{\Rot} \LU{0}{\talpha}\cConfig
    local angular acceleration vector of body

Definition of quantities

intermediate variables
symbol
description
\pRefG\cConfig + \pRefG\cRef = \LU{0}{{\mathbf{p}}}(n_0)\cConfig
reference point, equal to the position of :ref:`COM <COM>`; provided by node n_0 in any configuration (except reference)
:ref:`COM <COM>` displacement
\LU{0}{{\mathbf{u}}}\cConfig =\pRefG\cConfig = [q_0,\;q_1,\;0]\cConfig\tp = \LU{0}{{\mathbf{u}}}(n_0)\cConfig
displacement of center of mass which is provided by node n_0 in any configuration; NOTE that for configurations other than reference, it is follows that \pRefG\cRef - \pRefG\cConfig
\LU{0}{{\mathbf{v}}}\cConfig = [\dot q_0,\;\dot q_1,\;0]\cConfig\tp = \LU{0}{{\mathbf{v}}}(n_0)\cConfig
velocity of center of mass which is provided by node n_0 in any configuration
body rotation
\LU{0}{\theta}_{0\mathrm{config}} = \theta_0(n_0)\cConfig = \psi_0(n_0)\cRef + \psi_0(n_0)\cConfig
rotation of body as provided by node n_0 in any configuration
body rotation matrix
\LU{0b}{\Rot}\cConfig = \LU{0b}{\Rot}(n_0)\cConfig
rotation matrix which transforms local to global coordinates as given by node
local position
\pLocB = [\LU{b}{b_0},\,\LU{b}{b_1},\,0]\tp
local position as used by markers or sensors
body angular velocity
\LU{0}{\tomega}\cConfig = \LU{0}{[\omega_0(n_0),\,0,\,0]}\cConfig\tp
rotation of body as provided by node n_0 in any configuration
(generalized) coordinates
{\mathbf{c}}\cConfig = [q_0,q_1,\;\psi_0]\tp
generalized coordinates of body (= coordinates of node)
generalized forces
\LU{0}{{\mathbf{f}}} = [f_0,\;f_1,\;\tau_2]\tp
generalized forces applied to body
applied forces
\LU{0}{{\mathbf{f}}}_a = [f_0,\;f_1,\;0]\tp
applied forces (loads, connectors, joint reaction forces, ...)
applied torques
\LU{0}{\ttau}_a = [0,\;0,\;\tau_2]\tp
applied torques (loads, connectors, joint reaction forces, ...)

Equations of motion

\mr{m}{0}{0} {0}{m}{0} {0}{0}{J} \vr{\ddot q_0}{\ddot q_1}{\ddot \psi_0} = \vr{f_0}{f_1}{\tau_2} = {\mathbf{f}}.

For example, a LoadCoordinate on coordinate 2 of the node would add a torque \tau_2 on the RHS.

Position-based markers can measure position {\mathbf{p}}\cConfig(\pLocB) depending on the local position \pLocB. The position jacobian depends on the local position \pLocB and is defined as,

\LU{0}{{\mathbf{J}}_{pos}} = \partial \LU{0}{{\mathbf{p}}}\cConfig(\pLocB)\cCur / \partial {\mathbf{c}}\cCur = \mr{1}{0}{-\sin(\theta)\LU{b}{b_0} - \cos(\theta)\LU{b}{b_1}} {0}{1}{\cos(\theta)\LU{b}{b_0}-\sin(\theta)\LU{b}{b_1}} {0}{0}{0}

which transforms the action of global forces \LU{0}{{\mathbf{f}}} of position-based markers on the coordinates {\mathbf{c}},

{\mathbf{Q}} = \LU{0}{{\mathbf{J}}_{pos}\tp} \LU{0}{{\mathbf{f}}}_a

The rotation jacobian, which is computed from angular velocity, reads

\LU{0}{{\mathbf{J}}_{rot}} = \partial \LU{0}{\tomega}\cCur / \partial \dot {\mathbf{c}}\cCur = \mr{0}{0}{0} {0}{0}{0} {0}{0}{1}

and transforms the action of global torques \LU{0}{\ttau} of orientation-based markers on the coordinates {\mathbf{c}},

{\mathbf{Q}} = \LU{0}{{\mathbf{J}}_{rot}\tp} \, \LU{0}{\ttau}_a

Userfunction: graphicsDataUserFunction(mbs, itemNumber)

A user function, which is called by the visualization thread in order to draw user-defined objects. The function can be used to generate any BodyGraphicsData, see Section :ref:`sec-graphicsdata`. Use graphicsDataUtilities functions, see Section :ref:`sec-module-graphicsdatautilities`, to create more complicated objects. Note that graphicsDataUserFunction needs to copy lots of data and is therefore inefficient and only designed to enable simpler tests, but not large scale problems.

For an example for graphicsDataUserFunction see ObjectGround, Section :ref:`sec-item-objectground`.

arguments / return
type or size
description
mbs
MainSystem
provides reference to mbs, which can be used in user function to access all data of the object
itemNumber
int
integer number of the object in mbs, allowing easy access
returnValue
BodyGraphicsData
list of GraphicsData dictionaries, see Section :ref:`sec-graphicsdata`

MINI EXAMPLE for ObjectRigidBody2D

node = mbs.AddNode(NodeRigidBody2D(referenceCoordinates = [1,1,0.25*np.pi],
                                   initialCoordinates=[0.5,0,0],
                                   initialVelocities=[0.5,0,0.75*np.pi]))
mbs.AddObject(RigidBody2D(nodeNumber = node, physicsMass=1, physicsInertia=2))

#assemble and solve system for default parameters
mbs.Assemble()
mbs.SolveDynamic()

#check result
exudynTestGlobals.testResult = mbs.GetNodeOutput(node, exu.OutputVariableType.Position)[0]
exudynTestGlobals.testResult+= mbs.GetNodeOutput(node, exu.OutputVariableType.Coordinates)[2]
#final x-coordinate of position shall be 2, angle theta shall be np.pi

Relevant Examples and TestModels with weblink:

beltDriveALE.py (Examples/), beltDriveReevingSystem.py (Examples/), beltDrivesComparison.py (Examples/), reevingSystem.py (Examples/), reevingSystemOpen.py (Examples/), sliderCrank3DwithANCFbeltDrive2.py (Examples/), ANCFmovingRigidbody.py (Examples/), ANCFslidingJoint2D.py (Examples/), ANCFslidingJoint2Drigid.py (Examples/), ANCFswitchingSlidingJoint2D.py (Examples/), doublePendulum2D.py (Examples/), finiteSegmentMethod.py (Examples/), ANCFbeltDrive.py (TestModels/), ANCFgeneralContactCircle.py (TestModels/), ANCFcontactFrictionTest.py (TestModels/)

The web version may not be complete. For details, consider also the Exudyn PDF documentation : theDoc.pdf