WOLFRAM SYSTEMMODELER

World

World coordinate system + gravity field + default animation definition

Wolfram Language

In[1]:=
SystemModel["Modelica.Mechanics.MultiBody.World"]
Out[1]:=

Information

This information is part of the Modelica Standard Library maintained by the Modelica Association.

Model World represents a global coordinate system fixed in ground. This model serves several purposes:

  • It is used as inertial system in which the equations of all elements of the MultiBody library are defined.
  • It is the world frame of an animation window in which all elements of the MultiBody library are visualized.
  • It is used to define the gravity field in which a multi-body model is present. Default is a uniform gravity field where the gravity acceleration vector g is the same at every position. Additionally, a point gravity field or no gravity can be selected. Also, function gravityAcceleration can be redeclared to a user-defined function that computes the gravity acceleration, see example Examples.Elementary.UserDefinedGravityField.
  • It is used to define default settings of animation properties (e.g., the diameter of a sphere representing by default the center of mass of a body, or the diameters of the cylinders representing a revolute joint).
  • It is used to define a visual representation of the world model (= 3 coordinate axes with labels), of the defined gravity field and of a ground plane perpendicular to the gravity direction.
    MultiBody.World

Since the gravity field function is required from all bodies with mass and the default settings of animation properties are required from nearly every component, exactly one instance of model World needs to be present in every model on the top level. The basic declaration needs to be:

inner Modelica.Mechanics.MultiBody.World world

Note, it must be an inner declaration with instance name world in order that this world object can be accessed from all objects in the model. When dragging the "World" object from the package browser into the diagram layer, this declaration is automatically generated (this is defined via annotations in model World).

All vectors and tensors of a mechanical system are resolved in a frame that is local to the corresponding component. Usually, if all relative joint coordinates vanish, the local frames of all components are parallel to each other, as well as to the world frame (this holds as long as a Parts.FixedRotation, component is not used). In this "reference configuration" it is therefore alternatively possible to resolve all vectors in the world frame, since all frames are parallel to each other. This is often very convenient. In order to give some visual support in such a situation, in the icon of a World instance two axes of the world frame are shown and the labels of these axes can be set via parameters.

Parameters (33)

enableAnimation

Value: true

Type: Boolean

Description: = true, if animation of all components is enabled

animateWorld

Value: true

Type: Boolean

Description: = true, if world coordinate system shall be visualized

animateGravity

Value: true

Type: Boolean

Description: = true, if gravity field shall be visualized (acceleration vector or field center)

animateGround

Value: false

Type: Boolean

Description: = true, if ground plane shall be visualized

label1

Value: "x"

Type: AxisLabel

Description: Label of horizontal axis in icon

label2

Value: "y"

Type: AxisLabel

Description: Label of vertical axis in icon

gravityType

Value: GravityTypes.UniformGravity

Type: GravityTypes

Description: Type of gravity field

g

Value: Modelica.Constants.g_n

Type: Acceleration (m/s²)

Description: Constant gravity acceleration

n

Value: {0, -1, 0}

Type: Axis

Description: Direction of gravity resolved in world frame (gravity = g*n/length(n))

mue

Value: 3.986004418e14

Type: Real (m³/s²)

Description: Gravity field constant (default = field constant of earth)

driveTrainMechanics3D

Value: true

Type: Boolean

Description: = true, if 3-dim. mechanical effects of Parts.Mounting1D/Rotor1D/BevelGear1D shall be taken into account

axisLength

Value: nominalLength / 2

Type: Distance (m)

Description: Length of world axes arrows

axisDiameter

Value: axisLength / defaultFrameDiameterFraction

Type: Distance (m)

Description: Diameter of world axes arrows

axisShowLabels

Value: true

Type: Boolean

Description: = true, if labels shall be shown

gravityArrowTail

Value: {0, 0, 0}

Type: Position[3] (m)

Description: Position vector from origin of world frame to arrow tail, resolved in world frame

gravityArrowLength

Value: axisLength / 2

Type: Length (m)

Description: Length of gravity arrow

gravityArrowDiameter

Value: gravityArrowLength / defaultWidthFraction

Type: Diameter (m)

Description: Diameter of gravity arrow

gravitySphereDiameter

Value: 12742000

Type: Diameter (m)

Description: Diameter of sphere representing gravity center (default = mean diameter of earth)

groundAxis_u

Value: if abs(n[1]) >= 0.99 then {0, 1, 0} else {1, 0, 0}

Type: Axis

Description: Vector along 1st axis (called u) of ground plane, resolved in world frame (should be perpendicular to gravity direction)

groundLength_u

Value: 2

Type: Length (m)

Description: Length of ground plane along groundAxis_u

nominalLength

Value: 1

Type: Length (m)

Description: "Nominal" length of multi-body system

defaultAxisLength

Value: nominalLength / 5

Type: Length (m)

Description: Default for length of a frame axis (but not world frame)

defaultJointLength

Value: nominalLength / 10

Type: Length (m)

Description: Default for the fixed length of a shape representing a joint

defaultJointWidth

Value: nominalLength / 20

Type: Length (m)

Description: Default for the fixed width of a shape representing a joint

defaultForceLength

Value: nominalLength / 10

Type: Length (m)

Description: Default for the fixed length of a shape representing a force (e.g., damper)

defaultForceWidth

Value: nominalLength / 20

Type: Length (m)

Description: Default for the fixed width of a shape representing a force (e.g., spring, bushing)

defaultBodyDiameter

Value: nominalLength / 9

Type: Length (m)

Description: Default for diameter of sphere representing the center of mass of a body

defaultWidthFraction

Value: 20

Type: Real

Description: Default for shape width as a fraction of shape length (e.g., for Parts.FixedTranslation)

defaultArrowDiameter

Value: nominalLength / 40

Type: Length (m)

Description: Default for arrow diameter (e.g., of forces, torques, sensors)

defaultFrameDiameterFraction

Value: 40

Type: Real

Description: Default for arrow diameter of a coordinate system as a fraction of axis length

defaultSpecularCoefficient

Value: 0.7

Type: Real

Description: Default reflection of ambient light (= 0: light is completely absorbed)

defaultN_to_m

Value: 1000

Type: Real (N/m)

Description: Default scaling of force arrows (length = force/defaultN_to_m)

defaultNm_to_m

Value: 1000

Type: Real (N·m/m)

Description: Default scaling of torque arrows (length = torque/defaultNm_to_m)

Inputs (6)

axisColor_x

Default Value: Modelica.Mechanics.MultiBody.Types.Defaults.FrameColor

Type: Color

Description: Color of x-arrow

axisColor_y

Default Value: axisColor_x

Type: Color

axisColor_z

Default Value: axisColor_x

Type: Color

Description: Color of z-arrow

gravityArrowColor

Default Value: {0, 230, 0}

Type: Color

Description: Color of gravity arrow

gravitySphereColor

Default Value: {0, 230, 0}

Type: Color

Description: Color of gravity sphere

groundColor

Default Value: {200, 200, 200}

Type: Color

Description: Color of ground plane

Connectors (1)

frame_b

Type: Frame_b

Description: Coordinate system fixed in the origin of the world frame

Components (13)

x_arrowLine

Type: Shape

x_arrowHead

Type: Shape

x_label

Type: Lines

y_arrowLine

Type: Shape

y_arrowHead

Type: Shape

y_label

Type: Lines

z_arrowLine

Type: Shape

z_arrowHead

Type: Shape

z_label

Type: Lines

gravityArrowLine

Type: Shape

gravityArrowHead

Type: Shape

gravitySphere

Type: Shape

vis

Type: Shape

Used in Examples (38)

DoublePendulum

Modelica.Mechanics.MultiBody.Examples.Elementary

Simple double pendulum with two revolute joints and two bodies

DoublePendulumInitTip

Modelica.Mechanics.MultiBody.Examples.Elementary

Demonstrate how to initialize a double pendulum so that its tip starts at a predefined position

ForceAndTorque

Modelica.Mechanics.MultiBody.Examples.Elementary

Demonstrate usage of ForceAndTorque element

FreeBody

Modelica.Mechanics.MultiBody.Examples.Elementary

Free flying body attached by two springs to environment

InitSpringConstant

Modelica.Mechanics.MultiBody.Examples.Elementary

Determine spring constant such that system is in steady state at given position

LineForceWithTwoMasses

Modelica.Mechanics.MultiBody.Examples.Elementary

Demonstrate line force with two point masses using a JointUPS and alternatively a LineForceWithTwoMasses component

Pendulum

Modelica.Mechanics.MultiBody.Examples.Elementary

Simple pendulum with one revolute joint and one body

PendulumWithSpringDamper

Modelica.Mechanics.MultiBody.Examples.Elementary

Simple spring/damper/mass system

PointGravity

Modelica.Mechanics.MultiBody.Examples.Elementary

Two point masses in a point gravity field

PointGravityWithPointMasses

Modelica.Mechanics.MultiBody.Examples.Elementary

Two point masses in a point gravity field (rotation of bodies is neglected)

PointGravityWithPointMasses2

Modelica.Mechanics.MultiBody.Examples.Elementary

Rigidly connected point masses in a point gravity field

SpringDamperSystem

Modelica.Mechanics.MultiBody.Examples.Elementary

Simple spring/damper/mass system

SpringMassSystem

Modelica.Mechanics.MultiBody.Examples.Elementary

Mass attached with a spring to the world frame

SpringWithMass

Modelica.Mechanics.MultiBody.Examples.Elementary

Point mass hanging on a spring

ThreeSprings

Modelica.Mechanics.MultiBody.Examples.Elementary

3-dim. springs in series and parallel connection

RollingWheel

Modelica.Mechanics.MultiBody.Examples.Elementary

Single wheel rolling on ground starting from an initial speed

RollingWheelSetDriving

Modelica.Mechanics.MultiBody.Examples.Elementary

Rolling wheel set that is driven by torques driving the wheels

RollingWheelSetPulling

Modelica.Mechanics.MultiBody.Examples.Elementary

Rolling wheel set that is pulled by a force

HeatLosses

Modelica.Mechanics.MultiBody.Examples.Elementary

Demonstrate the modeling of heat losses

UserDefinedGravityField

Modelica.Mechanics.MultiBody.Examples.Elementary

Demonstrate the modeling of a user-defined gravity field

Surfaces

Modelica.Mechanics.MultiBody.Examples.Elementary

Demonstrate the visualization of a sine surface, as well as a torus and a wheel constructed from a surface

Engine1a

Modelica.Mechanics.MultiBody.Examples.Loops

Model of one cylinder engine

EngineV6

Modelica.Mechanics.MultiBody.Examples.Loops

V6 engine with 6 cylinders, 6 planar loops and 1 degree-of-freedom

EngineV6_analytic

Modelica.Mechanics.MultiBody.Examples.Loops

V6 engine with 6 cylinders, 6 planar loops, 1 degree-of-freedom and analytic handling of kinematic loops

Fourbar1

Modelica.Mechanics.MultiBody.Examples.Loops

One kinematic loop with four bars (with only revolute joints; 5 non-linear equations)

Fourbar2

Modelica.Mechanics.MultiBody.Examples.Loops

One kinematic loop with four bars (with UniversalSpherical joint; 1 non-linear equation)

Fourbar_analytic

Modelica.Mechanics.MultiBody.Examples.Loops

One kinematic loop with four bars (with JointSSP joint; analytic solution of non-linear algebraic loop)

PlanarFourbar

Modelica.Mechanics.MultiBody.Examples.Loops

Planar four bars mechanism with one kinematic loop (with RevolutePlanarLoopConstraint joint)

PlanarLoops_analytic

Modelica.Mechanics.MultiBody.Examples.Loops

Mechanism with three planar kinematic loops and one degree-of-freedom with analytic loop handling (with JointRRR joints)

GyroscopicEffects

Modelica.Mechanics.MultiBody.Examples.Rotational3DEffects

Demonstrates that a cylindrical body can be replaced by Rotor1D model

ActuatedDrive

Modelica.Mechanics.MultiBody.Examples.Rotational3DEffects

Demonstrates usage of models Rotor1D and Mounting1D

MovingActuatedDrive

Modelica.Mechanics.MultiBody.Examples.Rotational3DEffects

Demonstrates usage of model Rotor1D mounted on a moving body

GearConstraint

Modelica.Mechanics.MultiBody.Examples.Rotational3DEffects

Demonstrate usage of GearConstraint model

BevelGear1D

Modelica.Mechanics.MultiBody.Examples.Rotational3DEffects

Demonstrates the usage of a BevelGear1D model and how to calculate the power of such an element

PrismaticConstraint

Modelica.Mechanics.MultiBody.Examples.Constraints

Body attached by one spring and two prismatic joints or constrained to environment

RevoluteConstraint

Modelica.Mechanics.MultiBody.Examples.Constraints

Body attached by one spring and revolute joint or constrained to environment

SphericalConstraint

Modelica.Mechanics.MultiBody.Examples.Constraints

Body attached by one spring and spherical joint or constrained to environment

UniversalConstraint

Modelica.Mechanics.MultiBody.Examples.Constraints

Body attached by one spring and universal joint or constrained to environment

Used in Components (31)

Engine1bBase

Modelica.Mechanics.MultiBody.Examples.Loops.Utilities

Model of one cylinder engine with gas force

MechanicalStructure

Modelica.Mechanics.MultiBody.Examples.Systems.RobotR3.Components

Model of the mechanical part of the r3 robot (without animation)

PartialTwoFrames

Modelica.Mechanics.MultiBody.Interfaces

Base model for components providing two frame connectors + outer world + assert to guarantee that the component is connected

PartialTwoFramesDoubleSize

Modelica.Mechanics.MultiBody.Interfaces

Base model for components providing two frame connectors + outer world + assert to guarantee that the component is connected (default icon size is factor 2 larger as usual)

PartialOneFrame_a

Modelica.Mechanics.MultiBody.Interfaces

Base model for components providing one frame_a connector + outer world + assert to guarantee that the component is connected

PartialOneFrame_b

Modelica.Mechanics.MultiBody.Interfaces

Base model for components providing one frame_b connector + outer world + assert to guarantee that the component is connected

PartialElementaryJoint

Modelica.Mechanics.MultiBody.Interfaces

Base model for elementary joints (has two frames + outer world + assert to guarantee that the joint is connected)

PartialAbsoluteSensor

Modelica.Mechanics.MultiBody.Interfaces

Base model to measure an absolute frame variable

PartialRelativeSensor

Modelica.Mechanics.MultiBody.Interfaces

Base model to measure a relative variable between two frames

PartialVisualizer

Modelica.Mechanics.MultiBody.Interfaces

Base model for visualizers (has a frame_a on the left side + outer world + assert to guarantee that the component is connected)

Revolute

Modelica.Mechanics.MultiBody.Joints

Revolute joint (1 rotational degree-of-freedom, 2 potential states, optional axis flange)

RevolutePlanarLoopConstraint

Modelica.Mechanics.MultiBody.Joints

Revolute joint that is described by 2 positional constraints for usage in a planar loop (the ambiguous cut-force perpendicular to the loop and the ambiguous cut-torques are set arbitrarily to zero)

Fixed

Modelica.Mechanics.MultiBody.Parts

Frame fixed in the world frame at a given position

FixedTranslation

Modelica.Mechanics.MultiBody.Parts

Fixed translation of frame_b with respect to frame_a

FixedRotation

Modelica.Mechanics.MultiBody.Parts

Fixed translation followed by a fixed rotation of frame_b with respect to frame_a

Body

Modelica.Mechanics.MultiBody.Parts

Rigid body with mass, inertia tensor and one frame connector (12 potential states)

BodyShape

Modelica.Mechanics.MultiBody.Parts

Rigid body with mass, inertia tensor, different shapes for animation, and two frame connectors (12 potential states)

BodyBox

Modelica.Mechanics.MultiBody.Parts

Rigid body with box shape. Mass and animation properties are computed from box data and density (12 potential states)

BodyCylinder

Modelica.Mechanics.MultiBody.Parts

Rigid body with cylinder shape. Mass and animation properties are computed from cylinder data and density (12 potential states)

PointMass

Modelica.Mechanics.MultiBody.Parts

Rigid body where body rotation and inertia tensor is neglected (6 potential states)

Mounting1D

Modelica.Mechanics.MultiBody.Parts

Propagate 1-dim. support torque to 3-dim. system (provided world.driveTrainMechanics3D=true)

Rotor1D

Modelica.Mechanics.MultiBody.Parts

1D inertia attachable on 3-dim. bodies (3D dynamic effects are taken into account if world.driveTrainMechanics3D=true)

RotorWith3DEffects

Modelica.Mechanics.MultiBody.Parts.Rotor1D

1D inertia attachable on 3-dim. bodies (3D dynamic effects are taken into account)

BevelGear1D

Modelica.Mechanics.MultiBody.Parts

1D gearbox with arbitrary shaft directions and 3-dim. bearing frame (3D dynamic effects are taken into account provided world.driveTrainMechanics3D=true)

AbsoluteSensor

Modelica.Mechanics.MultiBody.Sensors

Measure absolute kinematic quantities of frame connector

RelativeSensor

Modelica.Mechanics.MultiBody.Sensors

Measure relative kinematic quantities between two frame connectors

PartialCutForceSensor

Modelica.Mechanics.MultiBody.Sensors.Internal

Base class to measure cut force and/or torque between two frames, defined by components

PartialCutForceBaseSensor

Modelica.Mechanics.MultiBody.Sensors.Internal

Base class to measure cut force and/or torque between two frames, defined by equations (frame_resolve must be connected exactly once)

FixedShape2

Modelica.Mechanics.MultiBody.Visualizers

Visualizing an elementary shape with dynamically varying shape attributes (has two frame connectors)

Arrow

Modelica.Mechanics.MultiBody.Visualizers.Advanced

Visualizing an arrow with variable size; all data have to be set as modifiers (see info layer)

DoubleArrow

Modelica.Mechanics.MultiBody.Visualizers.Advanced

Visualizing a double arrow with variable size; all data have to be set as modifiers (see info layer)