World

World coordinate system + gravity field + default animation definition

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.

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 (34)

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))
mu	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
groundLength_v	Value: groundLength_u Type: Length (m) Description: Length of ground plane perpendicular to 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

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
	surface	Type: Surface

Used in Examples (37)

	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
	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)

	Engine1Base Modelica.Mechanics.MultiBody.Examples.Loops.Utilities Base model for one cylinder engine
	MechanicalStructure Modelica.Mechanics.MultiBody.Examples.Systems.RobotR3.Utilities 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
	DoubleArrow Modelica.Mechanics.MultiBody.Visualizers.Advanced Visualizing a double arrow with variable size