model World "World coordinate system + gravity field + default animation definition"
import Modelica.Mechanics.MultiBody.Types.GravityTypes;
import Modelica.Mechanics.MultiBody.Types;
import Modelica.Constants.pi;
Interfaces.Frame_b frame_b "Coordinate system fixed in the origin of the world frame"
annotation (Placement(transformation(extent = {
{84, -16},
{116, 16}})));
parameter Boolean enableAnimation = true "= true, if animation of all components is enabled";
parameter Boolean animateWorld = true "= true, if world coordinate system shall be visualized"
annotation (Dialog(enable = enableAnimation));
parameter Boolean animateGravity = true "= true, if gravity field shall be visualized (acceleration vector or field center)"
annotation (Dialog(enable = enableAnimation));
parameter Boolean animateGround = false "= true, if ground plane shall be visualized"
annotation (Dialog(enable = enableAnimation));
parameter Types.AxisLabel label1 = "x" "Label of horizontal axis in icon";
parameter Types.AxisLabel label2 = "y" "Label of vertical axis in icon";
parameter Types.GravityTypes gravityType = GravityTypes.UniformGravity "Type of gravity field"
annotation (Evaluate = true);
parameter SI.Acceleration g = Modelica.Constants.g_n "Constant gravity acceleration"
annotation (Dialog(enable = gravityType == Modelica.Mechanics.MultiBody.Types.GravityTypes.UniformGravity));
parameter Types.Axis n = {0, -1, 0} "Direction of gravity resolved in world frame (gravity = g*n/length(n))"
annotation (
Evaluate = true,
Dialog(enable = gravityType == Modelica.Mechanics.MultiBody.Types.GravityTypes.UniformGravity));
parameter Real mue(unit = "m3/s2", min = 0) = 3.986004418e+14 "Gravity field constant (default = field constant of earth)"
annotation (Dialog(enable = gravityType == Modelica.Mechanics.MultiBody.Types.GravityTypes.PointGravity));
parameter Boolean driveTrainMechanics3D = true "= true, if 3-dim. mechanical effects of Parts.Mounting1D/Rotor1D/BevelGear1D shall be taken into account";
parameter SI.Distance axisLength = 0.5 * nominalLength "Length of world axes arrows"
annotation (Dialog(
tab = "Animation",
group = "if animateWorld = true",
enable = enableAnimation and animateWorld));
parameter SI.Distance axisDiameter = axisLength / defaultFrameDiameterFraction "Diameter of world axes arrows"
annotation (Dialog(
tab = "Animation",
group = "if animateWorld = true",
enable = enableAnimation and animateWorld));
parameter Boolean axisShowLabels = true "= true, if labels shall be shown"
annotation (Dialog(
tab = "Animation",
group = "if animateWorld = true",
enable = enableAnimation and animateWorld));
input Types.Color axisColor_x = Modelica.Mechanics.MultiBody.Types.Defaults.FrameColor "Color of x-arrow"
annotation (Dialog(
colorSelector = true,
tab = "Animation",
group = "if animateWorld = true",
enable = enableAnimation and animateWorld));
input Types.Color axisColor_y = axisColor_x annotation (Dialog(
colorSelector = true,
tab = "Animation",
group = "if animateWorld = true",
enable = enableAnimation and animateWorld));
input Types.Color axisColor_z = axisColor_x "Color of z-arrow"
annotation (Dialog(
colorSelector = true,
tab = "Animation",
group = "if animateWorld = true",
enable = enableAnimation and animateWorld));
parameter SI.Position gravityArrowTail[3] = {0, 0, 0} "Position vector from origin of world frame to arrow tail, resolved in world frame"
annotation (Dialog(
tab = "Animation",
group = "if animateGravity = true and gravityType = UniformGravity",
enable = enableAnimation and animateGravity and gravityType == GravityTypes.UniformGravity));
parameter SI.Length gravityArrowLength = 0.5 * axisLength "Length of gravity arrow"
annotation (Dialog(
tab = "Animation",
group = "if animateGravity = true and gravityType = UniformGravity",
enable = enableAnimation and animateGravity and gravityType == GravityTypes.UniformGravity));
parameter SI.Diameter gravityArrowDiameter = gravityArrowLength / defaultWidthFraction "Diameter of gravity arrow"
annotation (Dialog(
tab = "Animation",
group = "if animateGravity = true and gravityType = UniformGravity",
enable = enableAnimation and animateGravity and gravityType == GravityTypes.UniformGravity));
input Types.Color gravityArrowColor = {0, 230, 0} "Color of gravity arrow"
annotation (Dialog(
colorSelector = true,
tab = "Animation",
group = "if animateGravity = true and gravityType = UniformGravity",
enable = enableAnimation and animateGravity and gravityType == GravityTypes.UniformGravity));
parameter SI.Diameter gravitySphereDiameter = 1.2742e+7 "Diameter of sphere representing gravity center (default = mean diameter of earth)"
annotation (Dialog(
tab = "Animation",
group = "if animateGravity = true and gravityType = PointGravity",
enable = enableAnimation and animateGravity and gravityType == GravityTypes.PointGravity));
input Types.Color gravitySphereColor = {0, 230, 0} "Color of gravity sphere"
annotation (Dialog(
colorSelector = true,
tab = "Animation",
group = "if animateGravity = true and gravityType = PointGravity",
enable = enableAnimation and animateGravity and gravityType == GravityTypes.PointGravity));
parameter MultiBody.Types.Axis groundAxis_u = if 0.99 <= abs(n[1]) then {0, 1, 0} else {1, 0, 0} "Vector along 1st axis (called u) of ground plane, resolved in world frame (should be perpendicular to gravity direction)"
annotation (Dialog(
tab = "Animation",
group = "if animateGround = true and gravityType = UniformGravity",
enable = enableAnimation and animateGround and gravityType == GravityTypes.UniformGravity));
parameter Modelica.SIunits.Length groundLength_u = 2 "Length of ground plane along groundAxis_u"
annotation (Dialog(
tab = "Animation",
group = "if animateGround = true and gravityType = UniformGravity",
enable = enableAnimation and animateGround and gravityType == GravityTypes.UniformGravity));
parameter Modelica.SIunits.Length groundLength_v = groundLength_u "Length of ground plane perpendicular to groundAxis_u"
annotation (Dialog(
tab = "Animation",
group = "if animateGround = true and gravityType = UniformGravity",
enable = enableAnimation and animateGround and gravityType == GravityTypes.UniformGravity));
input Types.Color groundColor = {200, 200, 200} "Color of ground plane"
annotation (Dialog(
colorSelector = true,
tab = "Animation",
group = "if animateGround = true and gravityType = UniformGravity",
enable = enableAnimation and animateGround and gravityType == GravityTypes.UniformGravity));
parameter SI.Length nominalLength = 1 "\"Nominal\" length of multi-body system"
annotation (Dialog(tab = "Defaults"));
parameter SI.Length defaultAxisLength = 0.2 * nominalLength "Default for length of a frame axis (but not world frame)"
annotation (Dialog(tab = "Defaults"));
parameter SI.Length defaultJointLength = 0.1 * nominalLength "Default for the fixed length of a shape representing a joint"
annotation (Dialog(tab = "Defaults"));
parameter SI.Length defaultJointWidth = 0.05 * nominalLength "Default for the fixed width of a shape representing a joint"
annotation (Dialog(tab = "Defaults"));
parameter SI.Length defaultForceLength = 0.1 * nominalLength "Default for the fixed length of a shape representing a force (e.g., damper)"
annotation (Dialog(tab = "Defaults"));
parameter SI.Length defaultForceWidth = 0.05 * nominalLength "Default for the fixed width of a shape representing a force (e.g., spring, bushing)"
annotation (Dialog(tab = "Defaults"));
parameter SI.Length defaultBodyDiameter = 0.111111111111111 * nominalLength "Default for diameter of sphere representing the center of mass of a body"
annotation (Dialog(tab = "Defaults"));
parameter Real defaultWidthFraction = 20 "Default for shape width as a fraction of shape length (e.g., for Parts.FixedTranslation)"
annotation (Dialog(tab = "Defaults"));
parameter SI.Length defaultArrowDiameter = 0.025 * nominalLength "Default for arrow diameter (e.g., of forces, torques, sensors)"
annotation (Dialog(tab = "Defaults"));
parameter Real defaultFrameDiameterFraction = 40 "Default for arrow diameter of a coordinate system as a fraction of axis length"
annotation (Dialog(tab = "Defaults"));
parameter Real defaultSpecularCoefficient(min = 0) = 0.7 "Default reflection of ambient light (= 0: light is completely absorbed)"
annotation (Dialog(tab = "Defaults"));
parameter Real defaultN_to_m(unit = "N/m", min = 0) = 1000 "Default scaling of force arrows (length = force/defaultN_to_m)"
annotation (Dialog(tab = "Defaults"));
parameter Real defaultNm_to_m(unit = "N.m/m", min = 0) = 1000 "Default scaling of torque arrows (length = torque/defaultNm_to_m)"
annotation (Dialog(tab = "Defaults"));
replaceable function gravityAcceleration = Modelica.Mechanics.MultiBody.Forces.Internal.standardGravityAcceleration(gravityType = gravityType, g = g * Modelica.Math.Vectors.normalizeWithAssert(n), mue = mue) constrainedby Modelica.Mechanics.MultiBody.Interfaces.partialGravityAcceleration "Function to compute the gravity acceleration, resolved in world frame"
annotation (
choicesAllMatching = true,
Dialog(enable = gravityType == Modelica.Mechanics.MultiBody.Types.GravityTypes.NoGravity),
Documentation(info = "<html>\n<p>Replaceable function to define the gravity field.\n Default is function\n <a href=\"modelica://Modelica.Mechanics.MultiBody.Forces.Internal.standardGravityAcceleration\">standardGravityAcceleration</a>\n that provides some simple gravity fields (no gravity, constant parallel gravity field,\n point gravity field).\n By redeclaring this function, any type of gravity field can be defined, see example\n <a href=\"modelica://Modelica.Mechanics.MultiBody.Examples.Elementary.UserDefinedGravityField\">Examples.Elementary.UserDefinedGravityField</a>.\n</p>\n</html>"));
protected
parameter Integer ndim = if enableAnimation and animateWorld then 1 else 0;
parameter Integer ndim2 = if enableAnimation and animateWorld and axisShowLabels then 1 else 0;
parameter SI.Length headLength = min(axisLength, axisDiameter * Types.Defaults.FrameHeadLengthFraction);
parameter SI.Length headWidth = axisDiameter * Types.Defaults.FrameHeadWidthFraction;
parameter SI.Length lineLength = max(0, axisLength - headLength);
parameter SI.Length lineWidth = axisDiameter;
parameter SI.Length scaledLabel = Modelica.Mechanics.MultiBody.Types.Defaults.FrameLabelHeightFraction * axisDiameter;
parameter SI.Length labelStart = 1.05 * axisLength;
Modelica.Mechanics.MultiBody.Visualizers.Advanced.Shape x_arrowLine(shapeType = "cylinder", length = lineLength, width = lineWidth, height = lineWidth, lengthDirection = {1, 0, 0}, widthDirection = {0, 1, 0}, color = axisColor_x, specularCoefficient = 0) if enableAnimation and animateWorld;
Modelica.Mechanics.MultiBody.Visualizers.Advanced.Shape x_arrowHead(shapeType = "cone", length = headLength, width = headWidth, height = headWidth, lengthDirection = {1, 0, 0}, widthDirection = {0, 1, 0}, color = axisColor_x, r = {lineLength, 0, 0}, specularCoefficient = 0) if enableAnimation and animateWorld;
Modelica.Mechanics.MultiBody.Visualizers.Internal.Lines x_label(lines = scaledLabel * {[0,0; 1,1], [0,1; 1,0]}, diameter = axisDiameter, color = axisColor_x, r_lines = {labelStart, 0, 0}, n_x = {1, 0, 0}, n_y = {0, 1, 0}, specularCoefficient = 0) if enableAnimation and animateWorld and axisShowLabels;
Modelica.Mechanics.MultiBody.Visualizers.Advanced.Shape y_arrowLine(shapeType = "cylinder", length = lineLength, width = lineWidth, height = lineWidth, lengthDirection = {0, 1, 0}, widthDirection = {1, 0, 0}, color = axisColor_y, specularCoefficient = 0) if enableAnimation and animateWorld;
Modelica.Mechanics.MultiBody.Visualizers.Advanced.Shape y_arrowHead(shapeType = "cone", length = headLength, width = headWidth, height = headWidth, lengthDirection = {0, 1, 0}, widthDirection = {1, 0, 0}, color = axisColor_y, r = {0, lineLength, 0}, specularCoefficient = 0) if enableAnimation and animateWorld;
Modelica.Mechanics.MultiBody.Visualizers.Internal.Lines y_label(lines = scaledLabel * {[0,0; 1,1.5], [0,1.5; 0.5,0.75]}, diameter = axisDiameter, color = axisColor_y, r_lines = {0, labelStart, 0}, n_x = {0, 1, 0}, n_y = {-1, 0, 0}, specularCoefficient = 0) if enableAnimation and animateWorld and axisShowLabels;
Modelica.Mechanics.MultiBody.Visualizers.Advanced.Shape z_arrowLine(shapeType = "cylinder", length = lineLength, width = lineWidth, height = lineWidth, lengthDirection = {0, 0, 1}, widthDirection = {0, 1, 0}, color = axisColor_z, specularCoefficient = 0) if enableAnimation and animateWorld;
Modelica.Mechanics.MultiBody.Visualizers.Advanced.Shape z_arrowHead(shapeType = "cone", length = headLength, width = headWidth, height = headWidth, lengthDirection = {0, 0, 1}, widthDirection = {0, 1, 0}, color = axisColor_z, r = {0, 0, lineLength}, specularCoefficient = 0) if enableAnimation and animateWorld;
Modelica.Mechanics.MultiBody.Visualizers.Internal.Lines z_label(lines = scaledLabel * {[0,0; 1,0], [0,1; 1,1], [0,1; 1,0]}, diameter = axisDiameter, color = axisColor_z, r_lines = {0, 0, labelStart}, n_x = {0, 0, 1}, n_y = {0, 1, 0}, specularCoefficient = 0) if enableAnimation and animateWorld and axisShowLabels;
parameter SI.Length gravityHeadLength = min(gravityArrowLength, gravityArrowDiameter * Types.Defaults.ArrowHeadLengthFraction);
parameter SI.Length gravityHeadWidth = gravityArrowDiameter * Types.Defaults.ArrowHeadWidthFraction;
parameter SI.Length gravityLineLength = max(0, gravityArrowLength - gravityHeadLength);
Modelica.Mechanics.MultiBody.Visualizers.Advanced.Shape gravityArrowLine(shapeType = "cylinder", length = gravityLineLength, width = gravityArrowDiameter, height = gravityArrowDiameter, lengthDirection = n, widthDirection = {0, 1, 0}, color = gravityArrowColor, r_shape = gravityArrowTail, specularCoefficient = 0) if enableAnimation and animateGravity and gravityType == GravityTypes.UniformGravity;
Modelica.Mechanics.MultiBody.Visualizers.Advanced.Shape gravityArrowHead(shapeType = "cone", length = gravityHeadLength, width = gravityHeadWidth, height = gravityHeadWidth, lengthDirection = n, widthDirection = {0, 1, 0}, color = gravityArrowColor, r_shape = gravityArrowTail + Modelica.Math.Vectors.normalize(n) * gravityLineLength, specularCoefficient = 0) if enableAnimation and animateGravity and gravityType == GravityTypes.UniformGravity;
parameter Integer ndim_pointGravity = if enableAnimation and animateGravity and gravityType == GravityTypes.UniformGravity then 1 else 0;
Modelica.Mechanics.MultiBody.Visualizers.Advanced.Shape gravitySphere(shapeType = "sphere", r_shape = {-0.5 * gravitySphereDiameter, 0, 0}, lengthDirection = {1, 0, 0}, length = gravitySphereDiameter, width = gravitySphereDiameter, height = gravitySphereDiameter, color = gravitySphereColor, specularCoefficient = 0) if enableAnimation and animateGravity and gravityType == GravityTypes.PointGravity;
Modelica.Mechanics.MultiBody.Visualizers.Advanced.Surface surface(final multiColoredSurface = false, final wireframe = false, final color = groundColor, final specularCoefficient = 0, final transparency = 0, final R = Modelica.Mechanics.MultiBody.Frames.absoluteRotation(Modelica.Mechanics.MultiBody.Frames.from_nxy(n, groundAxis_u), Modelica.Mechanics.MultiBody.Frames.axesRotations({1, 2, 3}, {0.5 * pi, 0.5 * pi, 0}, {0, 0, 0})), final r_0 = zeros(3), final nu = 2, final nv = 2, redeclare function surfaceCharacteristic = Modelica.Mechanics.MultiBody.Visualizers.Advanced.SurfaceCharacteristics.rectangle(lu = groundLength_u, lv = groundLength_v)) if enableAnimation and animateGround and gravityType == GravityTypes.UniformGravity;
equation
assert(1e-10 < Modelica.Math.Vectors.length(n), "Parameter n of World object is wrong (length(n) > 0 required)");
Connections.root(frame_b.R);
frame_b.R = Frames.nullRotation();
frame_b.r_0 = zeros(3);
annotation (
defaultComponentName = "world",
defaultComponentPrefixes = "inner",
missingInnerMessage = "No \"world\" component is defined. A default world\ncomponent with the default gravity field will be used\n(g=9.81 in negative y-axis). If this is not desired,\ndrag Modelica.Mechanics.MultiBody.World into the top level of your model.",
Icon(
coordinateSystem(
preserveAspectRatio = true,
extent = {
{-100, -100},
{100, 100}}),
graphics = {
Rectangle(
extent = {
{-100, 100},
{100, -100}},
fillColor = {255, 255, 255},
fillPattern = FillPattern.Solid),
Line(
points = {
{-100, -118},
{-100, 61}},
thickness = 0.5),
Polygon(
points = {
{-100, 100},
{-120, 60},
{-80, 60},
{-100, 100},
{-100, 100}},
fillPattern = FillPattern.Solid),
Line(
points = {
{-119, -100},
{59, -100}},
thickness = 0.5),
Polygon(
points = {
{99, -100},
{59, -80},
{59, -120},
{99, -100}},
fillPattern = FillPattern.Solid),
Text(
extent = {
{-150, 145},
{150, 105}},
textString = "%name",
lineColor = {0, 0, 255}),
Text(
extent = {
{95, -113},
{144, -162}},
textString = "%label1"),
Text(
extent = {
{-170, 127},
{-119, 77}},
textString = "%label2"),
Line(
points = {
{-56, 78},
{-56, -26}},
color = {0, 0, 255}),
Polygon(
points = {
{-68, -26},
{-56, -66},
{-44, -26},
{-68, -26}},
fillColor = {0, 0, 255},
fillPattern = FillPattern.Solid,
lineColor = {0, 0, 255}),
Line(
points = {
{2, 78},
{2, -26}},
color = {0, 0, 255}),
Polygon(
points = {
{-10, -26},
{2, -66},
{14, -26},
{-10, -26}},
fillColor = {0, 0, 255},
fillPattern = FillPattern.Solid,
lineColor = {0, 0, 255}),
Line(
points = {
{66, 80},
{66, -26}},
color = {0, 0, 255}),
Polygon(
points = {
{54, -26},
{66, -66},
{78, -26},
{54, -26}},
fillColor = {0, 0, 255},
fillPattern = FillPattern.Solid,
lineColor = {0, 0, 255})}),
Documentation(info = "<html>\n<p>\nModel <strong>World</strong> represents a global coordinate system fixed in\nground. This model serves several purposes:\n</p>\n<ul>\n<li> It is used as <strong>inertial system</strong> in which\n the equations of all elements of the MultiBody library\n are defined.</li>\n<li> It is the world frame of an <strong>animation window</strong> in which\n all elements of the MultiBody library are visualized.</li>\n<li> It is used to define the <strong>gravity field</strong> in which a\n multi-body model is present. Default is a uniform gravity\n field where the gravity acceleration vector g is the\n same at every position. Additionally, a point gravity field or no\n gravity can be selected. Also, function gravityAcceleration can\n be redeclared to a user-defined function that computes the gravity\n acceleration, see example\n <a href=\"modelica://Modelica.Mechanics.MultiBody.Examples.Elementary.UserDefinedGravityField\">Examples.Elementary.UserDefinedGravityField</a>.\n </li>\n<li> It is used to define <strong>default settings</strong> of animation properties\n (e.g., the diameter of a sphere representing by default\n the center of mass of a body, or the diameters of the cylinders\n representing a revolute joint).</li>\n<li> It is used to define a <strong>visual representation</strong> of the\n world model (= 3 coordinate axes with labels), of the defined\n gravity field and of a ground plane perpendicular to the gravity direction.<br>\n <img src=\"modelica://Modelica/Resources/Images/Mechanics/MultiBody/world.png\" alt=\"MultiBody.World\">\n</li>\n</ul>\n<p>\nSince the gravity field function is required from all bodies with mass\nand the default settings of animation properties are required\nfrom nearly every component, exactly one instance of model World needs\nto be present in every model on the top level. The basic declaration\nneeds to be:\n</p>\n\n<blockquote><pre>\n<strong>inner</strong> Modelica.Mechanics.MultiBody.World world\n</pre></blockquote>\n\n<p>\nNote, it must be an <strong>inner</strong> declaration with instance name <strong>world</strong>\nin order that this world object can be accessed from all objects in the\nmodel. When dragging the \"World\" object from the package browser into\nthe diagram layer, this declaration is automatically generated\n(this is defined via annotations in model World).\n</p>\n<p>\nAll vectors and tensors of a mechanical system are resolved in a\nframe that is local to the corresponding component. Usually,\nif all relative joint coordinates vanish, the local frames\nof all components are parallel to each other, as well as to the\nworld frame (this holds as long as a Parts.FixedRotation,\ncomponent is <strong>not</strong> used). In this \"reference configuration\"\nit is therefore\nalternatively possible to resolve all vectors in the world\nframe, since all frames are parallel to each other.\nThis is often very convenient. In order to give some visual\nsupport in such a situation, in the icon of a World instance\ntwo axes of the world frame are shown and the labels\nof these axes can be set via parameters.\n</p>\n</html>"));
end World;