Modelica.Mechanics.MultiBody.Examples.Elementary

Information

This package contains elementary example models to demonstrate the usage of the MultiBody library

Content

Model	Description
DoublePendulum	Simple double pendulum with two revolute joints and two bodies.
ForceAndTorque	Demonstrates usage of Forces.ForceAndTorque element.
FreeBody	Free flying body attached by two springs to environment.
InitSpringConstant	Determine spring constant such that system is in steady state at given position.
LineForceWithTwoMasses	Demonstrates a line force with two point masses using a Joints.Assemblies.JointUPS and alternatively a Forces.LineForceWithTwoMasses component.
Pendulum	Simple pendulum with one revolute joint and one body.
PendulumWithSpringDamper	Simple spring/damper/mass system
PointGravity	Two bodies in a point gravity field
PointGravityWithPointMasses	Two point masses in a point gravity field (rotation of bodies is neglected)
PointGravityWithPointMasses2	Rigidly connected point masses in a point gravity field
RollingWheel	Single wheel rolling on ground starting from an initial speed
RollingWheelSetDriving	Rolling wheel set that is driven by torques driving the wheels
RollingWheelSetPulling	Rolling wheel set that is pulled by a force
SpringDamperSystem	Spring/damper system with a prismatic joint and attached on free flying body
SpringMassSystem	Mass attached via a prismatic joint and a spring to the world frame
SpringWithMass	Point mass hanging on a spring
ThreeSprings	3-dimensional springs in series and parallel connection
HeatLosses	Demonstrate the modeling of heat losses.
UserDefinedGravityField	Demonstrate the modeling of a user-defined gravity field.
Surfaces	Demonstrate the visualization of a sine surface, as well as a torus and a wheel constucted from a surface

Extends from Modelica.Icons.ExamplesPackage (Icon for packages containing runnable examples).

Package Content

Name	Description
DoublePendulum	Simple double pendulum with two revolute joints and two bodies
DoublePendulumInitTip	Demonstrate how to initialize a double pendulum so that its tip starts at a predefined position
ForceAndTorque	Demonstrate usage of ForceAndTorque element
FreeBody	Free flying body attached by two springs to environment
InitSpringConstant	Determine spring constant such that system is in steady state at given position
LineForceWithTwoMasses	Demonstrate line force with two point masses using a JointUPS and alternatively a LineForceWithTwoMasses component
Pendulum	Simple pendulum with one revolute joint and one body
PendulumWithSpringDamper	Simple spring/damper/mass system
PointGravity	Two point masses in a point gravity field
PointGravityWithPointMasses	Two point masses in a point gravity field (rotation of bodies is neglected)
PointGravityWithPointMasses2	Rigidly connected point masses in a point gravity field
SpringDamperSystem	Simple spring/damper/mass system
SpringMassSystem	Mass attached with a spring to the world frame
SpringWithMass	Point mass hanging on a spring
ThreeSprings	3-dim. springs in series and parallel connection
RollingWheel	Single wheel rolling on ground starting from an initial speed
RollingWheelSetDriving	Rolling wheel set that is driven by torques driving the wheels
RollingWheelSetPulling	Rolling wheel set that is pulled by a force
HeatLosses	Demonstrate the modeling of heat losses
UserDefinedGravityField	Demonstrate the modeling of a user-defined gravity field
Surfaces	Demonstrate the visualization of a sine surface, as well as a torus and a wheel constucted from a surface
Utilities	Utility models and functions used by MultiBody.Examples.Elementary

Modelica.Mechanics.MultiBody.Examples.Elementary.DoublePendulum

Information

This example demonstrates that by using joint and body elements animation is automatically available. Also the revolute joints are animated. Note, that animation of every component can be switched of by setting the first parameter animation to false or by setting enableAnimation in the world object to false to switch off animation of all components.

Extends from Modelica.Icons.Example (Icon for runnable examples).

Modelica definition

model DoublePendulum 
  "Simple double pendulum with two revolute joints and two bodies"

  extends Modelica.Icons.Example;
  inner Modelica.Mechanics.MultiBody.World world;
  Modelica.Mechanics.MultiBody.Joints.Revolute revolute1(useAxisFlange=true,phi(fixed=true),
      w(fixed=true));
  Modelica.Mechanics.Rotational.Components.Damper damper(
                                              d=0.1);
  Modelica.Mechanics.MultiBody.Parts.BodyBox boxBody1(r={0.5,0,0}, width=0.06);
  Modelica.Mechanics.MultiBody.Joints.Revolute revolute2(phi(fixed=true), w(
        fixed=true));
  Modelica.Mechanics.MultiBody.Parts.BodyBox boxBody2(r={0.5,0,0}, width=0.06);
equation 

  connect(damper.flange_b, revolute1.axis);
  connect(revolute1.support, damper.flange_a);
  connect(revolute1.frame_b, boxBody1.frame_a);
  connect(revolute2.frame_b, boxBody2.frame_a);
  connect(boxBody1.frame_b, revolute2.frame_a);
  connect(world.frame_b, revolute1.frame_a);
end DoublePendulum;

Modelica.Mechanics.MultiBody.Examples.Elementary.DoublePendulumInitTip

Information

This example demonstrates at hand of a double pendulum, how no-standard initialization can be defined: The absolute position of the pendulum tip, and its absolute speed shall be initially defined. This can be performed with the Joints.FreeMotionScalarInit joint that allows to initialize individual elements of its relative vectors. In this case, the x-, and y-coordinates of the relative position vector (visualized by the yellow arrow in the figure below) and of its derivative shall have a defined value at initial time. The configuration of the double pendulum at the initial time is shown below, where the tip position is required to have the coordinates x=0.7, y=0.3.

Extends from Modelica.Icons.Example (Icon for runnable examples).

Modelica definition

model DoublePendulumInitTip 
  "Demonstrate how to initialize a double pendulum so that its tip starts at a predefined position"
  extends Modelica.Icons.Example;
  inner World world;
  Joints.Revolute revolute1(                             useAxisFlange=true);
  Rotational.Components.Damper damper(        d=0.1);
  Parts.BodyBox boxBody1(                             r={0.5,0,0}, width=0.06);
  Joints.Revolute revolute2;
  Parts.BodyBox boxBody2(                             r={0.5,0,0}, width=0.06);
  Modelica.Mechanics.MultiBody.Joints.FreeMotionScalarInit freeMotionScalarInit(
    use_r=true,
    r_rel_a_1(start=0.7, fixed=true),
    r_rel_a_2(start=0.3, fixed=true),
    use_v=true,
    v_rel_a_1(fixed=true),
    v_rel_a_2(fixed=true));
equation 
  connect(damper.flange_b,revolute1. axis);
  connect(revolute1.support,damper. flange_a);
  connect(revolute1.frame_b,boxBody1. frame_a);
  connect(revolute2.frame_b,boxBody2. frame_a);
  connect(boxBody1.frame_b,revolute2. frame_a);
  connect(world.frame_b,revolute1. frame_a);
  connect(world.frame_b, freeMotionScalarInit.frame_a);
  connect(freeMotionScalarInit.frame_b, boxBody2.frame_b);
end DoublePendulumInitTip;

Modelica.Mechanics.MultiBody.Examples.Elementary.ForceAndTorque

Information

In this example the usage of the general force element "ForceAndTorque" is shown. A "ForceAndTorque" element is connected between a body and a fixed point in the world system. The force and torque is defined by the "Constant" block. The two vectors are resolved in the coordinate system defined by the "fixedRotation" component that is fixed in the world system:

The animation view at time = 0 is shown in the figure below. The yellow line is directed from frame_a to frame_b of the forceAndTorque component. The green arrow characterizes the force acting at the body whereas the green double arrow characterizes the torque acting at the body. The lengths of the two vectors are proportional to the lengths of the force and torque vectors (constant scaling factors are defined as parameters in the forceAndTorque component):

Extends from Modelica.Icons.Example (Icon for runnable examples).

Modelica definition

model ForceAndTorque "Demonstrate usage of ForceAndTorque element"
  extends Modelica.Icons.Example;
  inner World world(animateGravity=false);
  Parts.BodyCylinder body(r={1,0,0});
  Parts.Fixed fixed1(r={0,-0.5,0}, width=0.03);
  Parts.FixedRotation fixedRotation(n={0,0,1}, angle=30);
  Forces.ForceAndTorque forceAndTorque(Nm_to_m=120, N_to_m=1200,
    resolveInFrame=Modelica.Mechanics.MultiBody.Types.ResolveInFrameAB.frame_resolve);
  Joints.Revolute revolute2(n={0,1,0},
    phi(fixed=true),
    w(fixed=true));
  Modelica.Blocks.Sources.Constant torque[3](k={-100,100,0});
  Joints.Revolute revolute1(phi(fixed=true), w(fixed=true));
  Parts.Fixed fixed2(width=0.03, r={1.5,0.25,0});
  Modelica.Blocks.Sources.Constant force[3](k={0,1000,0});
equation 
  connect(revolute2.frame_b, body.frame_a);
  connect(forceAndTorque.frame_b, body.frame_b);
  connect(fixed1.frame_b, revolute1.frame_a);
  connect(revolute1.frame_b, revolute2.frame_a);
  connect(fixed2.frame_b, forceAndTorque.frame_a);
  connect(fixedRotation.frame_a, fixed1.frame_b);
  connect(forceAndTorque.frame_resolve, fixedRotation.frame_b);
  connect(force.y, forceAndTorque.force);
  connect(torque.y, forceAndTorque.torque);
end ForceAndTorque;

Modelica.Mechanics.MultiBody.Examples.Elementary.FreeBody

Information

This example demonstrates:

• The animation of spring and damper components
• A body can be freely moving without any connection to a joint. In this case body coordinates are used automatically as states (whenever joints are present, it is first tried to use the generalized coordinates of the joints as states).
• If a body is freely moving, the initial position and velocity of the body can be defined with the "Initialization" menu as shown with the body "body1" in the left part (click on "Initialization").

Extends from Modelica.Icons.Example (Icon for runnable examples).

Parameters

Type	Name	Default	Description
Boolean	animation	true	= true, if animation shall be enabled

Modelica definition

model FreeBody 
  "Free flying body attached by two springs to environment"
  extends Modelica.Icons.Example;
  parameter Boolean animation=true "= true, if animation shall be enabled";
  inner Modelica.Mechanics.MultiBody.World world;
  Modelica.Mechanics.MultiBody.Parts.FixedTranslation bar2(r={0.8,0,0}, animation=false);
  Modelica.Mechanics.MultiBody.Forces.Spring spring1(
    width=0.1,
    coilWidth=0.005,
    numberOfWindings=5,
    c=20,
    s_unstretched=0);
  Modelica.Mechanics.MultiBody.Parts.BodyShape body(
    m=1,
    I_11=1,
    I_22=1,
    I_33=1,
    r={0.4,0,0},
    r_CM={0.2,0,0},
    width=0.05,
    r_0(start={0.2,-0.5,0.1}, fixed=true),
    v_0(fixed=true),
    angles_fixed=true,
    w_0_fixed=true,
    angles_start={0.174532925199433,0.174532925199433,0.174532925199433});
  Modelica.Mechanics.MultiBody.Forces.Spring spring2(
    c=20,
    s_unstretched=0,
    width=0.1,
    coilWidth=0.005,
    numberOfWindings=5);
equation 
  connect(bar2.frame_a, world.frame_b);
  connect(spring1.frame_b, body.frame_a);
  connect(bar2.frame_b, spring2.frame_a);
  connect(spring1.frame_a, world.frame_b);
  connect(body.frame_b, spring2.frame_b);
end FreeBody;

Modelica.Mechanics.MultiBody.Examples.Elementary.InitSpringConstant

Information

This example demonstrates a non-standard type of initialization by calculating a spring constant such that a simple pendulum is at a defined position in steady state.

The goal is that the pendulum should be in steady state when the rotation angle of the pendulum is zero. The spring constant of the spring shall be calculated during initialization such that this goal is reached.

The pendulum has one degree of freedom, i.e., two states. Therefore, two additional equations have to be provided for initialization. However, parameter "c" of the spring component is defined with attribute "fixed = false", i.e., the value of this parameter is computed during initialization. Therefore, there is one additional equation required during initialization. The 3 initial equations are the rotational angle of the revolute joint and its first and second derivative. The latter ones are zero, in order to initialize in steady state. By setting the start values of phi, w, a to zero and their fixed attributes to true, the required 3 initial equations are defined.

After translation, this model is initialized in steady-state. The spring constant is computed as c = 49.05 N/m. An animation of this simulation is shown in the figure below.

Extends from Modelica.Icons.Example (Icon for runnable examples).

Modelica definition

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

  extends Modelica.Icons.Example;
  inner Modelica.Mechanics.MultiBody.World world(gravityType=Modelica.Mechanics.MultiBody.Types.GravityTypes.
        UniformGravity);
  Modelica.Mechanics.MultiBody.Joints.Revolute rev(useAxisFlange=true,n={0,0,1},
    phi(fixed=true),
    w(fixed=true),
    a(fixed=true));
  Modelica.Mechanics.Rotational.Components.Damper damper(
                                              d=0.1);
  Modelica.Mechanics.MultiBody.Parts.BodyShape body(
    r={1,0,0},
    r_CM={0.5,0,0},
    m=1);
  Modelica.Mechanics.MultiBody.Parts.Fixed fixed(r={1,0.2,0}, width=0.02);
  Modelica.Mechanics.MultiBody.Forces.Spring spring(s_unstretched=0.1, c(fixed=false) = 100);

equation 
  connect(world.frame_b, rev.frame_a);
  connect(damper.flange_b, rev.axis);
  connect(rev.support, damper.flange_a);
  connect(rev.frame_b, body.frame_a);
  connect(fixed.frame_b, spring.frame_a);
  connect(body.frame_b, spring.frame_b);
end InitSpringConstant;

Modelica.Mechanics.MultiBody.Examples.Elementary.LineForceWithTwoMasses

Information

It is demonstrated how to implement line force components that shall have mass properties. Two alternative implementations are given:

• With JointUPS:
  Modelica.Mechanics.MultiBody.Joints.Assemblies.JointUPS is an aggregation of a universal, a prismatic and a spherical joint that approximates a real force component, such as a hydraulic cylinder. At the two frames of the prismatic joint (frame_ia, frame_ib of jointUPS) two bodies are attached. The parameters are selected such that the center of masses of the two bodies are located on the line connecting frame_a and frame_b of the jointUPS component. Both bodies have the same mass and the inertia tensor is set to zero, i.e., the two bodies are treated as point masses.
• With LineForceWithTwoMasses:
  Modelica.Mechanics.MultiBody.Forces.LineForceWithTwoMasses is a line force component with the built-in property that two point masses are located on the line on which the line force is acting. The parameters are selected in such a way that the same system as with the jointUPS component is described.

In both cases, a linear 1-dimensional translational damper from the Modelica.Mechanics.Translational library is used as line force between the two attachment points. Simulate this system and plot the differences of the cut forces at both sides of the line force component ("rod_f_diff" and "body_f_diff"). Both vectors should be zero (depending on the choosen relative tolerance of the integration, the difference is in the order of 1.e-10 ... 1.e-15).

Note, that the implementation with the LineForceWithTwoMasses component is simpler and more convenient. An animation of this simulation is shown in the figure below. The system on the left side in the front is the animation with the LineForceWithTwoMasses component whereas the system on the right side in the back is the animation with the JointUPS component.

Extends from Modelica.Icons.Example (Icon for runnable examples).

Parameters

Type	Name	Default	Description
Mass	m	1	Mass of point masses [kg]

Modelica definition

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

  import SI = Modelica.SIunits;

  extends Modelica.Icons.Example;
  parameter Modelica.SIunits.Mass m=1 "Mass of point masses";
  SI.Force rod_f_diff[3]=rod1.frame_b.f - rod3.frame_b.f 
    "Difference of cut-forces in rod1 and rod3";
  SI.Force body_f_diff[3]=bodyBox1.frame_b.f - bodyBox2.frame_b.f 
    "Difference of cut-forces in bodyBox1 and bodyBox2";

  inner Modelica.Mechanics.MultiBody.World world;
  Modelica.Mechanics.MultiBody.Joints.Revolute revolute1(phi(fixed=true), w(
        fixed=true));
  Modelica.Mechanics.MultiBody.Parts.BodyBox bodyBox1(r={0.7,0,0});
  Modelica.Mechanics.MultiBody.Parts.FixedTranslation rod1(
    r={0,-0.9,0},
    width=0.01,
    animation=false);
  Modelica.Mechanics.MultiBody.Joints.Assemblies.JointUPS jointUPS(nAxis_ia={0.7,1.2,0}, animation=
       true);
  Modelica.Mechanics.MultiBody.Parts.Body body1(
    r_CM=0.2*jointUPS.eAxis_ia,
    cylinderDiameter=0.05,
    animation=true,
    m=m,
    I_11=0,
    I_22=0,
    I_33=0);
  Modelica.Mechanics.MultiBody.Parts.Body body2(
    r_CM=-0.2*jointUPS.eAxis_ia,
    cylinderDiameter=0.05,
    animation=true,
    m=m,
    I_11=0,
    I_22=0,
    I_33=0);
  Modelica.Mechanics.MultiBody.Parts.FixedTranslation rod2(
    r={0,0.3,0},
    width=0.01,
    animation=false);
  Modelica.Mechanics.Translational.Components.Damper damper1(
                                                  d=3);
  Modelica.Mechanics.MultiBody.Joints.Revolute revolute2(phi(fixed=true), w(
        fixed=true));
  Modelica.Mechanics.MultiBody.Parts.BodyBox bodyBox2(r={0.7,0,0});
  Modelica.Mechanics.MultiBody.Parts.FixedTranslation rod3(
    width=0.01,
    r={0,-0.9,0.3},
    animation=false);
  Modelica.Mechanics.MultiBody.Parts.FixedTranslation rod4(
    width=0.01,
    r={0,0.3,0.3},
    animation=false);
  Modelica.Mechanics.Translational.Components.Damper damper2(
                                                  d=3);
  Modelica.Mechanics.MultiBody.Forces.LineForceWithTwoMasses
    lineForceWithTwoMasses(
    L_a=0.2,
    L_b=0.2,
    cylinderLength_a=0.2,
    cylinderLength_b=1.2,
    massDiameterFaction=2.2,
    m_a=m,
    m_b=m);
equation 
  connect(jointUPS.bearing, damper1.flange_a);
  connect(jointUPS.axis, damper1.flange_b);
  connect(jointUPS.frame_ib, body2.frame_a);
  connect(world.frame_b, rod2.frame_a);
  connect(world.frame_b, rod1.frame_a);
  connect(rod2.frame_b, revolute1.frame_a);
  connect(revolute1.frame_b, bodyBox1.frame_a);
  connect(bodyBox1.frame_b, jointUPS.frame_b);
  connect(body1.frame_a, jointUPS.frame_ia);
  connect(rod1.frame_b, jointUPS.frame_a);
  connect(rod4.frame_b, revolute2.frame_a);
  connect(revolute2.frame_b, bodyBox2.frame_a);
  connect(world.frame_b, rod4.frame_a);
  connect(rod3.frame_a, rod4.frame_a);
  connect(lineForceWithTwoMasses.frame_a, rod3.frame_b);
  connect(lineForceWithTwoMasses.frame_b, bodyBox2.frame_b);
  connect(lineForceWithTwoMasses.flange_b, damper2.flange_b);
  connect(lineForceWithTwoMasses.flange_a, damper2.flange_a);
end LineForceWithTwoMasses;

Modelica.Mechanics.MultiBody.Examples.Elementary.Pendulum

Information

This simple model demonstrates that by just dragging components default animation is defined that shows the structure of the assembled system.

Extends from Modelica.Icons.Example (Icon for runnable examples).

Modelica definition

model Pendulum "Simple pendulum with one revolute joint and one body"
  extends Modelica.Icons.Example;
  inner Modelica.Mechanics.MultiBody.World world(gravityType=Modelica.Mechanics.MultiBody.Types.GravityTypes.
        UniformGravity);
  Modelica.Mechanics.MultiBody.Joints.Revolute rev(n={0,0,1},useAxisFlange=true,
    phi(fixed=true),
    w(fixed=true));
  Modelica.Mechanics.Rotational.Components.Damper damper(
                                              d=0.1);
  Modelica.Mechanics.MultiBody.Parts.Body body(m=1.0, r_CM={0.5,0,0});
equation 
  connect(world.frame_b, rev.frame_a);
  connect(damper.flange_b, rev.axis);
  connect(rev.support, damper.flange_a);
  connect(body.frame_a, rev.frame_b);
end Pendulum;

Modelica.Mechanics.MultiBody.Examples.Elementary.PendulumWithSpringDamper

Information

A body is attached on a revolute and prismatic joint. A 3-dim. spring and a 3-dim. damper are connected between the body and a point fixed in the world frame:

Extends from Modelica.Icons.Example (Icon for runnable examples).

Parameters

Type	Name	Default	Description
Boolean	animation	true	= true, if animation shall be enabled

Modelica definition

model PendulumWithSpringDamper "Simple spring/damper/mass system"
  extends Modelica.Icons.Example;
  parameter Boolean animation=true "= true, if animation shall be enabled";
  inner Modelica.Mechanics.MultiBody.World world(axisLength=0.6);
  Modelica.Mechanics.MultiBody.Parts.Body body1(
    m=1,
    animation=animation,
    I_11=1,
    I_22=1,
    I_33=1,
    r_CM={0,0,0},
    cylinderDiameter=0.05,
    sphereDiameter=0.2);
  Modelica.Mechanics.MultiBody.Parts.FixedTranslation bar1(animation=animation, r={0.3,0,0});
  Modelica.Mechanics.MultiBody.Forces.Spring spring1(
    coilWidth=0.01,
    numberOfWindings=5,
    c=20,
    s_unstretched=0.2);
  Modelica.Mechanics.MultiBody.Forces.Damper damper1(
    d=1,
    length_a=0.1,
    diameter_a=0.08,
    animation=false);
  Modelica.Mechanics.MultiBody.Joints.Revolute revolute(phi(fixed=true), w(
        fixed=true));
  Modelica.Mechanics.MultiBody.Joints.Prismatic prismatic(
    boxWidth=0.04,
    boxColor={255,65,65},
    s(fixed=true, start=0.5),
    v(fixed=true));
equation 
  connect(world.frame_b, bar1.frame_a);
  connect(revolute.frame_a, bar1.frame_b);
  connect(prismatic.frame_a, revolute.frame_b);
  connect(damper1.frame_a, bar1.frame_b);
  connect(damper1.frame_b, prismatic.frame_b);
  connect(spring1.frame_a, bar1.frame_b);
  connect(spring1.frame_b, prismatic.frame_b);
  connect(body1.frame_a, prismatic.frame_b);
end PendulumWithSpringDamper;

Modelica.Mechanics.MultiBody.Examples.Elementary.PointGravity

Information

This model demonstrates a point gravity field. Two bodies are placed in the gravity field. The initial positions and velocities of these bodies are selected such that one body rotates on a circle and the other body rotates on an ellipse around the center of the point gravity field.

Extends from Modelica.Icons.Example (Icon for runnable examples).

Modelica definition

model PointGravity "Two point masses in a point gravity field"
  import SI = Modelica.SIunits;
  extends Modelica.Icons.Example;
  inner Modelica.Mechanics.MultiBody.World world(
    mue=1,
    gravitySphereDiameter=0.1,
    gravityType=Modelica.Mechanics.MultiBody.Types.GravityTypes.PointGravity);
  Modelica.Mechanics.MultiBody.Parts.Body body1(
    m=1,
    sphereDiameter=0.1,
    I_11=0.1,
    I_22=0.1,
    I_33=0.1,
    r_0(start={0,0.6,0}, fixed=true),
    v_0(start={1,0,0}, fixed=true),
    angles_fixed=true,
    w_0_fixed=true,
    r_CM={0,0,0});
  Modelica.Mechanics.MultiBody.Parts.Body body2(
    m=1,
    sphereDiameter=0.1,
    I_11=0.1,
    I_22=0.1,
    I_33=0.1,
    r_0(start={0.6,0.6,0}, fixed=true),
    v_0(start={0.6,0,0}, fixed=true),
    angles_fixed=true,
    w_0_fixed=true,
    r_CM={0,0,0});
equation 

end PointGravity;

Modelica.Mechanics.MultiBody.Examples.Elementary.PointGravityWithPointMasses

Information

This model demonstrates the usage of model Parts.PointMass in a point gravity field. The PointMass model has the feature that that rotation is not taken into account and can therefore also not be calculated. This example demonstrates two cases where this does not matter: If a PointMass is not connected (body1, body2), the orientation object in these point masses is set to a unit rotation. If a PointMass is connected by a line force element, such as the used Forces.LineForceWithMass component, then the orientation object is set to a unit rotation within the line force element. These are the two cases where the rotation is automatically set to a default value, when the physical system does not provide the equations.

Extends from Modelica.Icons.Example (Icon for runnable examples).

Modelica definition

model PointGravityWithPointMasses 
  "Two point masses in a point gravity field (rotation of bodies is neglected)"
  import SI = Modelica.SIunits;
  extends Modelica.Icons.Example;
  inner Modelica.Mechanics.MultiBody.World world(
    mue=1,
    gravitySphereDiameter=0.1,
    gravityType=Modelica.Mechanics.MultiBody.Types.GravityTypes.PointGravity);
  Modelica.Mechanics.MultiBody.Parts.PointMass body1(
    m=1,
    sphereDiameter=0.1,
    r_0(start={0,0.6,0}, fixed=true),
    v_0(start={1,0,0}, fixed=true));
  Modelica.Mechanics.MultiBody.Parts.PointMass body2(
    m=1,
    sphereDiameter=0.1,
    r_0(start={0.6,0.6,0}, fixed=true),
    v_0(start={0.6,0,0}, fixed=true));
  Modelica.Mechanics.MultiBody.Parts.PointMass body3(
    m=1,
    sphereDiameter=0.1,
    r_0(start={0,0.8,0}, fixed=true),
    v_0(start={0.6,0,0}, fixed=true));
  Modelica.Mechanics.MultiBody.Parts.PointMass body4(
    m=1,
    sphereDiameter=0.1,
    r_0(start={0.3,0.8,0}, fixed=true),
    v_0(start={0.6,0,0}, fixed=true));
  Forces.Spring spring(showMass=false, c=10,
    fixedRotationAtFrame_b=true,
    fixedRotationAtFrame_a=true);
equation 

  connect(spring.frame_a, body3.frame_a);
  connect(spring.frame_b, body4.frame_a);
end PointGravityWithPointMasses;

Modelica.Mechanics.MultiBody.Examples.Elementary.PointGravityWithPointMasses2

Information

This model demonstrates the usage of model Parts.PointMass in a point gravity field. 6 point masses are connected rigidly together. Translating such a model results in an error, because point masses do not define an orientation object. The example demonstrates that in such a case (when the orientation object is not defined by an object that is connected to a point mass), a "MultiBody.Joints.FreeMotion" joint has to be used, to define the the degrees of freedom of this structure.

In order to demonstrate that this approach is correct, in model "referenceSystem", the same system is again provided, but this time modeled with a generic body (Parts.Body) where the inertia tensor is set to zero. In this case, no FreeMotion object is needed because every body provides its absolute translational and rotational position and velocity as potential states.

The two systems should move exactly in the same way. The system with the PointMasses object visulizes the point masses in "red", whereas the "referenceSystem" shows its bodies in "blue".

Extends from Modelica.Icons.Example (Icon for runnable examples).

Modelica definition

model PointGravityWithPointMasses2 
  "Rigidly connected point masses in a point gravity field"
  extends Modelica.Icons.Example;
  model PointMass = Modelica.Mechanics.MultiBody.Parts.PointMass (m=1, sphereColor={
          255,0,0}) "Point mass used at all places of this example";

  PointMass pointMass1(r_0(start={3,0,0}, fixed=true), v_0(start={0,0,-1},
        fixed=true));

  PointMass pointMass2;
  PointMass pointMass3(r_0(start={2,1,0}, fixed=true), v_0(start={0,0,-1},
        fixed=true));
  PointMass pointMass4;
  PointMass pointMass5;
  PointMass pointMass6;

  Modelica.Mechanics.MultiBody.Parts.FixedTranslation fixedTranslation(r={1,0,0});
  Modelica.Mechanics.MultiBody.Parts.FixedTranslation fixedTranslation1(r={-1,0,0});
  Modelica.Mechanics.MultiBody.Parts.FixedTranslation fixedTranslation2(r={0,1,0});
  Modelica.Mechanics.MultiBody.Parts.FixedTranslation fixedTranslation3(r={0,-1,0});
  Modelica.Mechanics.MultiBody.Parts.FixedTranslation fixedTranslation4(r={0,0,1});
  Modelica.Mechanics.MultiBody.Parts.FixedTranslation fixedTranslation5(r={0,0,-1});

  inner World world(                             gravityType=Modelica.Mechanics.MultiBody.Types.GravityTypes.PointGravity, mue=
        5);
  Joints.FreeMotion freeMotion;

model SystemWithStandardBodies 
    "For comparison purposes, an equivalent model with Bodies instead of PointMasses"
  model PointMass = Modelica.Mechanics.MultiBody.Parts.Body(m=1,I_11=0,I_22=0,I_33=0) 
      "Body used all places of the comparision model with zero inertia tensor";

  PointMass pointMass1(
      r_0(start={3,0,0}, fixed=true),
      v_0(start={0,0,-1}, fixed=true),
      angles_fixed=true,
      w_0_fixed=true,
      r_CM={0,0,0});
  PointMass pointMass2(r_CM={0,0,0});
  PointMass pointMass3(r_CM={0,0,0});
  PointMass pointMass4(r_CM={0,0,0});
  PointMass pointMass5(r_CM={0,0,0});
  PointMass pointMass6(r_CM={0,0,0});

  Modelica.Mechanics.MultiBody.Parts.FixedTranslation fixedTranslation( r={1,0,0});
  Modelica.Mechanics.MultiBody.Parts.FixedTranslation fixedTranslation1( r={-1,0,0});
  Modelica.Mechanics.MultiBody.Parts.FixedTranslation fixedTranslation2( r={0,1,0});
  Modelica.Mechanics.MultiBody.Parts.FixedTranslation fixedTranslation3( r={0,-1,0});
  Modelica.Mechanics.MultiBody.Parts.FixedTranslation fixedTranslation4( r={0,0,1});
  Modelica.Mechanics.MultiBody.Parts.FixedTranslation fixedTranslation5( r={0,0,-1});

equation 
  connect(fixedTranslation1.frame_a, fixedTranslation.frame_a);
  connect(fixedTranslation1.frame_a, fixedTranslation2.frame_a);
  connect(fixedTranslation3.frame_a, fixedTranslation.frame_a);
  connect(fixedTranslation1.frame_a, fixedTranslation4.frame_a);
  connect(fixedTranslation5.frame_a, fixedTranslation.frame_a);
  connect(fixedTranslation2.frame_b, pointMass3.frame_a);
  connect(fixedTranslation3.frame_b, pointMass4.frame_a);
  connect(pointMass5.frame_a, fixedTranslation4.frame_b);
  connect(fixedTranslation5.frame_b, pointMass6.frame_a);
  connect(fixedTranslation.frame_b, pointMass1.frame_a);
  connect(fixedTranslation1.frame_b, pointMass2.frame_a);
end SystemWithStandardBodies;

  SystemWithStandardBodies referenceSystem;
equation 
  connect(fixedTranslation1.frame_a, fixedTranslation.frame_a);
  connect(fixedTranslation1.frame_a, fixedTranslation2.frame_a);
  connect(fixedTranslation3.frame_a, fixedTranslation.frame_a);
  connect(fixedTranslation1.frame_a, fixedTranslation4.frame_a);
  connect(fixedTranslation5.frame_a, fixedTranslation.frame_a);
  connect(fixedTranslation2.frame_b, pointMass3.frame_a);
  connect(fixedTranslation3.frame_b, pointMass4.frame_a);
  connect(pointMass5.frame_a, fixedTranslation4.frame_b);
  connect(fixedTranslation5.frame_b, pointMass6.frame_a);
  connect(fixedTranslation.frame_b, pointMass1.frame_a);
  connect(fixedTranslation1.frame_b, pointMass2.frame_a);
  connect(world.frame_b, freeMotion.frame_a);
  connect(freeMotion.frame_b, fixedTranslation1.frame_a);
end PointGravityWithPointMasses2;

Modelica.Mechanics.MultiBody.Examples.Elementary.SpringDamperSystem

Information

This example demonstrates:

• The animation of spring and damper components
• A body can be freely moving without any connection to a joint. In this case body coordinates are used automatically as states (whenever joints are present, it is first tried to use the generalized coordinates of the joints as states).
• If a body is freely moving, the initial position and velocity of the body can be defined with the "Initialization" menu as shown with the body "body1" in the left part (click on "Initialization").

Extends from Modelica.Icons.Example (Icon for runnable examples).

Parameters

Type	Name	Default	Description
Boolean	animation	true	= true, if animation shall be enabled

Modelica definition

model SpringDamperSystem "Simple spring/damper/mass system"
  extends Modelica.Icons.Example;
  parameter Boolean animation=true "= true, if animation shall be enabled";
  inner Modelica.Mechanics.MultiBody.World world;
  Modelica.Mechanics.MultiBody.Parts.Body body1(
    m=1,
    animation=animation,
    r_CM={0,-0.2,0},
    cylinderDiameter=0.05,
    sphereDiameter=0.15,
    I_11=0.1,
    I_22=0.1,
    I_33=0.1,
    r_0(start={0.3,-0.2,0}, fixed=true),
    v_0(fixed=true),
    angles_fixed=true,
    w_0_fixed=true,
    w_0_start(displayUnit="deg/s") = {0,0,0.03490658503988659});
  Modelica.Mechanics.MultiBody.Parts.FixedTranslation bar1(animation=animation, r={0.3,0,0});
  Modelica.Mechanics.MultiBody.Parts.FixedTranslation bar2(animation=animation, r={0.6,0,0});
  Modelica.Mechanics.MultiBody.Parts.Body body2(
    m=1,
    animation=animation,
    cylinderDiameter=0.05,
    sphereDiameter=0.15,
    r_CM={0,0,0});
  Modelica.Mechanics.MultiBody.Joints.Prismatic p2(useAxisFlange=true,
    n={0,-1,0},
    animation=animation,
    boxWidth=0.05,
    stateSelect=StateSelect.always,
    v(fixed=true),
    s(fixed=true, start=0.1));
  Modelica.Mechanics.MultiBody.Forces.Spring spring2(
    c=30,
    s_unstretched=0.1,
    coilWidth=0.01,
    width=0.1);
  Modelica.Mechanics.MultiBody.Forces.Spring spring1(
    s_unstretched=0.1,
    coilWidth=0.01,
    c=30,
    numberOfWindings=10,
    width=0.1);
  Modelica.Mechanics.MultiBody.Forces.Damper damper1(d=2);
equation 
  connect(world.frame_b, bar1.frame_a);
  connect(bar1.frame_b, bar2.frame_a);
  connect(bar2.frame_b, p2.frame_a);
  connect(p2.frame_b, body2.frame_a);
  connect(bar2.frame_b, spring2.frame_a);
  connect(body2.frame_a, spring2.frame_b);
  connect(damper1.frame_a, bar1.frame_b);
  connect(spring1.frame_a, bar1.frame_b);
  connect(damper1.frame_b, body1.frame_a);
  connect(spring1.frame_b, body1.frame_a);
end SpringDamperSystem;

Modelica.Mechanics.MultiBody.Examples.Elementary.SpringMassSystem

Information

This example shows the two different ways how force laws can be utilized:

• In the left system a body is attached via a prismatic joint to the world frame. The prismatic joint has two 1-dimensional translational flanges (called "support" and "axis") that allows to connect elements from the Modelica.Mechanics.Translational library between the support and the axis connector. The effect is that the force generated by the 1-dimensional elements acts as driving force in the axis of the prismatic joint. In the example a simple spring is used.
  The advantage of this approach is that the many elements from the Translational library can be easily used here and that this implementation is usually more efficient as when using 3-dimensional springs.
• In the right system the same model is defined. The difference is that a 3-dimensional spring from the Modelica.Mechanics.MultiBody.Forces library is used. This has the advantage to get a nice animation of the force component.

Extends from Modelica.Icons.Example (Icon for runnable examples).

Parameters

Type	Name	Default	Description
Boolean	animation	true	= true, if animation shall be enabled

Modelica definition

model SpringMassSystem 
  "Mass attached with a spring to the world frame"
  extends Modelica.Icons.Example;
  parameter Boolean animation=true "= true, if animation shall be enabled";
  inner Modelica.Mechanics.MultiBody.World world;
  Modelica.Mechanics.MultiBody.Joints.Prismatic p1(useAxisFlange=true,
    n={0,-1,0},
    animation=animation,
    boxWidth=0.05,
    s(fixed=true, start=0.1),
    v(fixed=true));
  Modelica.Mechanics.Translational.Components.Spring spring1(
                                                  c=30, s_rel0=0.1);
  Modelica.Mechanics.MultiBody.Parts.Body body1(
    m=1,
    sphereDiameter=0.2,
    animation=animation,
    r_CM={0,0,0});
  Modelica.Mechanics.MultiBody.Parts.FixedTranslation bar1(animation=animation, r={0.3,0,0});
  Modelica.Mechanics.MultiBody.Parts.FixedTranslation bar2(animation=animation, r={0.3,0,0});
  Modelica.Mechanics.MultiBody.Parts.Body body2(
    m=1,
    sphereDiameter=0.2,
    animation=animation,
    r_CM={0,0,0});
  Modelica.Mechanics.MultiBody.Joints.Prismatic p2(useAxisFlange=true,
    n={0,-1,0},
    animation=animation,
    boxWidth=0.05,
    stateSelect=StateSelect.always,
    s(fixed=true, start=0.1),
    v(fixed=true));
  Modelica.Mechanics.MultiBody.Forces.Spring spring2(
    c=30,
    s_unstretched=0.1,
    width=0.1);
equation 
  connect(body1.frame_a, p1.frame_b);
  connect(world.frame_b, bar1.frame_a);
  connect(bar1.frame_b, p1.frame_a);
  connect(spring1.flange_b, p1.axis);
  connect(bar1.frame_b, bar2.frame_a);
  connect(bar2.frame_b, p2.frame_a);
  connect(p2.frame_b, body2.frame_a);
  connect(bar2.frame_b, spring2.frame_a);
  connect(body2.frame_a, spring2.frame_b);
  connect(spring1.flange_a, p1.support);
end SpringMassSystem;

Modelica.Mechanics.MultiBody.Examples.Elementary.SpringWithMass

Information

This example shows that a force component may have a mass. The 3-dimensional spring as used in this example, has an optional point mass between the two points where the spring is attached. In the animation, this point mass is represented by a small, light blue, sphere.

Extends from Modelica.Icons.Example (Icon for runnable examples).

Modelica definition

model SpringWithMass "Point mass hanging on a spring"
  extends Modelica.Icons.Example;
  inner Modelica.Mechanics.MultiBody.World world(animateGravity=false);
  Modelica.Mechanics.MultiBody.Forces.Spring spring(
    s_unstretched=0.2,
    m=0.5,
    c=40,
    width=0.1,
    massDiameter=0.07);
  Modelica.Mechanics.MultiBody.Parts.Body body(
    r_0(start={0,-0.3,0}, fixed=true),
    v_0(fixed=true),
    angles_fixed=true,
    w_0_fixed=true,
    r_CM={0,0,0},
    m=1);
equation 
  connect(world.frame_b, spring.frame_a);
  connect(body.frame_a, spring.frame_b);
end SpringWithMass;

Modelica.Mechanics.MultiBody.Examples.Elementary.ThreeSprings

Information

This example demonstrates that 3-dimensional line force elements (here: Modelica.Mechanics.MultiBody.Forces.Spring elements) can be connected together in series without having a body with mass at the connection point (as usually required by multi-body programs). This is advantageous since stiff systems can be avoided, say, due to a stiff spring and a small mass at the connection point.

For a more thorough explanation, see MultiBody.UsersGuide.Tutorial.ConnectionOfLineForces.

Extends from Modelica.Icons.Example (Icon for runnable examples).

Parameters

Type	Name	Default	Description
Boolean	animation	true	= true, if animation shall be enabled

Modelica definition

model ThreeSprings "3-dim. springs in series and parallel connection"
  extends Modelica.Icons.Example;
  parameter Boolean animation=true "= true, if animation shall be enabled";
  inner Modelica.Mechanics.MultiBody.World world(animateWorld=animation);
  Modelica.Mechanics.MultiBody.Parts.Body body1(
    animation=animation,
    r_CM={0,-0.2,0},
    m=0.8,
    I_11=0.1,
    I_22=0.1,
    I_33=0.1,
    sphereDiameter=0.2,
    r_0(start={0.5,-0.3,0}, fixed=true),
    v_0(fixed=true),
    angles_fixed=true,
    w_0_fixed=true);
  Modelica.Mechanics.MultiBody.Parts.FixedTranslation bar1(animation=animation, r={0.3,0,0});
  Modelica.Mechanics.MultiBody.Forces.Spring spring1(
    lineForce(r_rel_0(start={-0.2,-0.2,0.2})),
    s_unstretched=0.1,
    width=0.1,
    coilWidth=0.005,
    numberOfWindings=5,
    c=20,
    animation=animation);
  Modelica.Mechanics.MultiBody.Parts.FixedTranslation bar2(animation=animation, r={0,0,0.3});
  Modelica.Mechanics.MultiBody.Forces.Spring spring2(
    s_unstretched=0.1,
    width=0.1,
    coilWidth=0.005,
    numberOfWindings=5,
    c=40,
    animation=animation);
  Modelica.Mechanics.MultiBody.Forces.Spring spring3(
    s_unstretched=0.1,
    width=0.1,
    coilWidth=0.005,
    numberOfWindings=5,
    c=20,
    animation=animation,
    fixedRotationAtFrame_b=true);
equation 
  connect(world.frame_b, bar1.frame_a);
  connect(world.frame_b, bar2.frame_a);
  connect(bar1.frame_b, spring1.frame_a);
  connect(bar2.frame_b, spring3.frame_a);
  connect(spring2.frame_b, body1.frame_a);
  connect(spring3.frame_b, spring1.frame_b);
  connect(spring2.frame_a, spring1.frame_b);
end ThreeSprings;

Modelica.Mechanics.MultiBody.Examples.Elementary.RollingWheel

Information

Extends from Modelica.Icons.Example (Icon for runnable examples).

Modelica definition

model RollingWheel 
  "Single wheel rolling on ground starting from an initial speed"
   extends Modelica.Icons.Example;

  Modelica.Mechanics.MultiBody.Parts.RollingWheel wheel1(
    wheelRadius=0.3,
    wheelMass=2,
    wheel_I_axis=0.06,
    wheel_I_long=0.12,
    hollowFraction=0.6,
    x(start=0.2),
    y(start=0.2),
    der_angles(start={0,5,1}));
  inner Modelica.Mechanics.MultiBody.World world(label2="z", n={0,0,-1});
  Modelica.Mechanics.MultiBody.Visualizers.Ground ground(length=4);
end RollingWheel;

Modelica.Mechanics.MultiBody.Examples.Elementary.RollingWheelSetDriving

Information

Extends from Modelica.Icons.Example (Icon for runnable examples).

Modelica definition

model RollingWheelSetDriving 
  "Rolling wheel set that is driven by torques driving the wheels"
   extends Modelica.Icons.Example;

  Modelica.Mechanics.MultiBody.Visualizers.Ground ground(
                length=3, groundColor={0,255,0});
  inner Modelica.Mechanics.MultiBody.World world(label2="z", n={0,0,-1});
  Modelica.Mechanics.MultiBody.Parts.RollingWheelSet wheelSet(
    wheelRadius=0.1,
    wheelMass=0.5,
    wheel_I_axis=0.01,
    wheel_I_long=0.02,
    wheelDistance=0.5,
    x(start=0.1, fixed=true),
    y(start=0.1, fixed=true),
    phi(fixed=true),
    theta1(fixed=true),
    theta2(fixed=true),
    der_theta1(fixed=true),
    der_theta2(fixed=true));
  Modelica.Mechanics.MultiBody.Parts.Body body(m=0.01, r_CM={0,0,0},
    animation=false);
  Modelica.Mechanics.MultiBody.Parts.FixedTranslation fixedTranslation(
                       r={0.2,0,0},
    animation=true,
    width=0.04);
  Modelica.Blocks.Sources.Sine sine1(freqHz=1, amplitude=2);
  Modelica.Blocks.Sources.Sine sine2(
    freqHz=1,
    amplitude=2,
    phase=1.5707963267949);
  Modelica.Mechanics.Rotational.Sources.Torque2 torque1;
  Modelica.Mechanics.Rotational.Sources.Torque2 torque2;
  Modelica.Mechanics.MultiBody.Visualizers.FixedShape shape(
    final lengthDirection={0,1,0},
    final widthDirection={1,0,0},
    final shapeType="pipe",
    final r_shape={0,-wheelSet.wheelWidth,0},
    final length=2*wheelSet.wheelWidth,
    final width=2*wheelSet.wheelRadius,
    final height=2*wheelSet.wheelRadius,
    final color={0,128,255},
    final extra=0.8);
equation 
  connect(fixedTranslation.frame_a, wheelSet.frameMiddle);
  connect(fixedTranslation.frame_b, body.frame_a);
  connect(wheelSet.axis1, torque1.flange_a);
  connect(torque1.flange_b, wheelSet.support);
  connect(wheelSet.axis2, torque2.flange_a);
  connect(wheelSet.support, torque2.flange_b);
  connect(sine1.y, torque1.tau);
  connect(sine2.y, torque2.tau);
  connect(shape.frame_a, fixedTranslation.frame_b);
end RollingWheelSetDriving;

Modelica.Mechanics.MultiBody.Examples.Elementary.RollingWheelSetPulling

Information

Extends from Modelica.Icons.Example (Icon for runnable examples).

Modelica definition

model RollingWheelSetPulling 
  "Rolling wheel set that is pulled by a force"
   extends Modelica.Icons.Example;

  Modelica.Mechanics.MultiBody.Forces.WorldForce force(animation=false);
  Modelica.Mechanics.MultiBody.Visualizers.Ground ground(
                length=3);
  inner Modelica.Mechanics.MultiBody.World world(label2="z", n={0,0,-1});
  Modelica.Mechanics.MultiBody.Parts.RollingWheelSet wheelSet(
    wheelRadius=0.1,
    wheelMass=0.5,
    wheel_I_axis=0.01,
    wheel_I_long=0.02,
    wheelDistance=0.5,
    x(start=0.1, fixed=true),
    y(start=0.1, fixed=true),
    phi(fixed=true),
    theta1(fixed=true),
    theta2(fixed=true),
    der_theta1(fixed=true),
    der_theta2(fixed=true));
  Modelica.Mechanics.MultiBody.Parts.Body body(m=0.01, r_CM={0,0,0},
    animation=false);
  Modelica.Blocks.Sources.CombiTimeTable combiTimeTable(table=[0,1,0,0; 1,1,
        0,0; 2,0,2,0; 3,0,2,0]);
  Modelica.Mechanics.MultiBody.Parts.FixedTranslation fixedTranslation(
                       r={0.2,0,0},
    animation=true,
    width=0.04);
  Modelica.Mechanics.MultiBody.Visualizers.FixedShape shape(
    final lengthDirection={0,1,0},
    final widthDirection={1,0,0},
    final shapeType="pipe",
    final r_shape={0,-wheelSet.wheelWidth,0},
    final length=2*wheelSet.wheelWidth,
    final width=2*wheelSet.wheelRadius,
    final height=2*wheelSet.wheelRadius,
    final color={0,128,255},
    final extra=0.8);
equation 
  connect(combiTimeTable.y, force.force);
  connect(fixedTranslation.frame_a, wheelSet.frameMiddle);
  connect(fixedTranslation.frame_b, body.frame_a);
  connect(force.frame_b, fixedTranslation.frame_b);
  connect(shape.frame_a, fixedTranslation.frame_b);
end RollingWheelSetPulling;

Modelica.Mechanics.MultiBody.Examples.Elementary.HeatLosses

Information

This model demonstrates how to model the dissipated power of a multi-body force element by enabling the heatPort of all components and connecting these heatPorts via a convection element to the environment. The total heat flow generated by the elements of this multi-body system and transported to the environment is present in variable convection.fluid.

Extends from Modelica.Icons.Example (Icon for runnable examples).

Modelica definition

model HeatLosses "Demonstrate the modeling of heat losses"
   extends Modelica.Icons.Example;
  inner World                              world;
  Parts.Body                              body1(
    m=1,
    r_CM={0,-0.2,0},
    cylinderDiameter=0.05,
    sphereDiameter=0.15,
    I_11=0.1,
    I_22=0.1,
    I_33=0.1,
    r_0(start={0.3,-0.2,0}, fixed=true),
    v_0(fixed=true),
    angles_fixed=true,
    w_0_fixed=true,
    w_0_start(displayUnit="deg/s") = {0,0,0.034906585039887});
  Parts.FixedTranslation                              bar1(                     r={0.3,0,0});
  Parts.FixedTranslation                              bar2(r={0.3,0,0});
  Forces.Spring                              spring1(
    s_unstretched=0.1,
    coilWidth=0.01,
    c=30,
    numberOfWindings=10,
    width=0.1);
  Forces.Damper                              damper1(d=2, useHeatPort=true);
  Forces.SpringDamperParallel springDamper(
    d=2,
    c=30,
    s_unstretched=0.1,
    width=0.1,
    coilWidth=0.01,
    numberOfWindings=10,
    useHeatPort=true);
  Parts.Body                              body2(
    m=1,
    r_CM={0,-0.2,0},
    cylinderDiameter=0.05,
    sphereDiameter=0.15,
    I_11=0.1,
    I_22=0.1,
    I_33=0.1,
    v_0(fixed=true),
    angles_fixed=true,
    w_0_fixed=true,
    w_0_start(displayUnit="deg/s") = {0,0,0.034906585039887},
    r_0(start={0.6,-0.2,0}, fixed=true));
  Parts.FixedTranslation                              bar3(r={0.3,0,0});
  Forces.SpringDamperSeries springDamperSeries(
    d=2,
    c=30,
    s_unstretched=0.1,
    useHeatPort=true);
  Parts.Body                              body3(
    m=1,
    r_CM={0,-0.2,0},
    cylinderDiameter=0.05,
    sphereDiameter=0.15,
    I_11=0.1,
    I_22=0.1,
    I_33=0.1,
    v_0(fixed=true),
    angles_fixed=true,
    w_0_fixed=true,
    w_0_start(displayUnit="deg/s") = {0,0,0.034906585039887},
    r_0(start={0.9,-0.2,0}, fixed=true));
  Forces.Spring spring(
    s_unstretched=0.2,
    width=0.05,
    c=30);
  Blocks.Sources.Constant const(k=20);
  Thermal.HeatTransfer.Components.Convection convection;
  Thermal.HeatTransfer.Celsius.FixedTemperature TAmbient(T=25) 
    "Ambient temperature";
equation 

  connect(world.frame_b,bar1. frame_a);
  connect(bar1.frame_b,bar2. frame_a);
  connect(damper1.frame_a,bar1. frame_b);
  connect(spring1.frame_a,bar1. frame_b);
  connect(damper1.frame_b,body1. frame_a);
  connect(spring1.frame_b,body1. frame_a);
  connect(bar2.frame_b, springDamper.frame_a);
  connect(springDamper.frame_b, body2.frame_a);
  connect(bar3.frame_b, springDamperSeries.frame_a);
  connect(springDamperSeries.frame_b, body3.frame_a);
  connect(bar3.frame_a, bar2.frame_b);
  connect(bar3.frame_b, spring.frame_a);
  connect(spring.frame_b, body3.frame_a);
  connect(const.y,convection. Gc);
  connect(TAmbient.port,convection. fluid);
  connect(damper1.heatPort, convection.solid);
  connect(springDamper.heatPort, convection.solid);
  connect(springDamperSeries.heatPort, convection.solid);
end HeatLosses;

Modelica.Mechanics.MultiBody.Examples.Elementary.UserDefinedGravityField

Information

This example demonstrates a user defined gravity field. Function "world.gravityAcceleration" is redeclared to function theoreticalNormalGravityWGS84 that computes the theoretical gravity of the WGS84 ellipsoid earth model at and close to the earth ellipsoid surface. In the gravity field, a large, single pendulum is present. Via parameter "geodeticLatitude", the geodetic latitude on the earth can be defined, where the pendulum is present. The world frame is located at the WGS84 earth ellipsoid at this latitude. The result variable "gravity" is the gravity vector at the center of mass of the pendulum mass. Since the height of this mass is changing, the value of the gravity is also changing (the difference is in the order of 0.00001).

The result of the simulation is slightly different at the equator (geodeticLatitude=0) and at the poles (geodeticLatitude=90). For example, after 10 s of simulation time the rotation angle of the pendulum, rev.phi, has the following values:

Extends from Modelica.Icons.Example (Icon for runnable examples).

Parameters

Type	Name	Default	Description
Angle_deg	geodeticLatitude	0	Geodetic latitude [deg]
Position	height	20	Height of pendulum attachment point over WGS84 earth ellipsoid [m]

Modelica definition

model UserDefinedGravityField 
  "Demonstrate the modeling of a user-defined gravity field"
   extends Modelica.Icons.Example;
   parameter Modelica.SIunits.Conversions.NonSIunits.Angle_deg geodeticLatitude = 0 
    "Geodetic latitude";
   parameter Modelica.SIunits.Position height = 20 
    "Height of pendulum attachment point over WGS84 earth ellipsoid";
   Modelica.SIunits.Acceleration gravity[3]=body.g_0 
    "Gravity acceleration at center of mass of body";
  inner Modelica.Mechanics.MultiBody.World world(
    gravityType=Modelica.Mechanics.MultiBody.Types.GravityTypes.NoGravity,
      redeclare function gravityAcceleration =
        Modelica.Mechanics.MultiBody.Examples.Elementary.Utilities.theoreticalNormalGravityWGS84
        (mue=1, phi=geodeticLatitude),
    axisLength=10,
    nominalLength=10);
  Joints.Revolute rev(n={0,0,1},useAxisFlange=true,
    phi(fixed=true),
    w(fixed=true));
  Rotational.Components.Damper damper(d=0.1);
  Parts.Body body(r_CM={10,0,0},
    m=1000.0,
    sphereDiameter=1);
  Parts.FixedTranslation fixedTranslation(r={0,height,0}, width=0.3);
equation 
  connect(damper.flange_b,rev. axis);
  connect(rev.support,damper. flange_a);
  connect(body.frame_a,rev. frame_b);
  connect(world.frame_b, fixedTranslation.frame_a);
  connect(fixedTranslation.frame_b, rev.frame_a);
end UserDefinedGravityField;

Modelica.Mechanics.MultiBody.Examples.Elementary.Surfaces

Information

This example demonstrates the use of the Surface visualizer that visualizes a moving, parameterized surface. The "sine-wave" surface is a direct application of the surface model. Furthermore, the "torus" surface is an instance of Torus, the "wheel" surface is an instance of VoluminousWheel, and the "pipeWithScalarField surface is an instance of PipeWithScalarField. All latter visual shapes are constructed with the surface model. The following image shows a screen-shot of this example model:

Extends from Modelica.Icons.Example (Icon for runnable examples).

Parameters

Type	Name	Default	Description
Real	x_min	-1	Minimum value of x
Real	x_max	+1	Maximum value of x
Real	y_min	-1	Minimum value of y
Real	y_max	+1	Maximum value of y
Real	z_min	0	Minimum value of z
Real	z_max	1	Maximum value of z

Modelica definition

model Surfaces 
  "Demonstrate the visualization of a sine surface, as well as a torus and a wheel constucted from a surface"
  extends Modelica.Icons.Example;
  parameter Real x_min=-1 "Minimum value of x";
  parameter Real x_max=+1 "Maximum value of x";
  parameter Real y_min=-1 "Minimum value of y";
  parameter Real y_max=+1 "Maximum value of y";
  parameter Real z_min=0 "Minimum value of z";
  parameter Real z_max=1 "Maximum value of z";
  Real wz = time;
  Modelica.Mechanics.MultiBody.Visualizers.Advanced.Surface surface(
    redeclare function surfaceCharacteristic =
        Modelica.Mechanics.MultiBody.Examples.Elementary.Utilities.sineSurface
        (  x_min=x_min,
           x_max=x_max,
           y_min=y_min,
           y_max=y_max,
           z_min=z_min,
           z_max=z_max,
           wz=wz),
    multiColoredSurface=false,
    nu=50,
    nv=50);
  inner World world(axisLength=1, n={0,0,-1});
  Visualizers.Torus torus;
  Joints.Prismatic prismatic(useAxisFlange=true, animation=false,
    v(fixed=true));
  Translational.Sources.Position position;
  Blocks.Sources.Sine sine(amplitude=2, freqHz=0.5);
  Visualizers.Ground ground(          groundColor={215,215,215}, length=4);
  Parts.FixedTranslation fixedTranslation1(r={0,-1.3,torus.ro + torus.ri},
      animation=false);
  Parts.FixedTranslation fixedTranslation2(
      animation=false, r={0,-1.6,wheel.rTire});
  Visualizers.VoluminousWheel wheel;
  Visualizers.PipeWithScalarField pipeWithScalarField(
    rOuter=0.3,
    length=1,
    T_min=0,
    T_max=2,
    T=sin(Modelica.Constants.pi*pipeWithScalarField.xsi)*cos(Modelica.Constants.pi
        *time) .+ 1,
    n_colors=32);
  Parts.FixedTranslation fixedTranslation3(
      animation=false, r={0,-2.2,0});
equation 
  connect(world.frame_b, prismatic.frame_a);
  connect(position.flange, prismatic.axis);
  connect(sine.y, position.s_ref);
  connect(prismatic.frame_b, fixedTranslation1.frame_a);
  connect(fixedTranslation1.frame_b, torus.frame_a);
  connect(prismatic.frame_b, fixedTranslation2.frame_a);
  connect(fixedTranslation2.frame_b, wheel.frame_a);
  connect(world.frame_b, fixedTranslation3.frame_a);
  connect(fixedTranslation3.frame_b, pipeWithScalarField.frame_a);
end Surfaces;

Modelica.Mechanics.MultiBody.Examples.Elementary.PointGravityWithPointMasses2.PointMass

Parameters

Type	Name	Default	Description
Boolean	animation	true	= true, if animation shall be enabled (show sphere)
Mass	m	1	Mass of mass point [kg]
Initialization
Position	r_0.start[3]	{0,0,0}	Position vector from origin of world frame to origin of frame_a, resolved in world frame [m]
Velocity	v_0.start[3]	{0,0,0}	Absolute velocity of frame_a, resolved in world frame (= der(r_0)) [m/s]
Acceleration	a_0.start[3]	{0,0,0}	Absolute acceleration of frame_a resolved in world frame (= der(v_0)) [m/s2]
Animation
if animation = true
Diameter	sphereDiameter	world.defaultBodyDiameter	Diameter of sphere [m]
Color	sphereColor	{255,0,0}	Color of sphere
SpecularCoefficient	specularCoefficient	world.defaultSpecularCoeffic...	Reflection of ambient light (= 0: light is completely absorbed)
Advanced
StateSelect	stateSelect	StateSelect.avoid	Priority to use frame_a.r_0, v_0 (= der(frame_a.r_0)) as states

Connectors

Type	Name	Description
Frame_a	frame_a	Coordinate system fixed at center of mass point

Modelica definition

model PointMass = Modelica.Mechanics.MultiBody.Parts.PointMass (m=1, sphereColor={
        255,0,0}) "Point mass used at all places of this example";

Modelica.Mechanics.MultiBody.Examples.Elementary.PointGravityWithPointMasses2.SystemWithStandardBodies

Information

In order to compare the results of the "PointMass" example where 6 point masses are rigidly connected together, in this comparision model, an equivalent system is setup, with the only difference that the point masses are replaced by Bodies with zero inertia.

Modelica definition

model SystemWithStandardBodies 
  "For comparison purposes, an equivalent model with Bodies instead of PointMasses"
  model PointMass = Modelica.Mechanics.MultiBody.Parts.Body(m=1,I_11=0,I_22=0,I_33=0) 
    "Body used all places of the comparision model with zero inertia tensor";

  PointMass pointMass1(
      r_0(start={3,0,0}, fixed=true),
      v_0(start={0,0,-1}, fixed=true),
      angles_fixed=true,
      w_0_fixed=true,
      r_CM={0,0,0});
  PointMass pointMass2(r_CM={0,0,0});
  PointMass pointMass3(r_CM={0,0,0});
  PointMass pointMass4(r_CM={0,0,0});
  PointMass pointMass5(r_CM={0,0,0});
  PointMass pointMass6(r_CM={0,0,0});

  Modelica.Mechanics.MultiBody.Parts.FixedTranslation fixedTranslation( r={1,0,0});
  Modelica.Mechanics.MultiBody.Parts.FixedTranslation fixedTranslation1( r={-1,0,0});
  Modelica.Mechanics.MultiBody.Parts.FixedTranslation fixedTranslation2( r={0,1,0});
  Modelica.Mechanics.MultiBody.Parts.FixedTranslation fixedTranslation3( r={0,-1,0});
  Modelica.Mechanics.MultiBody.Parts.FixedTranslation fixedTranslation4( r={0,0,1});
  Modelica.Mechanics.MultiBody.Parts.FixedTranslation fixedTranslation5( r={0,0,-1});

equation 
  connect(fixedTranslation1.frame_a, fixedTranslation.frame_a);
  connect(fixedTranslation1.frame_a, fixedTranslation2.frame_a);
  connect(fixedTranslation3.frame_a, fixedTranslation.frame_a);
  connect(fixedTranslation1.frame_a, fixedTranslation4.frame_a);
  connect(fixedTranslation5.frame_a, fixedTranslation.frame_a);
  connect(fixedTranslation2.frame_b, pointMass3.frame_a);
  connect(fixedTranslation3.frame_b, pointMass4.frame_a);
  connect(pointMass5.frame_a, fixedTranslation4.frame_b);
  connect(fixedTranslation5.frame_b, pointMass6.frame_a);
  connect(fixedTranslation.frame_b, pointMass1.frame_a);
  connect(fixedTranslation1.frame_b, pointMass2.frame_a);
end SystemWithStandardBodies;

Modelica.Mechanics.MultiBody.Examples.Elementary.PointGravityWithPointMasses2.SystemWithStandardBodies.PointMass

Parameters

Type	Name	Default	Description
Boolean	animation	true	= true, if animation shall be enabled (show cylinder and sphere)
Position	r_CM[3]		Vector from frame_a to center of mass, resolved in frame_a [m]
Mass	m	1	Mass of rigid body [kg]
Inertia tensor (resolved in center of mass, parallel to frame_a)
Inertia	I_11	0	(1,1) element of inertia tensor [kg.m2]
Inertia	I_22	0	(2,2) element of inertia tensor [kg.m2]
Inertia	I_33	0	(3,3) element of inertia tensor [kg.m2]
Inertia	I_21	0	(2,1) element of inertia tensor [kg.m2]
Inertia	I_31	0	(3,1) element of inertia tensor [kg.m2]
Inertia	I_32	0	(3,2) element of inertia tensor [kg.m2]
Initialization
Position	r_0.start[3]	{0,0,0}	Position vector from origin of world frame to origin of frame_a [m]
Velocity	v_0.start[3]	{0,0,0}	Absolute velocity of frame_a, resolved in world frame (= der(r_0)) [m/s]
Acceleration	a_0.start[3]	{0,0,0}	Absolute acceleration of frame_a resolved in world frame (= der(v_0)) [m/s2]
Boolean	angles_fixed	false	= true, if angles_start are used as initial values, else as guess values
Angle	angles_start[3]	{0,0,0}	Initial values of angles to rotate frame_a around 'sequence_start' axes into frame_b [rad]
RotationSequence	sequence_start	{1,2,3}	Sequence of rotations to rotate frame_a into frame_b at initial time
Boolean	w_0_fixed	false	= true, if w_0_start are used as initial values, else as guess values
AngularVelocity	w_0_start[3]	{0,0,0}	Initial or guess values of angular velocity of frame_a resolved in world frame [rad/s]
Boolean	z_0_fixed	false	= true, if z_0_start are used as initial values, else as guess values
AngularAcceleration	z_0_start[3]	{0,0,0}	Initial values of angular acceleration z_0 = der(w_0) [rad/s2]
Animation
if animation = true
Diameter	sphereDiameter	world.defaultBodyDiameter	Diameter of sphere [m]
Color	sphereColor	Modelica.Mechanics.MultiBody...	Color of sphere
Diameter	cylinderDiameter	sphereDiameter/Types.Default...	Diameter of cylinder [m]
Color	cylinderColor	sphereColor	Color of cylinder
SpecularCoefficient	specularCoefficient	world.defaultSpecularCoeffic...	Reflection of ambient light (= 0: light is completely absorbed)
Advanced
Boolean	enforceStates	false	= true, if absolute variables of body object shall be used as states (StateSelect.always)
Boolean	useQuaternions	true	= true, if quaternions shall be used as potential states otherwise use 3 angles as potential states
RotationSequence	sequence_angleStates	{1,2,3}	Sequence of rotations to rotate world frame into frame_a around the 3 angles used as potential states

Connectors

Type	Name	Description
Frame_a	frame_a	Coordinate system fixed at body

Modelica definition

model PointMass = Modelica.Mechanics.MultiBody.Parts.Body(m=1,I_11=0,I_22=0,I_33=0) 
  "Body used all places of the comparision model with zero inertia tensor";