Modelica.Mechanics.MultiBody.Examples.Elementary

Elementary examples to demonstrate various features of the MultiBody library

Information

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

Content

ModelDescription
DoublePendulum
DoublePendulumInitTip
Simple double pendulum with two revolute joints and two bodies. In DoublePendulumInitTip, the initial position of the pendulum tip is given instead of common initialization by pendulum angles.
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 constructed from a surface

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

Package Content

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

Modelica.Mechanics.MultiBody.Examples.Elementary.DoublePendulum Modelica.Mechanics.MultiBody.Examples.Elementary.DoublePendulum

Simple double pendulum with two revolute joints and two bodies

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.

model Examples.Elementary.DoublePendulum

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

Modelica.Mechanics.MultiBody.Examples.Elementary.DoublePendulumInitTip Modelica.Mechanics.MultiBody.Examples.Elementary.DoublePendulumInitTip

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

Information

This example demonstrates at hand of a double pendulum, how non-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.

Setting only the tip's start position results in an ambiguous initialization since two valid solutions for revolute1.phi and revolute2.phi exist. Moreover, the calculated angles revolute1.phi and revolute2.phi can be a multiple of expected solution phi1 and phi2,

To clearly indicate the preferred solution, guess initial angles can be additionally given. In this example, it is simply done by revolute2.phi.start = Modelica.Constants.pi/2.

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

Modelica.Mechanics.MultiBody.Examples.Elementary.ForceAndTorque Modelica.Mechanics.MultiBody.Examples.Elementary.ForceAndTorque

Demonstrate usage of ForceAndTorque element

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.Mechanics.MultiBody.Examples.Elementary.FreeBody Modelica.Mechanics.MultiBody.Examples.Elementary.FreeBody

Free flying body attached by two springs to environment

Information

This example demonstrates:

model Examples.Elementary.FreeBody

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

Parameters

NameDescription
animation= true, if animation shall be enabled

Modelica.Mechanics.MultiBody.Examples.Elementary.InitSpringConstant Modelica.Mechanics.MultiBody.Examples.Elementary.InitSpringConstant

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

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.

model Examples.Elementary.InitSpringConstant

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

Modelica.Mechanics.MultiBody.Examples.Elementary.LineForceWithTwoMasses Modelica.Mechanics.MultiBody.Examples.Elementary.LineForceWithTwoMasses

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

Information

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

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 chosen relative tolerance of the integration, the difference is in the order of 1e-10 … 1e-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

NameDescription
mMass of point masses [kg]

Modelica.Mechanics.MultiBody.Examples.Elementary.Pendulum Modelica.Mechanics.MultiBody.Examples.Elementary.Pendulum

Simple pendulum with one revolute joint and one body

Information

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

model Examples.Elementary.Pendulum

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

Modelica.Mechanics.MultiBody.Examples.Elementary.PendulumWithSpringDamper Modelica.Mechanics.MultiBody.Examples.Elementary.PendulumWithSpringDamper

Simple spring/damper/mass system

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:

model Examples.Elementary.PendulumWithSpringDamper

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

Parameters

NameDescription
animation= true, if animation shall be enabled

Modelica.Mechanics.MultiBody.Examples.Elementary.PointGravity Modelica.Mechanics.MultiBody.Examples.Elementary.PointGravity

Two point masses in a point gravity field

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.

model Examples.Elementary.PointGravity

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

Modelica.Mechanics.MultiBody.Examples.Elementary.PointGravityWithPointMasses Modelica.Mechanics.MultiBody.Examples.Elementary.PointGravityWithPointMasses

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

Information

This model demonstrates the usage of model Parts.PointMass in a point gravity field. The PointMass model has the feature that the 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.Mechanics.MultiBody.Examples.Elementary.PointGravityWithPointMasses2 Modelica.Mechanics.MultiBody.Examples.Elementary.PointGravityWithPointMasses2

Rigidly connected point masses in a point gravity field

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 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 visualizes the point masses in "red", whereas the "referenceSystem" shows its bodies in "blue".

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

Modelica.Mechanics.MultiBody.Examples.Elementary.SpringDamperSystem Modelica.Mechanics.MultiBody.Examples.Elementary.SpringDamperSystem

Simple spring/damper/mass system

Information

This example demonstrates:

model Examples.Elementary.SpringDamperSystem

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

Parameters

NameDescription
animation= true, if animation shall be enabled

Modelica.Mechanics.MultiBody.Examples.Elementary.SpringMassSystem Modelica.Mechanics.MultiBody.Examples.Elementary.SpringMassSystem

Mass attached with a spring to the world frame

Information

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

model Examples.Elementary.SpringMassSystem

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

Parameters

NameDescription
animation= true, if animation shall be enabled

Modelica.Mechanics.MultiBody.Examples.Elementary.SpringWithMass Modelica.Mechanics.MultiBody.Examples.Elementary.SpringWithMass

Point mass hanging on a spring

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.

model Examples.Elementary.SpringWithMass

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

Modelica.Mechanics.MultiBody.Examples.Elementary.ThreeSprings Modelica.Mechanics.MultiBody.Examples.Elementary.ThreeSprings

3-dim. springs in series and parallel connection

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.

model Examples.Elementary.ThreeSprings

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

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

Parameters

NameDescription
animation= true, if animation shall be enabled

Modelica.Mechanics.MultiBody.Examples.Elementary.RollingWheel Modelica.Mechanics.MultiBody.Examples.Elementary.RollingWheel

Single wheel rolling on ground starting from an initial speed

Information

Demonstrates how a single wheel is rolling on ground (starting with an initial velocity).

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

Modelica.Mechanics.MultiBody.Examples.Elementary.RollingWheelSetDriving Modelica.Mechanics.MultiBody.Examples.Elementary.RollingWheelSetDriving

Rolling wheel set that is driven by torques driving the wheels

Information

Demonstrates how a RollingWheelSet (two wheels rigidly coupled together) is rolling on ground when driven by some external torques.

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

Modelica.Mechanics.MultiBody.Examples.Elementary.RollingWheelSetPulling Modelica.Mechanics.MultiBody.Examples.Elementary.RollingWheelSetPulling

Rolling wheel set that is pulled by a force

Information

Demonstrates how a RollingWheelSet (two wheels rigidly coupled together) is rolling on ground when pulled by an external force.

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

Modelica.Mechanics.MultiBody.Examples.Elementary.HeatLosses Modelica.Mechanics.MultiBody.Examples.Elementary.HeatLosses

Demonstrate the modeling of heat losses

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.Mechanics.MultiBody.Examples.Elementary.UserDefinedGravityField Modelica.Mechanics.MultiBody.Examples.Elementary.UserDefinedGravityField

Demonstrate the modeling of a user-defined gravity field

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:

latitude [deg] rev.phi [rad]
= 0 = -2.39 rad
= 90 = -2.42 rad

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

Parameters

NameDescription
geodeticLatitudeGeodetic latitude [deg]
heightHeight of pendulum attachment point over WGS84 earth ellipsoid [m]

Modelica.Mechanics.MultiBody.Examples.Elementary.Surfaces Modelica.Mechanics.MultiBody.Examples.Elementary.Surfaces

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

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

NameDescription
x_minMinimum value of x
x_maxMaximum value of x
y_minMinimum value of y
y_maxMaximum value of y
z_minMinimum value of z
z_maxMaximum value of z
Automatically generated Thu Oct 1 16:07:52 2020.