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 constructed from a surface

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 constructed 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.

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.

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):

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").

Parameters

Name	Description
animation	= true, if animation shall be enabled

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.

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 chosen 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.

Parameters

Name	Description
m	Mass of point masses [kg]

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.

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:

Parameters

Name	Description
animation	= true, if animation shall be enabled

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.

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.

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

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").

Parameters

Name	Description
animation	= true, if animation shall be enabled

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.

Parameters

Name	Description
animation	= true, if animation shall be enabled

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.

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.

Parameters

Name	Description
animation	= true, if animation shall be enabled

Modelica.Mechanics.MultiBody.Examples.Elementary.RollingWheel

Information

Modelica.Mechanics.MultiBody.Examples.Elementary.RollingWheelSetDriving

Information

Modelica.Mechanics.MultiBody.Examples.Elementary.RollingWheelSetPulling

Information

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.

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:

Parameters

Name	Description
geodeticLatitude	Geodetic latitude [deg]
height	Height of pendulum attachment point over WGS84 earth ellipsoid [m]

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:

Parameters

Name	Description
x_min	Minimum value of x
x_max	Maximum value of x
y_min	Minimum value of y
y_max	Maximum value of y
z_min	Minimum value of z
z_max	Maximum value of z