Modelica.Mechanics.MultiBody.UsersGuide

Library MultiBody is a free Modelica package providing 3-dimensional mechanical components to model in a convenient way mechanical systems, such as robots, mechanisms, vehicles. This package contains the User's Guide for the MultiBody library.

1. Tutorial gives an introduction into the most important aspects of the library.
2. Upgrade describes how to upgrade from former versions, especially from the "old" ModelicaAdditions.MultiBody library.
3. Literature provides references that have been used to design and implement this library.
4. Contact provides information about the author of the library as well as acknowledgments.

Package Content

Name	Description
Tutorial	Tutorial
Upgrade	Upgrade from Former Versions
Literature	Literature
Contact	Contact

Modelica.Mechanics.MultiBody.UsersGuide.Upgrade

If different versions of the MultiBody library are not compatible to each other, corresponding conversion scripts are provided. As a result, models build with an older version of the MultiBody library are automatically converted to the new version when the model is loaded. The user is prompted whether automatic conversion shall take place or not. Problems are not to be expected. Still one should first make a copy of such a model as backup before the conversion is performed.

Upgrade from ModelicaAdditions.MultiBody

There is now also a conversion script from the "old" ModelicaAdditions.MultiBody library to the "new" Modelica.Mechanics.MultiBody library. This script is also automatically invoked. Since the differences between the "old" and the "new" MultiBody library are so large, not everything is converted and it might be that some pieces have to be adapted manually. Still, this script is useful, since many class names, parameters and modifiers are automatically converted.

Components from the following sublibraries are automatically converted to the Modelica.Mechanics.MultiBody library:

• ModelicaAdditions.MultiBody.Parts
• ModelicaAdditions.MultiBody.Joints
• ModelicaAdditions.MultiBody.Forces
• Part of ModelicaAdditions.MultiBody.Interfaces

Models using the ModelicaAdditions.MultiBody library that are programmed with equations are only partly converted: The Frame connectors will be converted to the "new" Frame connectors of the MultiBody library, but the equations that reference variables of the Frame connectors will not be converted. For a manual conversion, the following table might be helpful showing how the variables of the "old" and the "new" Frame connectors are related to each other (resolve2 and angularVelocity2 are functions from library Modelica.Mechanics.MultiBody.Frames):

Upgrade from MultiBody 0.99 (and earlier) to 1.0 (and later)

The conversion from MultiBody 0.99 to 1.0 does not work in some rare cases, where own components are implemented using functions of the MultiBody.Frames package. In this case, the conversion has to be performed manually. The changes in 1.0 with regards to 0.99 are:

The definition of the Modelica.Mechanics.MultiBody.Frames.Orientation object has changed. In 0.99 this was just an alias type for a transformation matrix (now Modelica.Mechanics.MultiBody.Frames.TransformationMatrices.Orientation). In 1.0 the orientation object is a record holding the transformation matrix from frame 1 to frame 2 and the angular velocity of the transformation matrix resolved in frame 2. The reason is that this allows to compute the angular velocity in many cases by standard recursive formulas and not by differentiation of the transformation matrix. This is usually much more efficient. As a consequence, the following calls in 0.99 should be changed:

   Frames.angularVelocity1(T,der(T)) -> Frames.angularVelocity1(T)
   Frames.angularVelocity2(T,der(T)) -> Frames.angularVelocity2(T)
   Frames.from_T(T)                  -> Frames.from_T2(T,der(T))

Modelica.Mechanics.MultiBody.UsersGuide.Literature

• Technical details of this library are described in the 20 page paper:

  Otter M., Elmqvist H., and Mattsson S.E.:

  The New Modelica MultiBody Library. Modelica 2003 Conference, Linköping, Sweden, pp. 311-330, Nov. 3-4, 2003. Download from: https://www.modelica.org/events/Conference2003/papers/h37_Otter_multibody.pdf

• The method how to describe drive trains with 1-dimensional mechanics and to mount them on 3-dimensional components without neglecting dynamical effects is described in:

  Schweiger C., and Otter M.:

  Modelling 3-dim. Mechanical Effects of 1-dim. Powertrains. Modelica 2003 Conference, Linköping, Sweden, pp. 149-158, Nov. 3-4, 2003. Download from: https://www.modelica.org/events/Conference2003/papers/h06_Schweiger_powertrains_v5.pdf

• The method to solve a certain class of kinematic loops analytically is based on:

  Woernle C.:

  Ein systematisches Verfahren zur Aufstellung der geometrischen Schliessbedingungen in kinematischen Schleifen mit Anwendung bei der Rückwärtstransformation für Industrieroboter.
  Fortschritt-Berichte VDI, Reihe 18, Nr. 59, Duesseldorf: VDI-Verlag 1988, ISBN 3-18-145918-6.
   

  Hiller M., and Woernle C.:

  A Systematic Approach for Solving the Inverse Kinematic Problem of Robot Manipulators.
  Proceedings 7th World Congress Th. Mach. Mech., Sevilla 1987.

Modelica.Mechanics.MultiBody.UsersGuide.Contact

Library Officer:

Martin Otter
Deutsches Zentrum für Luft und Raumfahrt e.V. (DLR)
Institut für Robotik und Mechatronik
Abteilung für Entwurfsorientierte Regelungstechnik
Postfach 1116
D-82230 Wessling
Germany
email: Martin.Otter@dlr.de

Acknowledgements:

• The central idea to handle a certain class of overdetermined, consistent set of differential algebraic equations (i.e., there are more equations than unknowns) with symbolic transformation algorithms was developed together with Hilding Elmqvist and Sven Erik Mattsson from Dassault Systèmes AB, Lund, Sweden. The MultiBody library is heavily relying on this feature which is a prerequisite for a truly "object-oriented" multi-body systems library, where components can be connected together in any meaningful way.
• The Examples.Loops.EngineV6 demo of a six cylinder V6 engine with 6 planar loops and 1 degree of freedom is from Hilding Elmqvist and Sven Erik Mattsson.
• Modelica.Mechanics.MultiBody.Forces.LineForceWithMass is based on model "RelativeDistance" from the Modelica VehicleDynamics library of Johan Andreasson from Royal Institute of Technology, Stockholm, Sweden.
• The 1-dim. components (Parts.Rotor1D, Parts.BevelGear1D, Mounting1D) and Joints.GearConstraints are from Christian Schweiger.
• The design of this library is based on work carried out in the EU RealSim project (Real-time Simulation for Design of Multi-physics Systems) funded by the European Commission within the Information Societies Technology (IST) programme under contract number IST 1999-11979.