Page 111 - Mechatronic Systems Modelling and Simulation with HDLs

100 6 MECHANICS IN HARDWARE DESCRIPTION LANGUAGES

modelling using concentrated parameters and is thus comparable with a circuit
made up of components.
In some cases the abstraction of a continuum to the discrete elements of a multi-
body system is not suitable for the solving of the envisaged problem. For example,
this is the case if the exact deformation of an elastic body contributes significantly
to the system behaviour. In this case models need to be created and formulated
in hardware description languages that adequately describe the continuum with its
distributed parameters. Both multibody mechanics and continuum mechanics will
be considered in the following.

6.2 Multibody Mechanics

6.2.1 Introduction
When modelling multibody mechanics using hardware description languages, we
first have to raise the question of the perspective from which the system is to be
considered. One option focuses upon the system level, the other upon the com-
ponent level with the system models being generated by connecting component
models together. The first method is called system-oriented modelling and the
second method object-oriented modelling.
The first option has the advantage that equations of motion can be created using
standard engineering methods. Furthermore, we have access to a greater system
knowledge during the modelling, which can be beneficial. However, one problem is
that this type of consideration opposes one of the most important basic philosophies
for the development of electronics. In this field it is generally sufficient to model only
the fundamental components and to develop complex systems from these. Further
modelling is normally not necessary during the development of electronic systems.
As an alternative to this we can use object-oriented modelling to describe the
standard components — for example bodies, springs, dampers, joints, etc. — and put
these submodels together into a system model. Information about this system, such
as, for example, a favourable selection of generalised coordinates, is in principle
not available and thus cannot be used for the simplification or acceleration of the
model. However, the building of a system model can be considerably simplified if
the basic models that are required are available.
In the following we will consider how it is possible to obtain equations of motion
for multibody systems, see for example, Dankert and Dankert [79], Greenwood
[125], Hiller [144] or Nikravesh [299] for the basic principles shown. Multibody
systems typically include the following components:
• Particles with translational inertia.
• Rigid bodies with translational and rotational inertia.
• Suspensions and joints that limit the movement of individual particles and
bodies in relation to one another.
• Coupling elements, e.g. springs, dampers, servo motors, etc.