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6

Mechanics in Hardware

Description Languages

6.1 Introduction

The objective of this section is to highlight the most important strategies for obtain-
ing the equations of motion for mechanical components and systems and to clarify
the options for their subsequent representation in hardware description languages.
Both direct formulations of symbolic equations and indirect formulations based
upon the parametric calculation of the system matrices will be considered. The
latter is often also called the solution using numerical equations.
The use of hardware description languages for the modelling of mechanics also
implies that the solution of the mechanical equation takes place using the solver
of the circuit simulator. Naturally, solvers are generally optimised for various
domains. For electronics the focus tends to be upon the management of a large
number of degrees of freedom, whereas in mechanics numerical problems with
a large number of constraints require particular attention. On the other hand, the
example of the classical multibody simulator ADAMS shows that this contrast is
not irreconcilable, see Orlandea et al. [304] and [305]. The numerics of ADAMS
is largely based upon procedures that are also used in circuit simulation. We should
mention at this point that the equation system is not formulated using a minimum
number of equations according to the degrees of freedom. Rather, each individ-
ual equation is entered into an overall system. Thus the resulting system matrix
is sparse and can be processed using ‘sparse matrix’ techniques. The numerical
integration takes place using the Gear procedure that is also commonly used in
circuit simulation.
In mechanics — as in electronics — we can differentiate between various abstrac-
tions. Multibody mechanics and continuum mechanics are examples. According to
Schiehlen [361] a multibody system is characterised as a collection of rigid and/or
elastic bodies with inertia as well as springs, dampers and servo motors without
inertia. These are connected together by rigid bearings, joints or suspensions. Fric-
tion and contact forces can also be included if necessary. This corresponds with

Mechatronic Systems Georg Pelz
 2003 John Wiley & Sons, Ltd ISBN: 0-470-84979-7