# Translational

Library to model 1-dimensional, translational mechanical systems

## Package Contents

Components Components for 1D translational mechanical drive trains | |

Examples Demonstration examples of the components of this package | |

Interfaces Interfaces for 1-dim. translational mechanical components | |

Sensors Sensors for 1-dim. translational mechanical quantities | |

Sources Sources to drive 1D translational mechanical components |

This package contains components to model *1-dimensional translational
mechanical* systems.

The *filled* and *non-filled green squares* at the left and
right side of a component represent *mechanical flanges*.
Drawing a line between such squares means that the corresponding
flanges are *rigidly attached* to each other. The components of this
library can be usually connected together in an arbitrary way. E.g. it is
possible to connect two springs or two sliding masses with inertia directly
together.

The only *connection restriction* is that the Coulomb friction
elements (e.g. MassWithStopAndFriction) should be only connected
together provided a compliant element, such as a spring, is in between.
The reason is that otherwise the frictional force is not uniquely
defined if the elements are stuck at the same time instant (i.e., there
does not exist a unique solution) and some simulation systems may not be
able to handle this situation, since this leads to a singularity during
simulation. It can only be resolved in a "clean way" by combining the
two connected friction elements into
one component and resolving the ambiguity of the frictional force in the
stuck mode.

Another restriction arises if the hard stops in model MassWithStopAndFriction are used, i. e.
the movement of the mass is limited by a stop at smax or smin.
**This requires the states Stop.s and Stop.v** . If these states are eliminated during the index reduction
the model will not work. To avoid this any inertias should be connected via springs
to the Stop element, other sliding masses, dampers or hydraulic chambers must be avoided.

In the *icon* of every component an *arrow* is displayed in grey
color. This arrow characterizes the coordinate system in which the vectors
of the component are resolved. It is directed into the positive
translational direction (in the mathematical sense).
In the flanges of a component, a coordinate system is rigidly attached
to the flange. It is called *flange frame* and is directed in parallel
to the component coordinate system. As a result, e.g., the positive
cut-force of a "left" flange (flange_a) is directed into the flange, whereas
the positive cut-force of a "right" flange (flange_b) is directed out of the
flange. A flange is described by a Modelica connector containing
the following variables:

Modelica.SIunits.Position s "Absolute position of flange";flowModelica.SIunits.Force f "Cut-force in the flange";

This library is designed in a fully object oriented way in order that
components can be connected together in every meaningful combination
(e.g. direct connection of two springs or two shafts with inertia).
As a consequence, most models lead to a system of
differential-algebraic equations of *index 3* (= constraint
equations have to be differentiated twice in order to arrive at
a state space representation) and the Modelica translator or
the simulator has to cope with this system representation.
According to our present knowledge, this requires that the
Modelica translator is able to symbolically differentiate equations
(otherwise it is e.g. not possible to provide consistent initial
conditions; even if consistent initial conditions are present, most
numerical DAE integrators can cope at most with index 2 DAEs).

**Library Officer**- Martin Otter

Deutsches Zentrum für Luft und Raumfahrt e.V. (DLR)

Institut für Robotik und Mechatronik (DLR-RM)

Abteilung Systemdynamik und Regelungstechnik

Postfach 1116

D-82230 Wessling

Germany

email: Martin.Otter@dlr.de

**Contributors to this library:**

- Main author until 2006:

Peter Beater

Universität Paderborn, Abteilung Soest

Fachbereich Maschinenbau/Automatisierungstechnik

Lübecker Ring 2

D 59494 Soest

Germany

email: info@beater.de

- Anton Haumer

Technical Consulting & Electrical Engineering

A-3423 St.Andrae-Woerdern, Austria

email: a.haumer@haumer.at - Martin Otter (DLR-RM)

Copyright © 1998-2009, Modelica Association, Anton Haumer and Universität Paderborn, FB 12.

*This Modelica package is free software; it can be redistributed and/or modified
under the terms of the Modelica license, see the license conditions
and the accompanying disclaimer
here.*