Abstract

Abstract. The computational efficiency of symbolic generation was at the root of the emergence of symbolic multibody programs in the eighties. At present, it remains an attractive feature of it since the exponential increase in modern computer performances naturally provides the opportunity to investigate larger systems and more sophisticated models for which real-time computation is a real asset. Nowadays, in the context of mechatronic multibody systems, another interesting feature of the symbolic approach appears when dealing with enlarged multibody models, i.e. including electrical actuators, hydraulic devices, pneumatic suspensions, etc. and requiring specific analyses like control and optimization. Indeed, since symbolic multibody programs clearly distinguish the modeling phase from the analysis process, extracting the symbolic model, as well as some precious ingredients like analytical sensitivities, in order to export it towards any suitable environment (for control or optimization purposes) is quite straightforward. Symbolic multibody model portability is thus very attractive for the analysis of mechatronic applications. In this context, the main features and recent developments of the ROBOTRAN software developed at the Université catholique de Louvain (Belgium) are reviewed in this paper and illustrated via three multibody applications which highlight its capabilities for dealing with very large systems and coping with multiphysics issues.

Highlights

  • Before the appearance of efficient computer architectures for scientific numerical computations, only analytical methods were available for modeling systems

  • Numerous so-called multibody programs were developed all over the world as from the seventies (Schiehlen, 1990), each of them being described as a general purpose code in reality, faced with the huge variety of applications, they all impose some restrictions on the modeling and analysis processes

  • The inverse dynamics of a multibody system is the computation of the generalized joint forces φ to be applied to the joints for a given configuration (q, q, q) of the system to which external forces and torques are applied: φ = f (q, q, q, δ, f r, tr, g) in which the dimension of φ and q are equal for a fully actuated system

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Summary

Introduction

Before the appearance of efficient computer architectures for scientific numerical computations, only analytical methods were available for modeling systems. The analyses often used rather restrictive hypotheses (truncated and/or linearized models, for instance). The emergence of powerful processors and reliable and user-friendly languages and software led the scientific community to develop numerical programs able to cover a wide range of applications in a given field Numerous so-called multibody programs were developed all over the world as from the seventies (Schiehlen, 1990), each of them being described as a general purpose code in reality, faced with the huge variety of applications, they all impose some restrictions on the modeling and analysis processes

System modeling versus system analysis
Numerical versus symbolic implementation
State-of-the-art
ROBOTRAN formalisms
Dynamics of tree-like multibody systems
Direct dynamics
Inverse dynamics
Reaction dynamics
Symbolic engine
Expression simplification
Trigonometric simplification
Recursive scheme condensation
Memory allocation
Fully symbolic generation of constrained MBS
Recursive differentiation of multibody models
ROBOTRAN computer framework
Drawing the multibody system
Writing the multibody equations
Symbolic equations
User equations
MBsysLab modules for Matlab
MBsysLab for Simulink
Simulating and analyzing the multibody system
Illustrative applications
A modern car equipped with a KineticTM H2 suspension
A truck-mounted attenuator
A grand piano action
Findings
Conclusions
Full Text
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