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  • 1
    Electronic Resource
    Electronic Resource
    Symbolic generation of large multibody system dynamic equations using a new semi-explicit Newton/Euler recursive scheme (1996)
    Springer
    Archive of applied mechanics 66 (1996), S. 187-199 
    Details
    ISSN: 1432-0681
    Keywords: dynamic modelling ; multibody system ; symbolic generation ; computer simulation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Summary The aim of this paper is to show that multibody systems with a large number of degrees of freedom can be efficiently modelled, taking conjointly advantage of a recursive formulation of the equations of motion and of the symbolic generation capabilities. Recursive schemes are widely used in the field of multibody dynamics since they avoid the “explosion” of the number of arithmetical operations in case of large multibody models. Within the context of our field of applications (railway dynamics simulation), explicit integration schemes are still prefered and thus oblige us to compute the generalized accelerations at each time step. To achieve this, we propose a new formulation of the well-known Newton/Euler recursive method, whose efficiency will be compared with a so-called “O(N)” formulation. A regards the symbolic generation, often decried due to the size of the equations in case of large systems, we have recently implemented recursive multibody formalisms in the symbolic programme ROBOTRAN [1]. As we shall explain, the recursive nature of these formalisms is particularly well-suited to symbolic manipulation. All these developments have been successfully applied in the field of railway dynamics, and in particular allowed us to analyse the dynamic behaviour of several railway vehicles. Some typical results related to a completely non-conventional bogie will be presented before concluding.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00795220
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  • 2
    Electronic Resource
    Electronic Resource
    A new wheel/rail contact model for independent wheels (1994)
    Springer
    Archive of applied mechanics 64 (1994), S. 180-191 
    Details
    ISSN: 1432-0681
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Description / Table of Contents: Übersicht Die klassische Mehrkörper-Annäherung in der Dynamik der Eisenbahnfahrzeuge betrachtet als Rollelement das steife Achse-Räder-System, dessen geometrisches Problem des Kontaktes zwischen Rad und Gleis sowie dessen Formulierung der dynamischen Gleichungen heutzutage allbekannt sind. Neue Konzepte von unkonventionellen Drehgestellen führte die Autoren zur Entwicklung eines neuen Modells für unabhängige Räder, in welchem aufgrund des Fehlens einer gemeinsamen Achse zwischen linkem und rechtem Rad jeder Rad-Gleis-Kontakt getrennt betrachtet werden soll. Dieses Modell bildet einen zusätzlichen Gesichtspunkt der Mehrkörper-Methode für die Lösung solcher Probleme. Nach kurzer Betrachtung des klassischen Mehrkörper-Formalismus wird ein Modell des Rad-Gleis-Kontaktes für eine gerade Strecke entwickelt. Weiter folgt die Ausweitung des Modells auf ein gekrümmtes Gleis und schließlich werden die numerischen Ergebnisse für klassische und nicht-konventionelle Drehgestelle vorgelegt.
    Notes: Summary The classical multibody approach in railway vehicle dynamics considers as rolling element a rigid wheelset, for which the geometrical problem associated with the wheel/rail contact and the formulation of the dynamic equations are well known at the present time. New designs of non-conventional bogies led us to develop a new model for independent wheels in which each wheel/rail contact must be treated separately due to the absence of an axle between left and right wheels. This model constitutes an additional feature of the multibody approach for this type of application. The classical multibody formalism is first briefly reviewed and the wheel/rail contact model is then developed in the case of a straight track. The way the model has been extended to curved track is also explained. Finally, numerical results related to classical and non-conventional bogies will be presented before concluding.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00806816
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  • 3
    Electronic Resource
    Electronic Resource
    Symbolic generation of large multibody system dynamic equations using a new semi-explicit Newton/Euler recursive scheme (1996)
    Springer
    Archive of applied mechanics 66 (1996), S. 187-199 
    Details
    ISSN: 1432-0681
    Keywords:  dynamic modelling ; multibody system ; symbolic generation ; computer simulation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Summary  The aim of this paper is to show that multibody systems with a large number of degrees of freedom can be efficiently modelled, taking conjointly advantage of a recursive formulation of the equations of motion and of the symbolic generation capabilities. Recursive schemes are widely used in the field of multibody dynamics since they avoid the “explosion” of the number of arithmetical operations in case of large multibody models. Within the context of our field of applications (railway dynamics simulation), explicit integration schemes are still prefered and thus oblige us to compute the generalized accelerations at each time step. To achieve this, we propose a new formulation of the well-known Newton/Euler recursive method, whose efficiency will be compared with a so-called “O(N)” formulation. A regards the symbolic generation, often decried due to the size of the equations in case of large systems, we have recently implemented recursive multibody formalisms in the symbolic programme ROBOTRAN [1]. As we shall explain, the recursive nature of these formalisms is particularly well-suited to symbolic manipulation. All these developments have been successfully applied in the field of railway dynamics, and in particular allowed us to analyse the dynamic behaviour of several railway vehicles. Some typical results related to a completely non-conventional bogie will be presented before concluding.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00795220
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  • 4
    Electronic Resource
    Electronic Resource
    On the stability of interconnected rigid bodies (1973)
    Springer
    Archive of applied mechanics 42 (1973), S. 360-370 
    Details
    ISSN: 1432-0681
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Description / Table of Contents: Übersicht Es werden die Bedingungen für das Gleichgewicht eines Systems von miteinander verbundenen starren Körpern aufgestellt, die sich auf einer Umlaufbahn befinden. Die Stabilitätsbedingungen für eine gegebene Gleichgewichtslage werden berechnet. Die Bewegungsgleichungen werden nach dem Vorbild von Roberson-Wittenburg abgeleitet und in einem körperfesten Zwischensystem ausgedrückt. Dank der Vorteile dieses Vorgehens kann die Stabilitätsanalyse verhältnismäßig einfach nach der Ljapunovschen Methode durchgeführt werden.
    Notes: Summary The aim of this paper is to determine conditions for equilibrium of an orbiting system of interconnected rigid bodies and to find the stability conditions for a given equilibrium configuration. The equations were expressed in a body mean frame and derived from the Roberson-Wittenburg formalism, the combination of the advantages of these methods leading to a rather simple stability analysis by use of the Liapunov technique.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00535762
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  • 5
    Electronic Resource
    Electronic Resource
    Measurement of velocity fields in ball mills (1996)
    Springer
    Experimental mechanics 36 (1996), S. 251-257 
    Details
    ISSN: 1741-2765
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract This paper describes a computer vision technique used in measuring the velocity field related to the motion of balls in a ball mill. A camera combined with two color flashes facing an experimental ball mill is used to take pairs of pictures by triggering the flashes in sequence with a time interval Δt. In order to ensure consistency, the pictures are of different colors and in a single frame. The ball positions in each image are detected by image-processing techniques, and the velocity is then the displacement of each ball between two successive images divided by Δt. The measurement error is estimated by measuring the displacements from a pair of images when the balls remain stationary.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02318015
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  • 6
    Electronic Resource
    Electronic Resource
    Comparison of Various Techniques for Modelling Flexible Beams in Multibody Dynamics (1997)
    Springer
    Nonlinear dynamics 12 (1997), S. 367-397 
    Details
    ISSN: 1573-269X
    Keywords: Flexible ; simulation ; multibody ; dynamics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The modelling of flexible elements in mechanical systems has been widely investigated through several methods issuing from both the area of structural mechanics and the field of multibody dynamics. As regards the latter discipline, beside the problem of the generation of the multibody equations of motion, the choice of a spatial discretization method for modelling flexible elements has always been considered as a critical phase of the modelling. Although this subject is abundantly tackled in the open-literature, the latter probably lacks an objective comparison between the most commonly used approaches. This contribution presents an extensive investigation of several discretization techniques of flexible beams, in a pure multibody context. In particular, it is shown that shape functions based on power series monomials are very suitable and versatile to model beams being part of a multibody system and thus constitutes an interesting alternative to finite element analysis. For this purpose, a symbolic multibody program, in which various discretization techniques were implemented, was generalized to compute the equations of motion of a general multibody system containing flexible beams.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008204330035
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  • 7
    Electronic Resource
    Electronic Resource
    A Multibody Loop Constraints Approach for Modelling Cam/Follower Devices (2000)
    Springer
    Nonlinear dynamics 22 (2000), S. 335-359 
    Details
    ISSN: 1573-269X
    Keywords: dynamics ; multibody system ; loop constraint
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper proposes a formulation for modelling mechanisms witha cam/follower type of contact using a multibody approach in relativecoordinates. The proposed approach is inspired from the wheel/railcontact model developed by Fisette and Samin but, in the present case,possible intermittent contact between the cam and the follower isconsidered, for generality purposes. Loop kinematicconstraints are introduced to satisfy tangent and punctual contact aslong as the bodies lean against each other. The effective presence (ornot) of the contact is governed by the sign of the normal constraintforce which can be computed thanks to the Lagrange multiplierstechnique. The above-mentioned option to kinematicallyconstraint the bodies in their ‘contact phase’ unavoidably leads to ashift from one model to another when a contact disappears (or,conversely, reappears). Indeed, this increases (or decreases) the numberof degrees of freedom of the current system. The control of the variablepartitioning is thus absolutely necessary and is all the more complex sothat practical applications can contain several pairs of bodies inintermittent contact. Illustrative examples are proposed: acomparison with another multibody formalism, an experimental validationand the modelling of universal wheels of mobile robots which representsa quite original application of the proposed formulation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008316508951
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  • 8
    Electronic Resource
    Electronic Resource
    Minimal dynamic characterization of tree-like multibody systems (1996)
    Springer
    Nonlinear dynamics 9 (1996), S. 165-184 
    Details
    ISSN: 1573-269X
    Keywords: Multibody ; dynamics ; identification ; robot
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The dynamic model of tree-like multibody systems is linear with respect to the parameters of mass distribution for instance when barycentric parameters are used. Thus, assuming that the parameters related to the kinematics are perfectly known, these quantities can be estimated through linear regression techniques. The necessary data are obtained by measuring the joint forces and/or torques and the resulting motion given in terms of positions, velocities and accelerations. An alternative method uses measurements of the reaction forces and torques applied to the bedplate. The linearity of the dynamic and reaction models with respect to the barycentric quantities does not however imply that the latter constitute the minimum set of parameters characterizing the mass distribution of the system. In other words, some barycentric parameters may disappear from the models or may be redundant in the sense that they appear only via linear combinations. In the first case they are not identifiable, while in the second case the linear regression technique leads to estimated values which are correct for the combinations but can be erroneous for the individual parameters. The various options taken to derive the dynamic and reaction models by use of the ROBOTRAN programme are briefly reviewed. Then the rules leading to the minimal parametrization are presented and illustrated by means of a practical example related to a robot calibration problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01833299
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  • 9
    Electronic Resource
    Electronic Resource
    SYMBOLIC GENERATION OF A MULTIBODY FORMALISM OF ORDER N - EXTENSION TO CLOSED-LOOP SYSTEMS USING THE COORDINATE PARTITIONING METHOD (1996)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 4091-4112 
    Details
    ISSN: 0029-5981
    Keywords: modelling ; mechanics ; dynamics ; recursive ; symbolic ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The efficient computation of multibody systems dynamic equations certainly remains of a great importance in so far as both the increasing size and refinement of the mathematical models lead to a high complexity of the equations to be solved. Among the various multibody formalisms developed and implemented into computer programs, one generally admits that the so-called O(N) formulations have an intrinsic appeal: they require, in case of ‘tree’ multibody structures, a number of arithmetical operations which is only proportional to the number of degrees of freedom of the mechanical system under consideration. Obviously, this feature becomes really attractive in case of large multibody models, i.e. in which the number of degrees of freedom exceeds 20,…,30.In this contribution, we shall first present a pure symbolic generation of such a formalism in order to make it even more efficient. Secondly, we shall propose an original extension of the O(N) formulation to closed-loop systems by taking advantage, in terms of reliability, of the well-known ‘Co-ordinate Partitioning method’. Using the symbolic approach, this seems to exhibit a good equilibrium between reliability and efficiency to get the generalized accelerations required by explicit integrator schemes. The method is illustrated through a numerical example.
    Additional Material: 14 Ill.
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  • 10
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    On the stability of interconnected rigid bodies (1973)
    Springer
    Details
    Publication Date: 1973-01-01
    Print ISSN: 0020-1154
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Published by Springer
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