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Augmented Lagrangian index-3 semi-recursive formulations with projections

Kinematics and dynamics

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Abstract

MBSLIM (Multibody Systems at Laboratorio de Ingenieria Mecanica) multibody library includes some global formulations for the dynamics and sensitivity analysis of multibody systems. The extension of the library to accommodate topological formulations in relative (joint) coordinates and their implementation are going to be described in two separate works, this one being devoted to dynamics and the second one to a sensitivity analysis. With this extension in the scope, some topological semi-recursive formulations derived in the past are revisited, generalized and reformulated. The need for generalization of the previously published formulations was detected because the equations proposed were not general enough to be integrated in an all-purpose multibody library in natural coordinates like MBSLIM, especially because both set of coordinates need to coexist, the definition of the mechanisms has to be the original one and the library has to be automatic and all the existing models have to work with the new approach. Moreover the new solver takes advantage of some problems solved in natural coordinates, like the initial position and initial velocity problems for closed-loop systems. Finally, to test the new equations, two benchmark problems are presented and their results compared: a spatial slider–crank mechanism and a buggy vehicle model.

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Notes

  1. A special case of non-minimal joint coordinates is the spherical joint modeled with Euler parameters, where only three out of the four parameters are degrees of freedom. In order to use the formulation for open-loop systems with these joints, three parameters must be chosen as degrees of freedom and the other one expressed in terms of them. Otherwise the formulation for closed-loop systems should be used, adding the corresponding normalization constraint for the Euler parameters of each spherical (or floating) joint.

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Acknowledgement

The support of the Spanish Ministry of Economy and Competitiveness (MINECO) under project DPI2016-81005-P is greatly acknowledged.

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  1. Laboratorio de Ingeniería Mecánica, Universidade da Coruña, Mendizábal s/n, 15403, Ferrol, Spain

    Daniel Dopico Dopico, Álvaro López Varela & Alberto Luaces Fernández

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  1. Daniel Dopico Dopico
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  2. Álvaro López Varela
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Correspondence to Daniel Dopico Dopico.

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Dopico Dopico, D., López Varela, Á. & Luaces Fernández, A. Augmented Lagrangian index-3 semi-recursive formulations with projections. Multibody Syst Dyn 52, 377–405 (2021). https://doi.org/10.1007/s11044-020-09771-9

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