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Research Papers

Assessment of Linearization Approaches for Multibody Dynamics Formulations

[+] Author and Article Information
Francisco González

Laboratorio de Ingeniería Mecánica,
Universidade da Coruña,
Ferrol 15403, Spain
e-mail: f.gonzalez@udc.es

Pierangelo Masarati

Professor
Dipartimento di Scienze
e Tecnologie Aerospaziali,
Politecnico di Milano,
Milano 20156, Italy
e-mail: pierangelo.masarati@polimi.it

Javier Cuadrado

Professor
Laboratorio de Ingeniería Mecánica,
Universidade da Coruña,
Ferrol 15403, Spain
e-mail: javicuad@cdf.udc.es

Miguel A. Naya

Associate Professor
Laboratorio de Ingeniería Mecánica,
Universidade da Coruña,
Ferrol 15403, Spain
e-mail: minaya@udc.es

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received October 13, 2016; final manuscript received November 25, 2016; published online January 20, 2017. Assoc. Editor: Paramsothy Jayakumar.

J. Comput. Nonlinear Dynam 12(4), 041009 (Jan 20, 2017) (7 pages) Paper No: CND-16-1493; doi: 10.1115/1.4035410 History: Received October 13, 2016; Revised November 25, 2016

Formulating the dynamics equations of a mechanical system following a multibody dynamics approach often leads to a set of highly nonlinear differential-algebraic equations (DAEs). While this form of the equations of motion is suitable for a wide range of practical applications, in some cases it is necessary to have access to the linearized system dynamics. This is the case when stability and modal analyses are to be carried out; the definition of plant and system models for certain control algorithms and state estimators also requires a linear expression of the dynamics. A number of methods for the linearization of multibody dynamics can be found in the literature. They differ in both the approach that they follow to handle the equations of motion and the way in which they deliver their results, which in turn are determined by the selection of the generalized coordinates used to describe the mechanical system. This selection is closely related to the way in which the kinematic constraints of the system are treated. Three major approaches can be distinguished and used to categorize most of the linearization methods published so far. In this work, we demonstrate the properties of each approach in the linearization of systems in static equilibrium, illustrating them with the study of two representative examples.

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Figures

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Fig. 1

An N-loop four-bar linkage with spring elements

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Fig. 2

A flexible double pendulum

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Fig. 3

Coordinates used to describe the motion of each link

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Fig. 4

A singular static equilibrium configuration for the one-loop four-bar linkage with kf = 0

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Fig. 5

Sparsity pattern of the mass matrix of the flexible double pendulum with np = 5: (a) MCS: original Mr, (b) MCS: factorized Mr, (c) RCS: original Mq, (d) RCS: factorized Mq, (e) UCS: original Mp, and (f) UCS: factorized Mp

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