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

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

Javier Cuadrado

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.

Copyright © 2017 by ASME
Your Session has timed out. Please sign back in to continue.



Grahic Jump Location
Fig. 1

An N-loop four-bar linkage with spring elements

Grahic Jump Location
Fig. 2

A flexible double pendulum

Grahic Jump Location
Fig. 3

Coordinates used to describe the motion of each link

Grahic Jump Location
Fig. 4

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

Grahic Jump Location
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




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In