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Research Papers

Comparison of Selected Methods of Handling Redundant Constraints in Multibody Systems Simulations

[+] Author and Article Information
Marek Wojtyra

e-mail: mwojtyra@meil.pw.edu.pl

Janusz Frączek

e-mail: jfraczek@meil.pw.edu.pl
Institute of Aeronautics and Applied Mechanics,
Warsaw University of Technology,
Nowowiejska 24,
00-665 Warsaw, Poland

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNALOF COMPUTATIONALAND NONLINEAR DYNAMICS. Manuscript received October 24, 2011; final manuscript received June 6, 2012; published online July 23, 2012. Assoc. Editor: Jozsef Kovecses.

J. Comput. Nonlinear Dynam 8(2), 021007 (Jul 23, 2012) (9 pages) Paper No: CND-11-1179; doi: 10.1115/1.4006958 History: Received October 24, 2011; Revised June 06, 2012

When redundant constraints are present in a rigid body mechanism, only selected (if any at all) joint reactions can be determined uniquely, whereas others cannot. Analytic criteria and numerical methods of finding joints with uniquely solvable reactions are available. In this paper, the problem of joint reactions solvability is examined from the point of view of selected numerical methods frequently used for handling redundant constraints in practical simulations. Three different approaches are investigated in the paper: elimination of redundant constraints; pseudoinverse-based calculations; and the augmented Lagrangian formulation. Each method is briefly summarized; the discussion is focused on techniques of handling redundant constraints and on joint reactions calculation. In the case of multibody systems with redundant constraints, the rigid body equations of motion are insufficient to calculate some or all joint reactions. Thus, purely mathematical operations are performed in order to find the reaction solution. In each investigated method, the redundant constraints are treated differently, which—in the case of joints with nonunique reactions—leads to different reaction solutions. As a consequence, reactions reflecting the redundancy handling method rather than physics of the system are calculated. A simple example of each method usage is presented, and calculated joint reactions are examined. The paper points out the origins of nonuniqueness of constraint reactions in each examined approach. Moreover, it is shown that one and the same method may lead to different reaction solutions, provided that input data are prepared differently. Finally, it is demonstrated that—in case of joints with solvable reactions—the obtained solutions are unique, regardless of the method used for redundant constraints handling.

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Figures

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Fig. 1

A planar overconstrained mechanism

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Fig. 2

Coordinates of body 5 center of mass versus time

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Fig. 3

Unique joint reaction forces (all methods of handling redundant constraints)

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Fig. 4

Nonunique joint reaction forces (redundant constraints elimination method)

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Fig. 5

Nonunique joint reaction forces (pseudoinverse-based method)

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Fig. 6

Nonunique joint reaction forces (augmented Lagrangian method—different initial approximations)

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Fig. 7

Nonunique joint reaction forces (augmented Lagrangian method—different penalty factors)

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