A great variety of formulations exist for the numerical simulation of rigid-body systems, particularly of medium-large systems such as vehicles. Topological formulations, which are considered to be the most efficient ones, are often cumbersome and not necessarily easy to implement. As a consequence, there is a lack of comparative evidence to support the performance of these formulations. In this paper, we present and compare three state-of-the-art topological formulations for multibody dynamics: generalized semirecursive, double-step semirecursive, and subsystem synthesis methods. We analyze the background, underlying principles, numerical efficiency, and accuracy of these formulations in a systematic way. A 28-degree-of-freedom, open-loop rover model and a 16-degree-of-freedom, closed-loop sedan car model are selected as study cases. Insight on the key aspects toward performance is provided.

References

References
1.
Schiehlen
,
W.
,
2014
, “
History of Benchmark Problems in Multibody Dynamics
,”
Multibody Dynamics: Computational Methods and Applications
,
Springer
, Cham, Switzerland, pp.
357
368
.
2.
Pàmies-Vilà
,
R.
,
Font-Llagunes
,
J. M.
,
Lugrís
,
U.
,
Alonso
,
F. J.
, and
Cuadrado
,
J.
,
2015
, “
A Computational Benchmark for 2D Gait Analysis Problems
,”
New Trends in Mechanism and Machine Science
,
Springer
, Cham, Switzerland, pp.
689
697
.
3.
González
,
M.
,
Dopico
,
D.
,
Lugrís
,
U.
, and
Cuadrado
,
J.
,
2006
, “
A Benchmarking System for MBS Simulation Software: Problem Standardization and Performance Measurement
,”
Multibody Syst. Dyn.
,
16
(
2
), pp.
179
190
.
4.
Walker
,
M. W.
, and
Orin
,
D. E.
,
1982
, “
Efficient Dynamic Computer Simulation of Robotic Mechanisms
,”
ASME J. Dyn. Syst., Meas., Control
,
104
(
3
), pp.
205
211
.
5.
Jerkovsky
,
W.
,
1978
, “
The Structure of Multibody Dynamics Equations
,”
J. Guid. Control Dyn.
,
1
(
3
), pp.
173
182
.
6.
Avello
,
A.
,
Jiménez
,
J.
,
Bayo
,
E.
, and
García de Jalón
,
J.
,
1993
, “
A Simple and Highly Parallelizable Method for Real-Time Dynamic Simulation Based on Velocity Transformations
,”
Comput. Methods Appl. Mech. Eng.
,
107
(
3
), pp.
313
339
.
7.
Featherstone
,
R.
,
1983
, “
The Calculation of Robot Dynamics Using Articulated-Body Inertias
,”
Int. J. Rob. Res.
,
2
(
1
), pp.
13
30
.
8.
Stelzle
,
W.
,
Kecskeméthy
,
A.
, and
Hiller
,
M.
,
1995
, “
A Comparative Study of Recursive Methods
,”
Arch. Appl. Mech.
,
66
(
1
), pp.
9
19
.
9.
Bae
,
D.-S.
, and
Haug
,
E. J.
,
1987
, “
A Recursive Formulation for Constrained Mechanical System Dynamics: Part II. Closed Loop Systems
,”
J. Struct. Mech.
,
15
(
4
), pp.
481
506
.
10.
García de Jalón
,
J.
, and
Bayo
,
E.
,
1994
,
Kinematic and Dynamic Simulation of Multibody Systems: The Real-Time Challenge
,
Springer
, New York.
11.
García de Jalón
,
J.
,
Callejo
,
A.
, and
Hidalgo
,
A. F.
,
2012
, “
Efficient Solution of Maggi's Equations
,”
ASME J. Comput. Nonlinear Dyn.
,
7
(
2
), p.
021003
.
12.
Kim
,
S.
, and
Vanderploeg
,
M.
,
1986
, “
A General and Efficient Method for Dynamic Analysis of Mechanical Systems Using Velocity Transformations
,”
ASME J. Mech. Des.
,
108
(
2
), pp.
176
182
.
13.
Negrut
,
D.
,
Serban
,
R.
, and
Potra
,
F. A.
,
1997
, “
A Topology-Based Approach to Exploiting Sparsity in Multibody Dynamics: Joint Formulation
,”
J. Struct. Mech.
,
25
(
2
), pp.
221
241
.
14.
Bae
,
D.
,
Han
,
J.
, and
Yoo
,
H.
,
1999
, “
A Generalized Recursive Formulation for Constrained Mechanical System Dynamics
,”
Mech. Struct. Mach.
,
27
(
3
), pp.
293
315
.
15.
Bae
,
D.
,
Han
,
J.
, and
Choi
,
J.
,
2000
, “
An Implementation Method for Constrained Flexible Multibody Dynamics Using a Virtual Body and Joint
,”
Multibody Syst. Dyn.
,
4
(
4
), pp.
297
315
.
16.
Bae
,
D.
,
Lee
,
J.
,
Cho
,
H.
, and
Yae
,
H.
,
2000
, “
An Explicit Integration Method for Realtime Simulation of Multibody Vehicle Models
,”
Comput. Methods Appl. Mech. Eng.
,
187
(
1–2
), pp.
337
350
.
17.
Bae
,
D.
,
Cho
,
H.
,
Lee
,
S.
, and
Moon
,
W.
,
2001
, “
Recursive Formulas for Design Sensitivity Analysis of Mechanical Systems
,”
Comput. Methods Appl. Mech. Eng.
,
190
(
29–30
), pp.
3865
3879
.
18.
Bae
,
D. S.
,
Han
,
J. M.
,
Choi
,
J. H.
, and
Yang
,
S. M.
,
2001
, “
A Generalized Recursive Formulation for Constrained Flexible Multibody Dynamics
,”
Int. J. Numer. Methods Eng.
,
50
(
8
), pp.
1841
1859
.
19.
Ricón
,
J. L.
,
2014
, “
Implementación de la formulación implícita semi-recursiva de Bae para la simulación en tiempo real de sistemas multicuerpo
,” Master's thesis, ETSII—Technical University of Madrid, Madrid, Spain.
20.
Yen
,
J.
,
Haug
,
E. J.
, and
Potra
,
F. A.
,
1990
, “
Numerical Method for Constrained Equations of Motion in Mechanical Systems Dynamics
,”
Center for Simulation and Design Optimization
, University of Iowa, Iowa City, IA, Technical Report No. R-92.
21.
Funes
,
F. J.
, and
García de Jalón
,
J.
,
2016
, “
An Efficient Dynamic Formulation for Solving Rigid and Flexible Multibody Systems Based on Semirecursive Method and Implicit Integration
,”
ASME J. Comput. Nonlinear Dyn.
,
11
(
5
), p.
051001
.
22.
Rodríguez
,
J. I.
,
Jiménez
,
J. M.
,
Funes
,
F. J.
, and
García de Jalón
,
J.
,
2004
, “
Recursive and Residual Algorithms for the Efficient Numerical Integration of Multi-Body Systems
,”
Multibody Syst. Dyn.
,
11
(
4
), pp.
295
320
.
23.
García de Jalón
,
J.
,
Álvarez
,
E.
,
de Ribera
,
F. A.
,
Rodríguez
,
I.
, and
Funes
,
F. J.
,
2005
, “
A Fast and Simple Semi-Recursive Formulation for Multi-Rigid-Body Systems
,”
Advances in Computational Multibody Systems
(Computational Methods in Applied Sciences, Vol.
2
),
J.
Ambrósio
, ed.,
Springer
,
Dordrecht, The Netherlands
, pp.
1
23
.
24.
Jerkovsky
,
W.
,
1978
, “
The Structure of Multibody Dynamic Equations
,”
J. Guid. Control Dyn.
,
1
(
3
), pp.
173
182
.
25.
Wittenburg
,
J.
,
1977
,
Dynamics of Systems of Rigid Bodies
,
B. G. Teubner
,
Stuttgart, Germany
.
26.
von Schwerin
,
R.
,
1999
,
Multibody System Simulation, Numerical Methods, Algorithms and Software
,
Springer
, Berlin.
27.
Kurdila
,
A.
,
Papastavridis
,
J. G.
, and
Kamat
,
M. P.
,
1990
, “
Role of Maggi's Equations in Computational Methods for Constrained Multibody Systems
,”
J. Guid. Control Dyn.
,
13
(
1
), pp.
113
120
.
28.
Papastavridis
,
J. G.
,
1990
, “
Maggi's Equations of Motion and the Determination of Constraint Reactions
,”
J. Guid. Control Dyn.
,
13
(
2
), pp.
213
220
.
29.
Wampler
,
C.
,
Buffinton
,
K.
, and
Shu-hui
,
J.
,
1985
, “
Formulation of Equations of Motion for Systems Subject to Constraints
,”
ASME J. Appl. Mech.
,
52
(
2
), pp.
465
470
.
30.
Laulusa
,
A.
, and
Bauchau
,
O. A.
,
2007
, “
Review of Classical Approaches for Constraint Enforcement in Multibody Systems
,”
ASME J. Comput. Nonlinear Dyn.
,
3
(
1
), p.
011004
.
31.
Serban
,
R.
, and
Haug
,
E.
,
2000
, “
Globally Independent Coordinates for Real-Time Vehicle Simulation
,”
ASME J. Mech. Des.
,
122
(
4
), pp.
575
582
.
32.
Kim
,
S.-S.
,
2002
, “
A Subsystem Synthesis Method for Efficient Vehicle Multibody Dynamics
,”
Multibody Syst. Dyn.
,
7
(
2
), pp.
189
207
.
33.
Kim
,
S.-S.
, and
Wang
,
J.-H.
,
2005
, “
Subsystem Synthesis Methods With Independent Coordinates for Real-Time Multibody Dynamics
,”
J. Mech. Sci. Technol.
,
19
(
1
), pp.
312
319
.
34.
Kim
,
S.-S.
, and
Jeong
,
W.
,
2007
, “
Subsystem Synthesis Method With Approximate Function Approach for a Real-Time Multibody Vehicle Model
,”
Multibody Syst. Dyn.
,
17
(
2–3
), pp.
141
156
.
35.
Pacejka
,
H. B.
,
2012
,
Tyre and Vehicle Dynamics
,
Elsevier/Butterworth-Heinemann
, Oxford, UK.
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