This paper presents a method to study multibody system dynamics based on graph theory. The transfer function between any pair of bodies of nonhomogeneous multibody systems with arbitrary topology can be computed without any matrix inversion. The analysis is limited to one-dimensional topologies for clarity, although it can be extended to systems with higher dimensions. Examples illustrate its application to topologies of increasing complexity.
Issue Section:
Research Papers
1.
Bollobás
, B.
, 1998, Modern Graph Theory
, Springer
, Berlin
.2.
Wittenburg
, J.
, 1989, “Graph-Theoretical Methods in Multibody Dynamics
,” Dynamics and Control of Multibody Systems: Proceedings of the AMS-IMS-SIAM
, American Mathematical Society
, Brunswick, Maine
, Vol. 97
, p. 459
.3.
McPhee
, J.
, 1996, “On the Use of Linear Graph Theory in Multibody System Dynamics
,” Nonlinear Dyn.
0924-090X, 9
(1–2
), pp. 73
–90
.4.
Karnopp
, D.
, 1997, “Understanding Multibody Dynamics Using Bond Graph Representations
,” J. Franklin Inst.
0016-0032, 334
(4
), pp. 631
–642
.5.
Favre
, W.
, and Scavarda
, S.
, 1998, “Bond Graph Representation of Multibody Systems With Kinematic Loops
,” J. Franklin Inst.
0016-0032, 335
(4
), pp. 643
–660
.6.
Cho
, W.
, 1998, “A Bond Graph Approach to the Modeling of General Multibody Dynamic Systems
,” J. Mech. Sci. Technol.
1738-494X, 12
(5
), pp. 888
–898
.7.
Bruyninckx
, H.
, 2002, “A Free Software Framework for Advanced Robot Control
,” Seventh ESA Workshop on Advanced Space Technologies for Robotics and Automation ASTRA 2002
, ESTEC
, Noordwijk, The Netherlands
, pp. 1
–8
.8.
Mason
, S.
, 1953, “Feedback Theory: Some Properties of Signal Flow Graphs
,” Proc. IRE
0096-8390, 41
, pp. 1144
–1156
.9.
Mason
, S.
, 1956, “Feedback theory: further properties of signal flow graphs
,” Proc. IRE
0096-8390, 44
, pp. 920
–926
.10.
Jin
, Z.
, and Murray
, R. M.
, 2004, “Double-Graph Control Strategy of Multi-Vehicle Formations
,” 43rd IEEE Conference on Decision and Control, 2004 CDC
, Vol. 2
, pp. 1988
–1994
.11.
Holzer
, H.
, 1921, Analysis of Torsional Vibration
, Springer
, Berlin
.12.
Myklestad
, N.
, 1945, “New Method of Calculating Natural Modals of Coupled Bending-Torsion Vibration of Beams
,” Trans. ASME
0097-6822, 67
, pp. 61
–67
.13.
Rui
, X.
, He
, B.
, Lu
, Y.
, Lu
, W.
, and Wang
, G.
, 2005, “Discrete Time Transfer Matrix Method for Multibody System Dynamics
,” Multibody Syst. Dyn.
1384-5640, 14
, pp. 317
–344
.14.
Freund
, R. W.
, 2004, “SPRIM: Structure-Preserving Reduced-Order Interconnect Macromodeling
,” International Conference on Computer Aided Design (ICCAD’04)
, pp. 80
–87
.15.
O’Connor
, W.
, 2007, “Wave-Based Analysis and Control of Lump-Modeled Flexible Robots
,” IEEE Trans. Rob. Autom.
1042-296X, 23
, pp. 342
–352
.16.
O’Connor
, W.
, and Fumagalli
, A.
, 2009, “Refined Wave-Based Control Applied to Nonlinear, Bending, and Slewing Flexible Systems
,” ASME J. Appl. Mech.
0021-8936, 76
(4
), p. 041005
.Copyright © 2011
by American Society of Mechanical Engineers
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