A systematic method is presented for deriving the equations of motion of mechanisms involving multiple elastic structures connected together by any form of driven or undriven joints. It is assumed that deformations within components are small but there is no restriction on joint motions. Orthogonal coordinates are used to decouple the linear, angular and elastic partitions. The deformation coordinates represent a finite number of the free modes of vibration of each component. Algebraic constraint equations are defined generally for common joints and any new constraints are automatically generated using symbolic techniques. The chosen coordinates and the method of formulating the equations allow efficient numerical solution.
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References
1.
BookW. J.Recursive Lagrangian dynamics of flexible manipulator arms. Int. J. Robotics Res., 1984, 3(3), 87–101.
2.
CanavinJ. R.LikinsP. W.Floating reference frames for flexible spacecraft. J. Astronaut. Sci., 1979, 27(4), 724–732.
3.
SunadaW.DubowskyS.The application of finite element methods to the dynamic analysis of flexible spatial and co-planar linkage systems. Trans. ASME, J. Mech. Des., 1981, 103, 641–651.
4.
De SmetM.LiefoogheC.SasP.SnoeysR.Dynamic analysis of flexible structures using component mode synthesis. Trans. ASME, J. Appl. Mechanics, 1989, 56, 874–880.
5.
HurtyW. C.Dynamic analysis of structural systems using component modes. Am. Inst. Aeronaut. Astronaut. J., 1965, 3, 678–685.
6.
NagarajanS.TurcicD. A.Lagrangian formulation of the equations of motion for elastic mechanisms with mutual dependence between rigid body and elastic motions, Parts I and II. Trans. ASME, J. Dynamic System Measmt, and Control, 1990, 112, 203–224.
7.
HohenbichlerG.PlockingerP.LugnerP.Comparison of a modal expansion and a finite element model for a two beam flexible robot arm. Robot control, Karlsruhe, Germany, 1988, pp. 35–39 (IFAC).
8.
KopacekP.DesoyerK.LugnerP.Modelling of flexible robots. Robot control, Karlsruhe, Germany, 1988, pp. 21–28 (IFAC).
9.
MeirovitchL.Methods of analytical dynamics, 1975 (McGraw-Hill, New York).
10.
HaugE. J.Computer-aided kinematics and dynamics of mechanical systems, Vol. 1, Basic methods, 1989 (Allyn and Bacon, Boston).
11.
ShabanaA. A.Dynamics of multibody systems, 1989 (John Wiley, New York).
12.
GottliebD.OrszagS. A.Numerical analysis of spectral methods, 1977 (SIAM, Philadelphia, Pennsylvania).
13.
NikraveshP. E.Computer-aided analysis of mechanical systems, 1988 (Prentrice-Hall, Englewood Cliffs, New Jersey).
14.
RaynaG.REDUCE: software for algebraic computation, 1987 (Springer-Verlag, New York).
15.
FraserA. R.DanielsR. W.Perturbation techniques for flexible manipulators, 1991 (Kluwer, London).
16.
HaugE. J.ShihC. WuSung-SooKimDynamics of flexible machines: A variational approach. Symposium on Dynamics of multibody systems, Udine, 1985, pp. 55–67 (IUTAM/IFToMM).
17.
AmiroucheF. M. L.ShareefN. H.Gain in computational efficiency by vectorization in the dynamic simulation of multi-body systems. Comput. Structs, 1991, 41(2), 293–303.
18.
OrlandeaN.ChaceM. A.CalahanD. A.A sparsity-oriented approach to the dynamic analysis and design of mechanical systems, Parts I and II. J. Engng for Industry, 1977, 99, 773–784.
19.
WehageR. A.HaugE. J.Generalized coordinate partitioning for dimension reduction in analysis of constrained dynamic systems. J. Mech. Des., 1982, 104(1), 247–255.
20.
DavisonP.LongmoreD. K.BurrowsC. R.Generation of complex mechanical models in hydraulic system applications. Third Scandinavian International Conference on Fluid power, Linköping, Sweden, 1993, pp. 13–27.
21.
XuJ.Einflüsse der Elastizität von gelenkig befestigten Flügeln auf die Dynamik von Windturbinen. Colloquium on Dynamics and control of rotating machinery, Brunswig, Germany, 1993 (Euromech 293).
