Besseling, J. F. and Gong, D. G., 1994, “Numerical simulation of spatial mechanism and manipulators with flexible links”, Finite Elements in Analysis and Design, Vol.18, pp.121-128. Choy, F. K., Ruan, Y. F., Tu, Y. K., Zakrajsek, J. J. and Townsend, D. P., 1992, “Modal analysis of multistage gear systems coupled with gearbox vibrations”, Journal of Mechanical Design-Transactions of the ASME, Vol.114, n.3, Sep., pp.486-497. Garcia de Jalon, J. and Bayo E., 1994, Kinematic and Dynamic Simulation of Multibody Systems--the Real-Time Challenge, Springer-Verlag, New York. Ider, S. K. and Amirouche, F. M. L., 1990, “Stability analysis of constrained multibody systems”, Computational Mechanics, Vol.6, n.5-6, pp.327-340. Ishikawa, J., et al, 1957, “Deformation of Spur Gear Teeth”, Transactions of Tokyo (In Japanese), Vol.197, pp.251-260. Jonker, B., 1989, “A finite element dynamic analysis of flexible spatial mechanisms with flexible links”, Computer Methods in Applied Mechanics and Engineering, Vol.76, SUMMARY pp.17-40. A new spatial gear element which provides the possibJiolintyker, B., 1991, “Linearization of dynamic equations of to couple the transversal, the rotational and the fleaxxiiballe mechanisms-A finite element approach”, International flexibilities of gear is particularly developed based Joonu rnaal for Numerical Methods in Engineering, Vol.31, specific FEM theory. It can be used to model any kinpdp .1o3f 75-1392. external parallel-axis gears such as spur, helical and doKuabhleraman, A., Ozguven, H. N., Houser, D. R. and circle gears. The element can take into account theZ atikmraej-sek, J.J., 1992, “Dynamic analysis of geared rotors by variant meshing stiffness and the transmission errors offi ngiteea rse.lements”, Journal of Mechanical Design, Vol.114, The geared multibody system can be modelled with thpisp .n5e0w7-514. type of spatial gear element, together with those other eleKmoe, nSts. H. and Kwak, B. M., 1992, “Frictional dynamic previously developed for bar mechanisms only. The thceoonrtiaecst analysis in deformable multibody systems”, Finite about the specific FEM have been coded into a proEgleramments in Analysis and Design, Vol.12, n.1, Sep., pp.27-40. system, with which the kinematical and dynamic analysisK foooriman, G., 1987, SPACAR user manual, Delft University the gear-bar compound mechanisms can be carried oouft .T eTchhenology. displacement, velocity and acceleration of each node, loadNsi eomnann, G., und Munchen, J. B., 1970, “Drehwegiehler each node, the internal forces and deformations withiZna henafcehderharte und Gerausch bei Stirnradern”, VDI-Z, Band element can be computed. To demonstrate how the a1p1p2ro, aNcrh.4, pp.205-214. and program system work, a case study is provided regarSdainagda, A. and Velex, P., 1995, “Extended model for the the dynamic analysis of a flexible gear-planetary mecahnaanliysmsis of the dynamic behavior of planetary trains”, Journal consisting of gear, bar and slider. of Mechanical Design, Transactions Of the ASME, Vol.117, n.2, Jun., pp.241-247. ACKNOWLEDGMENTS Shabana, A. A., 1989, Dynamics of Multibody systems, A The research work reported has in part been suppoWrtileedy -bInyterscince Publication, New York. the City University of Hong Kong SRG project Nr. 700060S1habana, A. A., 1990, “Computer aided analysis of flexible and the Chinese Natural Science Foundation project (Grant Nr. multibody vehicle systems”, SAE Transactions, Vol.99, pp.969-59575003). 980. Song, J. O. and Hung, E. J., 1980, “Dynamic analysis of REFERENCES planar flexible mechanisms”, Computer Mehtod in Applied Amirouche, F. M. L., Xie, M., Shareef, N. H. and Valco,and Engineering,Vol.24, pp.359-381. M., 1993, “Finite element modeling of contact conditions inToshio, A., 1985, The precision and performance of gears multibody system dynamics”, Nonlinear Dynamics, Vol.4, n.1,(in Chinese). Translator Zhan Z., Agriculture Machine Press, Feb., pp.83-102. China.