Abstract
A unified methodology for modelling electromechanical multibody systemsis presented. The systems are comprised of rigid or flexible multibodysub-systems and electrical networks of analog components. The sub-systemsare coupled by transducers such as DC motors, moving-plate capacitors,and moving-coil inductors. The electromechanical system is represented bya single graph representation; linear graph theory is then used to generatea relatively small number of system equations. The graph-theoretic formulationis efficient, unifying, and systematic, andwas readily implemented in a computer algorithm using symbolic programming.The formulation and computer implementation are demonstrated using twoexamples of electromechanical systems: a simple condensator microphone anda robot manipulator actuated by DC motors.
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References
Schiehlen, W., ‘Multibody system dynamics: Roots and perspectives’ Multibody System Dynam. 1, 1997, 149–188.
Hadwich, V. and Pfeiffer, F., ‘The principle of virtual work in mechanical and electromechanical systems’ Arch. Appl. Mech. 65, 1995, 390–400.
Maisser, P., Enge, O., Freudenberg, H. and Kielau, G., ‘Electromechanical interactions in multibody systems containing electromechanical drives’ Multibody System Dynam. 1, 1997, 281–302.
Enge, O., Kielau, G. and Maisser, P., ‘Computer aided simulation of the dynamics of electromechanical systems’ Z. Angew. Math. Mech. 76, 1996, 397–398.
Schlacher, K., Kugi, A. and Scheidl, R., ‘Tensor analysis based symbolic computation for mechatronic systems’ Math. Comput. Simulation 46, 1998, 517–525.
Roe, P., Networks and Systems, Addison-Wesley, Reading, MA, 1966.
Koenig, H., Tokad, Y. and Kesavan, H., Analysis of Discrete Physical Systems, McGraw-Hill, New York, 1967.
Andrews, G., Richard, M. and Anderson, R., ‘A general vector-network formulation for dynamic systems with kinematic constraints’ Mech. Mach. Theory 33, 1988, 243–256.
McPhee, J., ‘Automatic generation of motion equations for planar mechanical systems using the new set of ‘branch coordinates'’ Mech. Mach. Theory 33, 1998, 805–823.
Shi, P. and McPhee, J., ‘Dynamics of flexible multibody systems using virtual work and linear graph theory’ Multibody System Dynam. 4, 2000, 355–381.
Biggs, N., Lloyd, E. and Wilson, R., Graph Theory: 1736–1936, Oxford University Press, Oxford, 1976.
Wittenburg, J., Dynamics of Systems of Rigid Bodies, B.G. Teubner, Stuttgart, 1977.
McPhee, J., ‘On the use of linear graph theory in multibody system dynamics’ Nonlinear Dynam. 9, 1996, 73–90.
Fayet, M. and Pfister, F., Analysis of multibody systems with indirect coordinates and global inertia tensors’ European J. Mech. A/Solids 13, 1994, 431–457.
McPhee, J., ‘A unified formulation of multibody kinematic equations in terms of absolute, joint, and indirect coordinates’ in Proceedings of ASME Design Engineering Technical Conference, Pittsburgh, PA, September 9–12, D.T. Mook (ed.), ASME, New York, 2001, CD-ROM Proceedings.
Muegge, B., ‘Graph-theoretic modelling and simulation of planar mechatronic systems’ Master's Thesis, University of Waterloo, Canada, 1996.
Karnopp, D., Margolis, D. and Rosenberg, R., System Dynamics: Modelling and Simulation of Mechatronic Systems, Wiley, New York, 2000.
Crandall, S., Karnopp, D., Kurtz, E. and Pridmore-Brown, D., Dynamics of Mechanical and Electromechanical Systems, McGraw-Hill, New York, 1968.
Char, B., Geddes, K., Gonnet, G., Leong, B., Monagan, M. and Watt, S., First Leaves: A Tutorial Introduction to Maple V, Springer-Verlag, Berlin, 1992.
Shi, P., ‘Flexible multibody dynamics: A new approach using virtual work and graph theory’ Ph.D. Thesis, University of Waterloo, Canada, 1998.
Gayford, M., Electroacoustics – Microphones, Earphones and Loudspeakers, Elsevier Publishing Company, New York, 1971.
Lovekin, D., Heppler, G. and McPhee, J., ‘Design and analysis of a facility for free-floating flexible robotic manipulators’ Trans. CSME 24(2), 2000, 375–390.
McPhee, J. and Shi, P., ‘Inverse dynamics of multibody systems using virtual work and graph theory’ in Proceedings of 10th World Congress on the Theory of Machines and Mechanisms, Oulu, Finland, T. Leinonen (ed.), Oulu University Press, 1999, 1258–1263.
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Scherrer, M., McPhee, J. Dynamic Modelling of Electromechanical Multibody Systems. Multibody System Dynamics 9, 87–115 (2003). https://doi.org/10.1023/A:1021675422011
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DOI: https://doi.org/10.1023/A:1021675422011