Summary
The methodology of multibody dynamics is briefly discussed. As an example of a descriptor formulation, the mass-orthogonal projection method is presented and it’s numerical efficiency illustrated by an example of a dynamic optimization problem. Typically, in a descriptor formulation, the numerical efficiency depends on the particular choice of the equations in the redundant variables. Also, the use of sparse-matrix techniques may be advantageous. In a second part, the geometric interpretation of dynamics is reviewed. As an example, the topology of the configuration space of a four-bar linkage is discussed.
Dedicated to my Friend John Tinsley Oden on the Occasion of his Sixtieth Birthday
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References
Bach, D.N. (1993), Ein Beitrag zur Starrkörpermechanik, Diss. ETH Nr. 10367.
Bach, D., Brauchli, H., Meiliger, O., Hilhner P. (1993), DYNAMITE: Multibody Dynamics via Projection Methods, in (Schiehlen 1993), pp. 355–360.
Bestie, D., Schiehlen W. (eds.), (1996), IUTAM Symposium on Optimization of Mechanical Systems, Kluwer Academic Publishers, Dordrecht.
Bianchi, G., Schiehlen, W. (eds.), (1986), Dynamics of Multibody Systems, IUTAM/ IFToMM Symposium Udine 1985, Springer-Verlag, Berlin.
Brauchli, H. (1991), Mass-Orthogonal Formulation of Equations of Motion for Multibody Systems, J. Appl. Math. Phys. (ZAMP) 42, pp. 169–182.
Brauchli, H. (1997), Konfigurationsräume einfacher Mechanismen, to appear in Elemente der Mathematik.
Brauchli H., Weber, R. (1991), Dynamical Equations in Natural Coordinates, Comp. Meth. Appl. Eng. 91, pp. 1403–1414.
Bremer, H., Pfeiffer, F. (1992), Elastische Mehrkörpersysteme, Teubner Studienbücher.
Chen, T., Brauchli, H. (1997), On the Geometry, Dynamics and Stability of Non-Holonomic Systems, presented at the NATO advanced Study Institute on Computational Methods in Mechanisms, Varna, Bulgaria.
Clavel, R. (1988), Delta, a Fast Robot with Parallel Geometry, Proc. Internat. Symposium on Industrial Robots, pp. 91–100.
Devaquet, G. (1993), Die Gleichungen der ersten Variation redundant modellierter Starrkörpersysteme, Diss. ETH Nr. 10395.
Devaquet, G., Brauchli, H. (1992), A Simple Model for the DELTA-Robot, Robotersysteme 8, pp. 193–199.
Hiller, M. (1983), Mechanische Systeme — eine Einführung in die analytische Mechanik und Systemdynamik, Springer-Verlag, Berlin.
García de Jalón, J., Cuadrado, J., Avello, A., Jimenez, J.M. (1994), Kinematic and Dynamic Simulation of Flexible Systems with Fully Cartesian Coordinates, in (Pereira and Ambrösio 1994), pp. 285–323.
García de Jalón, J., Serna M.A., Aviles R (1981), A Computer Method for Kinematic Analysis of Lower Pair Mechanisms. Part I: Velocities and Accelerations, Part II: Position Problems, Mechanism and Machine Theory 16, pp. 543–566.
Géradin, M., Cardona, A., Doan D.B., Duysens J. (1994), Finite Element Modeling Concepts in Multibody Dynamics, in (Pereira and Ambrósio 1994), pp. 233–284.
Kane, T.R., Levinson, D.A. (1985), Dynamics: Theory and Applications, McGraw-Hill, New York.
Magnus K. (ed.), (1978), Dynamics of Multibody Systems, IUTAM-Symposium Munich/Germany, August 29 — September 3, 1977, Springer-Verlag, Berlin.
Meirovitch, L. (1970), Methods of Analytical Dynamics, McGraw-Hill, New York.
Meiliger, O.F. (1994), Numerisch effiziente Methoden der Mehrkörperdynamik, Diss. ETH Nr. 10755.
Nikravesh, P.E. (1988), Computer-Aided Analysis of Mechanical Systems, Prentice-Hall, Englewood-Cliffs.
Obrist, D. (1996), Anwendung globaler Optimierungsverfahren auf die Optimierung der Dynamik eines Mechanismus mit einseitigen Bindungen und Stössen, Semesterarbeit, Institut für Mechanik, ETH-Zürich.
Penrose, R. (1955), A Generalized Inverse for Matrices, Proc. Cambr. Phil. Soc. 51, pp. 406–413.
Pereira, M.S., Ambrósio J.A.C. (eds.), (1994), Computer-Aided Analysis of Rigid and Flexible Mechanical Systems, NATO ASI Series E: Applied Sciences — Vol. 268, Kluwer Academic Publishers, Dordrecht.
Pereira, M.S., Ambrósio J.A.C. (eds.), (1995), Computational Dynamics in Multi-body Systems, Kluwer Academic Publishers, Dordrecht.
Petzold, L.R. (1994), Computational Challenges in Mechanical Systems Simulation, in (Pereira and Ambrósio 1994), pp. 483–499.
Renaud, M. (1975), Contribution à l’Etude de la Modélisation des Systèmes Mécaniques Articulés, Diss. Univ. Toulouse.
Schiehlen, W.O. (1990), Multibody Systems Handbook, Springer-Verlag, Berlin.
Schiehlen, W. (ed.), (1993) Advanced Multibody System Dynamics, Simulation and Software Tools, Kluwer Academic Publishers, Dordrecht.
Schulz, M. (1997), Optimierung von Mechanismen mit einseitigen Bindungen und Kollisionen, Diss. ETH Nr. 12041.
Schulz, M., Brauchli, H. (1996), Simulation, Sensitivity Analysis and Optimization of Constrained Multibody Systems with Impacts Based on Mass-Orthogonal Projections, in (Bestie and Schiehlen 1996), pp. 261–268.
Schulz, M., Mücke, R., Walser, H.-P. (1997), Optimisation of Mechanisms with Collisions and Unilateral Constraints, Multibody System Dynamics 1, pp. 223–240.
Schulz, M., Brauchli, H. (1997), Optimisation of Mechanisms and the Effect of Collisions, presented at the NATO advanced Study Institute on Computational Methods in Mechanisms, Varna, Bulgaria; submitted for publication.
Sofer M.M. (1991), On Equilibrium, Stability and Nonlocality in Elasticity Theory, Diss. ETH Nr. 9420.
Sofer, M., Melliger, O., Brauchli, H. (1992), Numerical behaviour of different formulations for multibody dynamics, Numerical Methods in Engineering ’92, Ch. Hirsch et al (eds.), Elsevier Science Publishers, Amsterdam.
Sofer, M., Brauchli, H., Melliger O. (1993), ODE Formulations for Multibody Dynamics: Numerical Aspects, in (Schiehlen 1993), pp. 397–402.
Sofer, M., Bach, D., Brauchli, H. (1995), Dynamics of Constrained Systems Based on Mass-Orthogonal Projections, in (Pereira and Ambrösio 1995), pp. 1–13.
Synge, J.L. (1927), On the Geometry of Dynamics, Phil. Trans. A 226, pp. 31–106.
Weber, R.W. (1981), Kanonische Theorie nichtholonomer Systeme, Diss. ETH Nr. 6876.
Weber, R. (1986), Hamiltonian Systems with Constraints and their Meaning in Mechanics, Arch. Rational Mech. Anal. 91, pp. 309–335.
Wittenburg, J. (1977) Dynamics of Systems of Rigid Bodies, Teubner, Stuttgart.
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Brauchli, H. (1998). Efficient Description and Geometrical Interpretation of the Dynamics of Constrained Systems. In: Angeles, J., Zakhariev, E. (eds) Computational Methods in Mechanical Systems. NATO ASI Series, vol 161. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03729-4_9
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DOI: https://doi.org/10.1007/978-3-662-03729-4_9
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