Abstract
A systematic process for constructing the equations of motion for multibody systems containing open or closed kinematic loops is presented. We first illustrate a nonconventional method for describing the configuration of a body in space using a set of dependent point coordinates, instead of the more classical set of translational and rotational body coordinates. Based on this point-coordinate description, body mass and applied loads are distributed to the points. For multibody systems, the equations of motion are constructed as a large set of mixed differential-algebraic equations. For open-loop systems, based on a velocity transformation process, the equations of motion are converted to a minimal set of equations in terms of the joint accelerations. For multibody systems with closed kinematic loops, the equations of motion are first written as a small set of differential-algebraic equations. Then, following a second velocity transformation, these equations are converted to a minimal set of differential equations. The combination of point-and joint-coordinate formulations provides some interesting features.
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References
Nikravesh, P. E. (1988) Computer-Aided Analysis of Mechanical Systems, Prentice-Hall.
Jerkovsky, W. (1978) “The Structure of Multibody Dynamics Equations,” J. Guidance and Control, Vol. 1, No. 3, pp. 173–182.
Kim, S. S. and Vanderploeg, M. J. (1986) “A General and Efficient Method for Dynamic Analysis of Mechanical Systems Using Velocity Transformations,” ASME J. Mech., Trans., and Auto. in Design, Vol. 108, No. 2, pp. 176–182.
Nikravesh, P. E. and Gim, G. (1993) “Systematic Construction of the Equations of Motion for Multibody Systems Containing Closed Kinematic Loops,” J. of Mechanical Design, Vol. 115, No. 1, pp. 143–149.
Serna, M. A., Aviles, R. and Garcia de Jalon, J. (1982) “Dynamic Analysis of Plane Mechanisms with Lower Pairs in Basic Coordinates,” Mechanisms and Machine Theory, Vol. 7, No. 6, pp. 397–403.
Garcia de Jalon, J., Unda, J., Avello, A. and Jimenez, J. M. (1986) “Dynamic Analysis of Three-Dimensional Mechanisms in Natural Coordinates,” ASME Design Engineering Technical conference, Columbus, OH, Paper No. 86-DET-137.
Affifi, H. A. (1992) “A Multi-Rigid-Body Formulation Based on Particles Dynamics and Velocity Transformation,” Research Report, Department of Aerospace and Mechanical Engineering, University of Arizona.
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© 1994 Springer Science+Business Media Dordrecht
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Nikravesh, P.E., Affifi, H.A. (1994). Construction of the Equations of Motion for Multibody Dynamics Using Point and Joint Coordinates. In: Seabra Pereira, M.F.O., Ambrósio, J.A.C. (eds) Computer-Aided Analysis of Rigid and Flexible Mechanical Systems. NATO ASI Series, vol 268. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1166-9_2
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DOI: https://doi.org/10.1007/978-94-011-1166-9_2
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-4508-7
Online ISBN: 978-94-011-1166-9
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