Abstract
The objective of this study is to present an accurate and simple method to describe the motion of constrained mechanical or structural systems. The proposed method is an elimination method to require less effort in computing Moore-Penrose inverse matrix than the generalized inverse method provided by Udwadia and Kalaba. Considering that the results by numerical integration of the derived second-order differential equation to describe constrained motion veer away the constrained trajectories, this study presents a numerical integration scheme to obtain more accurate results. Applications of holonomically or nonholonomically constrained systems illustrate the validity and effectiveness of the proposed method.
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References
Appell, P., 1911, “Example De Mouvement D’un Point Assujetti A Une Liaison Exprimee Par Une Relation Non Lineaire Entre Les Composantes De La Vitesse,”Rend. Circ. Matem. Palermo., Vol. 32, pp. 48–50.
Eun, H. C., Yang, K. H. and Chung, H. S., 2003, “Explicit Motion of Dynamic Systems with Position Constraints,”KSME International Journal, Vol. 17, No. 4, pp. 538–544.
Gibbs, J. W., 1879, “On the Fundamental Formulae of Dynamics,”American Journal of Mathematics, Vol. 2, pp. 49–64.
Graybill, F., 1983,Matrices and Applications to Statistics, 2nd Edition, Wadsworth, Belmont, California, 1983.
Kane. T. R., 1983, “Formulation of Dynamical Equations of Motion,”Am. J. Phys., Vol. 51, pp. 974–977.
Lee, D. C., Bae, D. S., Han, C. S., Seo, M. S. and Kim, J. Y., 1994a, “A Study on the Dynamic Analysis of Multibody System by the Relative Joint Coordinate Method,”Transactions of the KSME, Vol. 18, No. 7, pp. 1974–1984.
Lee, S. H., Bae, D. S. and Han, C. S., 1994b, “ADynamic Analysis of Constrained Multibody Systems,”Transactions of the KSME, Vol. 18, No. 9, pp. 2239–2348.
Park, J. H., Yoo, H. H., Hwang, Y. and Bae, D. S., 1997, “Dynamic Analysis of Constrained Systems Using Kane’s Method,”Transactions of the KSME, Vol. 21, No. 12, pp. 2156–2164.
Park, J. H., Yoo, H. H. and Hwang, Y., 2000, “Computational Method for Dynamic Analysis of Constrained Mechanical Systems Using Partial Velocity Matrix Transformation,”KSME International Journal, Vol. 14, No. 2, pp. 159–167.
The Math Works, 1997,MATLAB User’s Guide, South Natuck, MA 01760.
Udwadia, F. E. and Kalaba, R. E., 1992, “A New Perspective on Constrained Motion,”Proceedings of the Royal Society of London, Vol. 439, pp. 407–410.
You, S. S., 1996, “A Unified Dynamic Model and Control Synthesis for Robotic Manipulators with Geometric End-Effector Constraints,”KSME Journal, Vol. 10, No. 2, pp. 203–212.
You, S. S. and Jeong, S. K., 1998, “Kinematics and Dynamic Modeling Robot Systems through Principle of Workspace Orthogonalization,”KSME International Journal, Vol. 12, No. l2, pp. 170–180.
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Eun, HC., Park, SY., Lee, ET. et al. Analytical method for constrained mechanical and structural systems. KSME International Journal 18, 1691–1699 (2004). https://doi.org/10.1007/BF02984317
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DOI: https://doi.org/10.1007/BF02984317