Abstract
Optimal design of multibody systems is of primary importance to researchers working in various fields. The goal of the paper is to present a novel Hamiltonian based approach for finding design sensitivities of multibody systems (MBS) through the use of direct differentiation method. The total derivatives of Hamiltonian equations of motion (EOM) based on the augmented Lagrangian in terms of the design are determined in the text. An algorithm for the evaluation of a gradient of an objective function is also delivered. Sample test case is presented that demonstrates the validity of the proposed approach.
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References
K. Anderson and Y. Hsu. “Order-(n+m) direct differentiation determination of design sensitivity for constrained multibody dynamic systems”. In: Structural and Multidisciplinary Optimization 26.3 (2004), pp. 171–182. issn: 1615-1488. doi: 10.1007/s00158-003-0336-1.
D. Bestle and P. Eberhard. “Analyzing and optimizing multibody systems”. In: Mechanics of structures and machines 20 (1992), pp. 67–92. doi: 10.1080/08905459208905161.
K. D. Bhalerao, M. Poursina, and K. S. Anderson. “An efficient direct differentiation approach for sensitivity analysis of flexible multibody systems”. In: Multibody System Dynamics 23.2 (2010), pp. 121–140. issn: 1573-272X. doi: 10.1007/s11044-009-9176-0.
K. Chadaj, P. Malczyk, and J. Frączek. “Efficient parallel formulation for dynamics simulation of large articulated robotic systems”. In: 2015 20th International Conference on Methods and Models in Automation and Robotics (MMAR). 2015, pp. 441–446. doi: 10.1109/mmar.2015.7283916.
K. Chadaj, P. Malczyk, and J. Frączek. “A parallel Hamiltonian formulation for forward dynamics of closed-loop multibody systems”. In: Multibody System Dynamics 1.39 (2017), pp. 51–77. doi: 10.1007/s11044-016-9531-x.
K. Chadaj, P. Malczyk, and J. Frączek. “A Parallel Recursive Hamiltonian Algorithm for Forward Dynamics of Serial Kinematic Chains”. In: IEEE Transactions on Robotics 33.3 (2017), pp. 647–660. doi: 10.1109/tro.2017.2654507.
D. Dopico, Y. Zhu, A. Sandu, and C. Sandu. “Direct and Adjoint Sensitivity Analysis of Ordinary Differential Equation Multibody Formulations”. In: Journal of Computational and Nonlinear Dynamics 10.1 (2014). doi: 10.1115/1.4026492.
E. J. Haug and V. N. Sohoni. “Design sensitivity analysis and optimization of kinematically driven systems”. In: Computer aided analysis and optimization of mechanical system dynamics. Springer, 1984, pp. 499–554.
H. Lankarani and P. Nikravesh. “Application of the canonical equations of motion in problems of constrained multibody systems with intermittent motion”. English (US). In: American Society of Mechanical Engineers, Design Engineering Division (Publication) DE. Vol. 14. Publ by American Soc of Mechanical Engineers (ASME), 1988, pp. 417–423.
P. Maciąg, P. Malczyk, and J. Frączek. “Optimal Design of Multibody Systems Using the Adjoint Method”. In: Dynamical Systems Theory and Applications. Springer. 2017, pp. 241–253. doi: 10.1007/978-3-319-96601-4˙22.
P. Malczyk, P. Maciąg, and J. Frączek. “Hamiltonian based optimal design of planar multibody systems”. In: 26th International Conference on Theory of Machines and Mechatronic Systems. 2018.
F. Tepper and G. Lowen. “Shaking force optimization of four-bar linkage with adjustable constraints on ground bearing forces”. In: Journal of Engineering for Industry 97.2 (1975), pp. 643–651.
Acknowledgments
This work has been supported by National Science Center under grant No. 2018/29/B/ST8/00374. The first author would also like to acknowledge the support of the Institute of Aeronautics and Applied Mechanics funds for scientific research.
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Maciąg, P., Malczyk, P., Frączek, J. (2019). Direct sensitivity analysis of planar multibody systems in the Hamiltonian framework. In: Uhl, T. (eds) Advances in Mechanism and Machine Science. IFToMM WC 2019. Mechanisms and Machine Science, vol 73. Springer, Cham. https://doi.org/10.1007/978-3-030-20131-9_305
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DOI: https://doi.org/10.1007/978-3-030-20131-9_305
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