The Use of Lagrange Multiplier Formalism to Solve the Problem of Transverse Vibrations of the Lower-Limb Exoskeleton

M. Skotnicznya, D. Cekusa, P. Kwiatońa, P. Kwiatońc, M. Šoferb aDepartment of Mechanics and Machine Design Fundamentals, Faculty of Mechanical Engineering and Computer Science, Częstochowa University of Technology, al. Armii Krajowej 21, 42-201 Częstochowa, Poland bDepartment of Applied Mechanics, Faculty of Mechanical Engineering, VŠB-Technical University of Ostrava, 17. listopadu 15/2127, 708 33 Ostrava-Poruba, Czech Republic cGrupa SZYMBUD Sp. z o.o. Sp. j., Częstochowska 2G, 42-270 Kłomnice, Poland

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In the paper, the Lagrange multiplier formalism has been used to find a solution to the problem of free transverse vibrations of the lower-limb exoskeleton. Parts of the exoskeleton were replaced with continuous (beams) and discrete elements. The beams have been circumscribed according to the Bernoulli-Euler theory. The physical model takes into account properties that characterize the interaction between exoskeleton elements, contact with the ground and system load. On the basis of the presented mathematical model, an algorithm and a computational program were created. It permitted the research on the impact of selected model parameters on the transverse vibrations of the analyzed system. The presented model, coupled with the longitudinal vibration model, may constitute a complete description of the vibrations of the lower-limb exoskeleton.

DOI:10.12693/APhysPolA.142.133 topics: discrete-continuous system, exoskeleton, free vibration, Lagrange multiplier formalism