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A Tutorial for the Analysis of the Piecewise-Smooth Dynamics of a Constrained Multibody Model of Vertical Hopping

1,†, 1,†, 1,2,*,† and 1,3,†
1
Department of Applied Mechanics, Budapest University of Technology and Economics, Müegyetem rkp. 3, 1111 Budapest, Hungary
2
MTA-BME Lendület Human Balancing Research Group, Müegyetem rkp. 3, 1111 Budapest, Hungary
3
MTA-BME Research Group of Dynamics of Machines and Vehicles, Müegyetem rkp. 3, 1111 Budapest, Hungary
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Math. Comput. Appl. 2018, 23(4), 74; https://doi.org/10.3390/mca23040074
Received: 29 September 2018 / Revised: 12 November 2018 / Accepted: 13 November 2018 / Published: 14 November 2018
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Abstract

Contradictory demands are present in the dynamic modeling and analysis of legged locomotion: on the one hand, the high degrees-of-freedom (DoF) descriptive models are geometrically accurate, but the analysis of self-stability and motion pattern generation is extremely challenging; on the other hand, low DoF models of locomotion are thoroughly analyzed in the literature; however, these models do not describe the geometry accurately. We contribute by narrowing the gap between the two modeling approaches. Our goal is to develop a dynamic analysis methodology for the study of self-stable controlled multibody models of legged locomotion. An efficient way of modeling multibody systems is to use geometric constraints among the rigid bodies. It is especially effective when closed kinematic loops are present, such as in the case of walking models, when both legs are in contact with the ground. The mathematical representation of such constrained systems is the differential algebraic equation (DAE). We focus on the mathematical analysis methods of piecewise-smooth dynamic systems and we present their application for constrained multibody models of self-stable locomotion represented by DAE. Our numerical approach is demonstrated on a linear model of hopping and compared with analytically obtained reference results. View Full-Text
Keywords: non-linear analysis; periodic motion; piecewise-smooth systems; biomechanics of running; ground-foot impact non-linear analysis; periodic motion; piecewise-smooth systems; biomechanics of running; ground-foot impact
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MDPI and ACS Style

Zana, R.R.; Bodor, B.; Bencsik, L.; Zelei, A. A Tutorial for the Analysis of the Piecewise-Smooth Dynamics of a Constrained Multibody Model of Vertical Hopping. Math. Comput. Appl. 2018, 23, 74.

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