Abstract
The present work aims to incorporate control (or servo) constraints into finite-dimensional mechanical systems subject to holonomic constraints. In particular, we focus on underactuated systems, defined as systems in which the number of degrees of freedom exceeds the number of inputs. The corresponding equations of motion can be written in the form of differential-algebraic equations (DAEs) with a mixed set of holonomic and control constraints. Apart from closed-loop multibody systems, the present formulation accommodates the so-called rotationless formulation of multibody dynamics. The rotationless formulation has proven to be especially well-suited for the design of energy and momentum conserving schemes, which typically exhibit superior numerical stability properties (see [4, 7, 10]). Subsequent to the incorporation of the servo constraints, we deal with a reformulation of the underlying DAEs, which is amenable to a direct numerical discretization. To this end, we apply a specific projection method to the DAEs in terms of redundant coordinates. A similar projection approach has been previously developed in the framework of generalized coordinates by Blajer & Kolodziejczyk [12]. A numerical example is presented, which deals with a 3D rotary crane.
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Peter Betsch received his degree in aerospace engineering from the University of Stuttgart, Germany in 1991, his Ph.D. degree in computational mechanics from the University of Hanover, Germany in 1996, and his venia legendi (Habilitation) in mechanics from the University of Kaiserlautern, Germany in 2002. Since 2003 he has been a Professor of Computational Mechanics with the University of Siegen, Germany.
Mahmut Quasem received his BSc in mechanical engineering from Bangladesh University of Engineering and Technology, Dhaka in 2000. He then received his MSc in mechatronics from the University of Siegen, Germany in 2006. He has been working as a research assistant at the chair of computational mechanics at the University of Siegen, Germany since June 2006.
Stefan Uhlar received his degree in mechanical engineering from the University of Kaiserslautern, Germany in 2005. He is a Ph.D. candidate at the chair of computational mechanics at the University of Siegen, Germany.
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Betsch, P., Quasem, M. & Uhlar, S. Numerical integration of discrete mechanical systems with mixed holonomic and control constraints. J Mech Sci Technol 23, 1012–1018 (2009). https://doi.org/10.1007/s12206-009-0331-6
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DOI: https://doi.org/10.1007/s12206-009-0331-6