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Comparison of selected formulations for multibody system dynamics with redundant constraints

Pękal M., Frączek J.

Archive of Mechanical Engineering

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2016

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Vol. LXIII, nr 1

93--112

EN

This paper compares selected optimization-based methods for the analysis of multibody systems with redundant constraints. The following numerical schemes are examined: direct integration method, Udwadia-Kalaba formulation, two types of least-squares block solution method and Udwadia-Phohomsiri formulation. In order to compare efficiency of the algorithms, a series of simulations is performed on two exemplary McPherson struts. In the first variant, the mechanism has no redundant constraints whereas the other is overconstrained. Three constraint stabilization schemes are also compared in terms of integration errors.

PL

W pracy porównano wybrane metody analizy układów wieloczłonowych z więzami nadmiarowymi z zastosowaniem metod optymalizacji. Porównano następujące metody całkowania równań ruchu: metodę bezpośredniego całkowania, dwa rodzaje metody najmniejszych kwadratów oraz trzy różne sformułowania przedstawione w piśmiennictwie. Przeanalizowano trzy przypadki stabilizacji rozwiązania, przeprowadzono serie symulacji na dwóch przykładach mechanizmów kolumny McPhersona. Sformułowano wnioski co do efektywności rozwiązania układów równań ruchu mechanizmów, które mogą być przydatne dla doboru odpowiedniej metody całkowania.

2

Joint reactions in rigid or flexible body mechanisms with redundant constraints

Wojtyra M., Frączek J.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2012

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Vol. 60, nr 3

617-626

EN

The problem of joint reactions indeterminacy, in engineering simulations of rigid body mechanisms is most often caused by redundant constraints which are defined as constraints that can be removed without changing the kinematics of the system. In order to find a unique set of all joint reactions in an overconstrained system, it is necessary to reject the assumption that all bodies are rigid. Flexible bodies introduce additional degrees of freedom to the mechanism, which usually makes the constraint equations independent. Quite often only selected bodies are modelled as the flexible ones, whereas the other remain rigid. In this contribution it is shown that taking into account flexibility of selected mechanism bodies does not guarantee that unique joint reactions can be found. Problems typical for redundant constraints existence are encountered in partially flexible models, which are not overconstrained. A case study of a redundantly constrained spatial mechanism is presented. Different approaches to the mechanism modelling, ranging from a purely rigid body model to a fully flexible one, are investigated and the obtained results are compared and discussed.

3

Dynamic analysis of mechanisms with joint friction in the presence of redundant constraints

Frączek J., Wojtyra M.

International Journal of Applied Mechanics and Engineering

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2010

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Vol. 15, no 3

685-697

EN

This paper discusses the problem of calculating the joint friction forces in redundantly constrained rigid body mechanisms, described in absolute Cartesian coordinates. At the beginning the systems without joint friction are considered. It is shown that, under certain conditions, selected joint reaction forces can be uniquely determined despite the redundant constraints existence. A numerical method of such joints detection is proposed. Afterwards the equations of motion for mechanisms with redundant constraints and Coulomb friction in joints are formulated. In general, motion of such system is not defined uniquely. If, however, friction forces appear only in joints with uniquely determined reactions, motion can be determined uniquely. An example of dynamic analysis of a mechanism with redundant constraints and joint friction is presented.

4

Solving Sequential Planning Problems via Constraint Satisfaction

Bartak R., Toropila D.

Fundamenta Informaticae

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2010

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Vol. 99, nr 2

125-145

EN

Planning problems deal with finding a sequence of actions that transfer the initial state of the world into a desired state. Frequently such problems are solved by dedicated algorithms but there exist planners based on translating the planning problem into a different formalism such as constraint satisfaction or Boolean satisfiability and using a general solver for this formalism. The paper describes how to enhance existing constraintmodels of sequential planning problems by using techniques such as symmetry breaking (dominance rules), singleton consistency, nogoods, lifting, or techniques motivated by the partial-order planning.