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1

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.

2

Assessment of Muscle Forces and Joint Reaction in Lower Limbs During the Take-Off from the Springboard

Dziewiecki K., Mazur Z., Blajer W.

Acta Mechanica et Automatica

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2012

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Vol. 6, no. 4

11-14

EN

Computer simulation methods, based on the biomechanical models of human body and its motion apparatus, are commonly used for the assessment of muscle forces, joint reactions, and some external loads on the human body during its various activities. In this paper a planar musculoskeletal model of human body is presented, followed by its application to the inverse simulation study of a gymnast movement during the take)off from the springboard when performing the handspring somersault vault on the table. Using the kinematic da) ta of the movement, captured from optoelectronic photogrammetry, both the internal loads (muscle forces and joint reactions) in the gym) nast’s lower limbs and the external reactions from the springboard were evaluated. The calculated vertical reactions from the springboard were then compared to the values assessed using the captured board displacements and its measured elastic behaviors.

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

Efektywne wyznaczanie reakcji w węzłach kinematycznych mechanizmów

Blajer W.

Zeszyty Naukowe Katedry Mechaniki Stosowanej / Politechnika Śląska

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2003

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z. 20

22-27

PL

W pracy omawia się najpierw klasyczne sposoby generowania równań ruchu mechanizmów i wyznaczania reakcji w węzłach. Na tym tle prezentowana jest nowa metoda wyznaczania reakcji, w naturalny sposób powiązana z minimalno-wymiarowymi sformułowaniami dynamiki mechanizmów. Zaproponowane algorytmy nie wymagają odwracania macierzy - są dobrze dostosowane zarówno dla zastosowań numerycznych jak i przekształceń symbolicznych.

EN

In this paper some existing codes for obtaining equations of motion and the determination of joint reactions in mechanisms are first recalled. On this background a novel approach to the determination of joint reactions is presented, naturally associated with the reduced-dimension formulations of mechanism dynamics. The introduced schemes are especially efficient - no matrix inversion is required, and as such are well suited for both symbolic manipulations and computational implementations.

5

Wyznaczanie sił reakcji w stawach - rzutowa reprezentacja podejścia Kane'a

Czaplicki A., Jaszczuk J., Blajer W.

Zeszyty Naukowe Katedry Mechaniki Stosowanej / Politechnika Śląska

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2002

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nr 18

75-80

PL

W pracy przedstawia się efektywną metodę wyznaczania sił reakcji w stawach łańcucha biokinematycznego. Uwypukla się zalety proponowanego podejścia w stosunku do innych technik obliczeniowych. Zastosowanie metody ilustruje się na przykładzie łańcucha składajacego się z siedmiu ciał sztywnych połączonych przegubowo - prostego biomechanicznego modelu człowieka wykonującego ruchy z równolegle prowadzonymi kończynami dolnymi i górnymi. Przedstawiono przykład numeryczny, w którym wyznacza się reakcje w stawach sportowca wykonujacego salto w tył w pozycji kucznej na batucie.

EN

An efficient approach to the determination of joint reaction forces inopen-loop biokinematic linkages is proposed. The advantages of the novel method over the existing computational techniąues are emphasized. The method is introduced using an example of a seven-segment multibody system that models a human being with assumed collateral movements of the lower and upper extremities. A numerical example of determination of joint reactions during a back somersault in the tuck position performed on the trampoline is provided.

6

Determination of Joint Reactions in Multibody Systems: Some Existing Approaches and a Recent Contribution

Blajer W.

Machine Dynamics Problems

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2001

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Vol. 25, No. 3/4

7-19

EN

In this paper, first, some existing computer-oriented codes for the derivation of equations of motion and the determination of joint reactions in multibody systems are reviewed. Then, on this background, a novel approach to the determination of joint reactions is introduced, naturally related to the minimal-form formulations of multibody dynamics. For open-loop systems an augmented joint coordinate formulation is developed, and a modification of the coordinate partitioning method is proposed for closed-loop systems. The introduced schemes for the determination of joint reactions are especjally efficient - no matrix investion is required. As such they are well suited for both symbolic manipulations and computational implementations. An illustrative example is provided.