Motion equations of cooperative multi flexible mobile manipulator via recursive Gibbs–Appell formulation

Korayem, Moharam Habibnejad; Dehkordi, S. F.

doi:10.1016/j.apm.2018.08.035

Cited by 28 publications

(12 citation statements)

References 29 publications

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“…This disadvantage is offset by the significantly lower number of differentiation operations required compared to Lagrange's equations. The method is little used, although in recent years, the need for calculations has led to reconsideration of the method [47][48][49][50][51]. The main advantage is the lower number of differentiation operations required to obtain the final equations of motion.…”

Section: Fea Of Elastic Mbsmentioning

confidence: 99%

Finite Element Method-Based Elastic Analysis of Multibody Systems: A Review

2022

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This paper presents the main analytical methods, in the context of current developments in the study of complex multibody systems, to obtain evolution equations for a multibody system with deformable elements. The method used for analysis is the finite element method. To write the equations of motion, the most used methods are presented, namely the Lagrange equations method, the Gibbs–Appell equations, Maggi’s formalism and Hamilton’s equations. While the method of Lagrange’s equations is well documented, other methods have only begun to show their potential in recent times, when complex technical applications have revealed some of their advantages. This paper aims to present, in parallel, all these methods, which are more often used together with some of their engineering applications. The main advantages and disadvantages are comparatively presented. For a mechanical system that has certain peculiarities, it is possible that the alternative methods offered by analytical mechanics such as Lagrange’s equations have some advantages. These advantages can lead to computer time savings for concrete engineering applications. All these methods are alternative ways to obtain the equations of motion and response time of the studied systems. The difference between them consists only in the way of describing the systems and the application of the fundamental theorems of mechanics. However, this difference can be used to save time in modeling and analyzing systems, which is important in designing current engineering complex systems. The specifics of the analyzed mechanical system can guide us to use one of the methods presented in order to benefit from the advantages offered.

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Section: Fea Of Elastic Mbsmentioning

confidence: 99%

Finite Element Method-Based Elastic Analysis of Multibody Systems: A Review

2022

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“…From an economical point of view, the computation time used will be reduced when applying the Gibbs-Appell equations. Although the method is less common, we can mention that in the last decade more researchers apply the method in their work [15][16][17][18][19]. This fact is due to the ease of obtaining the equations of motion for the studied mechanical systems.…”

Section: Fea Of Elastic Mbsmentioning

confidence: 99%

New analytical formalisms used in finite element analysis of robots with elastic elements

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Negrean

Marín

et al. 2020

Journal of Taibah University for Science

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Obtaining the equations of motion for an element in finite element analysis (FEA) model in the analysis of a multi-body system (MBS) having component elastic elements represents an important (maybe the main) step to build a soft able to solve such a problem numerically. In use FEA in the study of a MBS with elastic elements, the method of Lagrange's equations is especially used at present. This method presents the advantages of a homogeneous writing and the possibility to follow the operations easier. However, there are also equivalent formulations, developed by analytical mechanics, for approaching such a mechanical system. The earning of these alternative forms will be presented, by comparison.

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“…Developed independently by Gibbs (1879) [7] and Appell (1899) [8], the method consists of replacing a Lagrange function by the energy of accelerations and is essentially based on the Gauss principle of least constraint. In recent years, the Gibbs-Appell formalism has begun to be applied more often to a class of MBS systems [9][10][11][12]. For nonholonomic systems, Kane's equations can also be used, and it seems that in the last decade, their use has begun to be applied to problems that require the dynamic analysis of complex systems.…”

Section: Introductionmentioning

confidence: 99%

New analytical method based on dynamic response of planar mechanical elastic systems

et al. 2020

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An important stage in an analysis of a multibody system (MBS) with elastic elements by the finite element method is the assembly of the equations of motion for the whole system. This assembly, which seems like an empirical process as it is applied and described, is in fact the result of applying variational formulations to the whole considered system, putting together all the finite elements used in modeling and introducing constraints between the elements, which are, in general, nonholonomic. In the paper, we apply the method of Maggi's equations to realize the assembly of the equations of motion for a planar mechanical systems using finite two-dimensional elements. This presents some advantages in the case of mechanical systems with nonholonomic liaisons.

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Motion equations of cooperative multi flexible mobile manipulator via recursive Gibbs–Appell formulation

Cited by 28 publications

References 29 publications

Finite Element Method-Based Elastic Analysis of Multibody Systems: A Review

Finite Element Method-Based Elastic Analysis of Multibody Systems: A Review

New analytical formalisms used in finite element analysis of robots with elastic elements

New analytical method based on dynamic response of planar mechanical elastic systems

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