Formulations about Dynamics of Mobile Robots

Negrean, Iuliu; Schonstein, Claudiu; Kacso, Kalman; Negrean, Calin; Duca, Adina

doi:10.4028/www.scientific.net/ssp.166-167.309

Cited by 12 publications

(25 citation statements)

References 2 publications

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“…Not many papers contain applications of the Gibbs-Appell equations. Generally, the papers present the Gibbs-Appell formalism as a secondary method to solve a problem (useful but not necessary) [62].…”

Section: Conclusion and Discussionmentioning

confidence: 99%

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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: Conclusion and Discussionmentioning

confidence: 99%

“…To use these, it is necessary to know the energy of acceleration, obtained in Equation (33). The Gibbs-Appell equations are [62]:…”

Section: Gibbs-appell Formalismmentioning

confidence: 99%

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

2022

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“…In the following, the dot placed above a scalar, vector or matrix size means the derivative of the respective size with respect to time. The notion energy of accelerations for a system of material points is defined as [27]:…”

Section: Gibbs-appell Formalismmentioning

confidence: 99%

“…There are a lot of papers using this formalism in the study of the dynamical system [26]. Interesting results are presented in [27][28][29]. The present paper only aims at obtaining the equations of motion for a three-dimensional finite element with a general motion.…”

Section: Introductionmentioning

confidence: 99%

Energy of Accelerations Used to Obtain the Motion Equations of a Three- Dimensional Finite Element

et al. 2020

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When analyzing the dynamic behavior of multi-body elastic systems, a commonly used method is the finite element method conjunctively with Lagrange’s equations. The central problem when approaching such a system is determining the equations of motion for a single finite element. The paper presents an alternative method of calculation theses using the Gibbs–Appell (GA) formulation, which requires a smaller number of calculations and, as a result, is easier to apply in practice. For this purpose, the energy of the accelerations for one single finite element is calculated, which will be used then in the GA equations. This method can have advantages in applying to the study of multi-body systems with elastic elements and in the case of robots and manipulators that have in their composition some elastic elements. The number of differentiation required when using the Gibbs–Appell method is smaller than if the Lagrange method is used which leads to a smaller number of operations to obtain the equations of motion.

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“…The Gibbs-Appell method was used for a wide class of applications [17][18][19][20][21]. The analytical methods of studying MBS and the possibilities of obtaining these equations are presented in [22][23][24][25]. The Gibbs-Appell method is a method rarely found in studies, but it may be of interest to researchers to use this method in analyzing MBS systems with elastic elements [26,27].…”

Section: Introductionmentioning

confidence: 99%

Maggi’s Equations Used in the Finite Element Analysis of the Multibody Systems with Elastic Elements

2020

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The main method used to determine the equations of motion of a multibody system (MBS) with elastic elements is the method of Lagrange’s multipliers. The assembly of equations for the whole system represents an important step in the elastodynamic analysis of such a system. This paper presents a new method of approaching this stage, by applying Maggi’s equations. In this way, the links that exist between the finite elements and the connections that exist between different bodies of the MBS system are conveniently taken into account, each body having a distinct velocity and acceleration field. Although Maggi’s equations have been used, sporadically, in some applications so far, we are not aware that they have been used in the study of elastic systems using the finite element method. Finally, an algorithm is presented that uses the Maggi formalism to obtain the equations of motion for an MBS system.

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Formulations about Dynamics of Mobile Robots

Cited by 12 publications

References 2 publications

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

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

Energy of Accelerations Used to Obtain the Motion Equations of a Three- Dimensional Finite Element

Maggi’s Equations Used in the Finite Element Analysis of the Multibody Systems with Elastic Elements

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