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Mathematics
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Applied Mathematics to Mechanisms and Machines II
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Applied Mathematics to Mechanisms and Machines II

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Engineering Mathematics".

Deadline for manuscript submissions: 31 July 2024 | Viewed by 5328

Special Issue Editors

Prof. Dr. Higinio Rubio Alonso

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Guest Editor
Department of Mechanical Engineering, Universidad Carlos III de Madrid, 28911 Leganés, Madrid, Spain
Interests: kinematical and dynamical systems; vibration analysis and machine learning
Special Issues, Collections and Topics in MDPI journals
Dr. Alejandro Bustos Caballero

E-Mail Website
Guest Editor
Department of Mechanics, National University of Distance Education, Calle Juan del Rosal 12, 28040 Madrid, Spain
Interests: railways; condition monitoring; vibration analysis; multibody dynamics systems; FEM
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Jesus Meneses Alonso

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Guest Editor
Department of Mechanical Engineering, Universidad Carlos III de Madrid, 28911 Leganés, Madrid, Spain
Interests: Kinematics and Dynamics of mechanisms and machines; Multibody Dynamics; Contact Models; Biped robots; Biomedical mechanical devices.
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Enrique Soriano-Heras

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Guest Editor
Department of Mechanical Engineering, Universidad Carlos III de Madrid, 28911 Leganés, Madrid, Spain
Interests: mechanisms; machines; machine-tools; grippers; collet-chuck
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

In mechanism and machine science, theoretical and computational analysis leads to problems, which can be solved using mathematical modelling and processing.

The different ways of approaching problems in the area of mechanical engineering, or related areas, include the use of integral and differential equations; interpolation; polynomial computation; least squares and regularization; vector algebra; matrix equations; control theory; synthesis process; discrete and continuous transforms; image and signal processing; Galerkin, finite element, finite difference, and finite volume methods.

This Special Issue compiles articles which explore the different mathematical processes used to solve mechanisms and machines problems. Special attention is devoted to the analysis and synthesis of mechanisms and machines; linear and nonlinear mechanical systems; transportation engineering (cars, trains, ships, etc.); vibration data analysis and machine learning; and kinematics, dynamics, and control in biomechanics, mechatronics, and micromachines.

Prof. Dr. Higinio Rubio Alonso
Dr. Alejandro Bustos
Prof. Dr. Jesus Meneses Alonso
Prof. Dr. Enrique Soriano-Heras
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • analytic synthesis
  • mechanisms and machines
  • kinematics and dynamics
  • vibrations analysis techniques
  • linear/nonlinear systems
  • machine learning
  • control algorithms
  • transportation engineering

Published Papers (5 papers)

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Research

15 pages, 2753 KiB  
Article
An Analysis of Power Friction Losses in Gear Engagement with Intermediate Rolling Elements and a Free Cage
by Egor A. Efremenkov, Nikita V. Martyushev, Svetlana K. Efremenkova and Egor S. Chavrov
Mathematics 2024, 12(6), 873; https://doi.org/10.3390/math12060873 - 16 Mar 2024
Viewed by 411
Abstract
Currently, mechanical gears with cycloid engagement are increasingly used in mechanisms along with involute ones. In modern drive mechanisms, using pin gears and gears with intermediate rolling elements (IRE) is widespread, which simultaneously use cycloid gears. To a greater extent, pin gears are [...] Read more.
Currently, mechanical gears with cycloid engagement are increasingly used in mechanisms along with involute ones. In modern drive mechanisms, using pin gears and gears with intermediate rolling elements (IRE) is widespread, which simultaneously use cycloid gears. To a greater extent, pin gears are now being investigated, but IRE gears have their undeniable advantages. Many works are devoted to the study of cycloid toothing for certain gears, but the efficiency, especially that of IRE gears, has practically not been investigated. Therefore, the analysis of power losses in the engagement of a gear with IRE and a free cage (IREFC) is relevant. In this analysis, the authors of the work have used laws of mechanics, methods of energy flows and a secant normal. Mathematical expressions have been obtained to estimate slip speeds and power friction losses in the engagement of a gear with IREFC, and a formula has been derived to determine the efficiency of a mentioned mechanical transmission. The calculation of slip speeds and power losses at the points of contact of a rolling element with cycloid profiles of wheels for selected initial parameters of a gear with IREFC has been presented. The friction power and the overall efficiency of the entire gear engagement have also been calculated. This work shows that power friction losses at the points of contact of a rolling element with cycloid profiles of tooth wheels of a gear with IREFC are not the same. The friction power in the contact of a rolling element with a cycloid profile of a cam is an order of magnitude higher than the friction power in the contact of a rolling element with a cycloid profile of a crown. Full article
(This article belongs to the Special Issue Applied Mathematics to Mechanisms and Machines II)
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19 pages, 2440 KiB  
Article
A Comprehensive Evaluation Method of Machining Center Components’ Importance Based on Combined Variable Weight
by Lan Luan, Guixiang Shen and Yingzhi Zhang
Mathematics 2024, 12(2), 330; https://doi.org/10.3390/math12020330 - 19 Jan 2024
Viewed by 488
Abstract
The fault transitivity of machining center components causes their fault propagation indexes to demonstrate dynamic time variability, which affects their importance. The method proposed in this study overcomes the biases of existing methods of evaluating the importance of system components, as they are [...] Read more.
The fault transitivity of machining center components causes their fault propagation indexes to demonstrate dynamic time variability, which affects their importance. The method proposed in this study overcomes the biases of existing methods of evaluating the importance of system components, as they are mostly based on single indexes; the fault propagation probability and fault propagation risk are selected to perform a comprehensive evaluation. This study first establishes a network hierarchical structure model for machining center components, and the degree of influence of fault propagation among the components is calculated. On this basis, the improved adjacent spreading paths (ASP) algorithm is used to calculate the fault propagation index of each component; from the two perspectives of fault propagation probability and fault propagation risk, an evaluation mechanism involving the combined variable weight is used to comprehensively evaluate components’ importance. Taking a certain type of machining center as an example, through a comparison with ranking results from other node importance methods, it is verified that the proposed method can more effectively distinguish the differences in the importance of each component, thus illustrating the effectiveness and practical value of this method. Full article
(This article belongs to the Special Issue Applied Mathematics to Mechanisms and Machines II)
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21 pages, 6281 KiB  
Article
A New RP1PR Type Coupling for Shafts with Crossed Axes
by Stelian Alaci, Ioan Doroftei, Florina-Carmen Ciornei, Ionut-Cristian Romanu, Ioan-Alexandru Doroftei and Mariana-Catalina Ciornei
Mathematics 2023, 11(9), 2025; https://doi.org/10.3390/math11092025 - 24 Apr 2023
Cited by 1 | Viewed by 862
Abstract
There are few examples of mechanical coupling solutions for the transmission of high torques between two rotating shafts that have non-coplanar, non-parallel axes. Based on the structural analysis, the paper proposes a solution for an RP1PR-type symmetrical coupling. The Hartenberg–Denavit methodology is not [...] Read more.
There are few examples of mechanical coupling solutions for the transmission of high torques between two rotating shafts that have non-coplanar, non-parallel axes. Based on the structural analysis, the paper proposes a solution for an RP1PR-type symmetrical coupling. The Hartenberg–Denavit methodology is not applicable for performing the kinematical analysis, hence the solution starts from the geometrical condition of the creation of planar pairs of the mechanism, expressed in vector form. The absolute motion of all elements of the mechanism’s structure can be expressed after developing the kinematical analysis. The theoretical results are validated via numerical analysis. By comparing the analytical results with the CATIA-modeled results, excellent compatibility is obtained. We also propose a constructive solution for the newly designed coupling mechanism. Full article
(This article belongs to the Special Issue Applied Mathematics to Mechanisms and Machines II)
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12 pages, 904 KiB  
Article
Analytical Modelling of an Active Vibration Absorber for a Beam
by Carlos Rincon, Jorge Alencastre and Richard Rivera
Mathematics 2023, 11(9), 2009; https://doi.org/10.3390/math11092009 - 24 Apr 2023
Viewed by 1530
Abstract
Attenuation of mechanical vibrations is an ongoing field of research in engineering aiming at reducing damage and improving performance in the presence of dynamical forces. Different alternatives have been proposed over time; the active vibration absorber can be highlighted as an alternative which [...] Read more.
Attenuation of mechanical vibrations is an ongoing field of research in engineering aiming at reducing damage and improving performance in the presence of dynamical forces. Different alternatives have been proposed over time; the active vibration absorber can be highlighted as an alternative which can absorb the vibration from system in real time. In this study, an active vibration absorber was modelled as an electromechanical device. It was applied to a cantilever beam, mathematically modelled as a continuous beam. A set of differential equations representing the dynamical behaviour of the cantilever beam and active vibration absorber was obtained and it was simulated in Matlab Simulink®. Results indicated that the active vibration absorber is able to significantly reduce the vibration amplitudes of a system, especially in resonance conditions. The analytical model and procedure developed here can easily spread to any more complex system. Full article
(This article belongs to the Special Issue Applied Mathematics to Mechanisms and Machines II)
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15 pages, 3406 KiB  
Article
Development of an Algorithm for Computing the Force and Stress Parameters of a Cycloid Reducer
by Egor A. Efremenkov, Sergey A. Shanin and Nikita V. Martyushev
Mathematics 2023, 11(4), 993; https://doi.org/10.3390/math11040993 - 15 Feb 2023
Cited by 10 | Viewed by 1332
Abstract
The paper is devoted to the development of an algorithm for the automated calculation of force characteristics of cycloid toothing when the initial parameters vary widely. The algorithm forms a structured data array that accelerates finding and outputting the necessary parameters and reduces [...] Read more.
The paper is devoted to the development of an algorithm for the automated calculation of force characteristics of cycloid toothing when the initial parameters vary widely. The algorithm forms a structured data array that accelerates finding and outputting the necessary parameters and reduces the probability of error in determining these parameters. The algorithm serves the basis for a program that allows for the examination of the change in force and geometrical parameters in various combinations. The study includes the analysis of the dependence of forces and contact stresses in transmission toothing with intermediate rolling elements and a free cage on the initial parameters of this transmission. The obtained results will make it possible to select optimal combinations of initial parameters in order to minimize the force impact on the mechanism parts when designing modern compact mechanisms based on the cycloid with intermediate rolling elements and a free cage. Full article
(This article belongs to the Special Issue Applied Mathematics to Mechanisms and Machines II)
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