Search Results (61)

The objective of this study is to design, develop, and analyze a tri-wheeled trolley integrated with a motor that incorporates adjustable and foldable features. The purpose of a trolley is to allow users to easily transport items from one place to another. However, problems arise when transporting objects across challenging surfaces, such as up a flight of stairs, using a conventional cart. This innovation uses multiple engineering skills to determine and develop the best possible design for a stair-climbing trolley. A tri-wheel mechanism is integrated into its motorized design, meticulously engineered for adjustability, ensuring compatibility with a wide range of staircase dimensions. The designed trolley was constructed considering elements and processes such as a literature review, conceptual design, concept screening, concept scoring, 3D modelling, engineering design calculations, and simulations. The trolley was tested, and the measured pulling force data were compared with the theoretical calculations. A graph of the pulling force vs. load was plotted, in which both datasets showed similar increasing trends; hence, the designed trolley worked as expected. The development of this stair-climbing trolley can benefit people living in rural areas or low-cost buildings that are not equipped with elevators and can reduce injuries among the elderly. The designed stair-climbing trolley will not only minimize the user’s physical effort but also enhance safety. On top of that, the adjustable and foldable features of the stair-climbing trolley would benefit users living in areas with limited space. Full article

The paper presents results of experimental research on tyre–road contact stress distributions, measured indoors for a motorsport slick tyre. The triaxial contact stress distributions have been measured using the complex transducer containing a transversal array of 30 sensing pins covering the entire contact patch width. Wheel displacement in the longitudinal direction was measured using a rotary encoder. The parameters allocated for the experimental programme have included different values of tyre inflation pressure, vertical load, camber angle and toe angle. All measurements were performed at low longitudinal speed in free-rolling conditions. The influence of tyre functional parameters on the contact patch shape and size has been discussed. The stress distributions on each orthogonal direction are presented in multiple formats, such as 2D graphs in which the curves show the stresses measured by each sensing element versus contact length; surfaces with stress values plotted as vertical coordinates versus contact patch length and width; and colour maps for stress distributions and orientations of shear stress vectors. The effects of different parameter types and values on stress distributions have been emphasised and analysed. Furthermore, the magnitude and position of local extreme values for each stress distribution have been investigated with respect to the above-mentioned tyre functional parameters. Full article

This study aims to explore the tracking control challenge in a swarm of multiple nonholonomic wheeled mobile robots (NWMRs) by utilizing a distributed leader–follower strategy grounded in the cascade system theory. Firstly, the kinematic control law is developed for the leader by constructing a sliding surface based on the error tracking model with a virtual reference trajectory. Secondly, a communication topology with the desired formation pattern is modeled for the multiple robots by using the graph theory. Further, in the leader–follower NWMR system, each follower lacks direct access to the leader’s information. Therefore, a novel distributed-based controller by PD-based controller for the follower is developed, enabling each follower to obtain the leader’s information. Thirdly, for each case, we give a further analysis of the closed-loop system to guarantee uniform global asymptotic stability with the conditions based on the cascade system theory. Finally, the trajectory tracking performance of the proposed controllers for the NWMR system is illustrated through simulation results. The leader robot achieved a low RMSE of 1.6572 (Robot 1), indicating accurate trajectory tracking. Follower robots showed RMSEs of 2.6425 (Robot 2), 3.0132 (Robot 3), and 4.2132 (Robot 3), reflecting minor variations due to the distributed control strategy and local disturbances. Full article

The increasing demand for real-time multimedia communications has driven the need for highly secure and computationally efficient encryption schemes. In this work, we present a novel chaos-based encryption system that provides remarkable levels of security and performance. It leverages the benefits of applying fast-to-evaluate chaotic maps, along with a 2-Dimensional Look-Up Table approach (2D-LUT), and simple but powerful periodic perturbations. The foundation of our encryption system is a Pseudo-Random Number Generator (PRNG) that consists of a fully connected random graph with M vertices representing chaotic maps that populate the 2D-LUT. In every iteration of the system, one of the M chaotic maps in the graph and the corresponding trajectories are randomly selected from the 2D-LUT using an emulated spin-wheel picker game. This approach exacerbates the complexity in the event of an attack, since the trajectories may come from the same or totally different maps in a non-sequential time order. We additionally perform two levels of perturbation, at the map and trajectory level. The first perturbation (map level) produces new trajectories that are retrieved from the 2D-LUT in non-sequential order and with different initial conditions. The second perturbation applies a p-point crossover scheme to combine a pair of trajectories retrieved from the 2D-LUT and used in the ciphering process, providing higher levels of security. As a final process in our methodology, we implemented a simple packet-based data integrity scheme that detects with high probability if the received information has been modified (for example, by a man-in-the-middle attack). Our results show that our proposed encryption scheme is robust to common cryptanalysis attacks, providing high levels of security and confidentiality while supporting high processing speeds on the order of gigabits per second. To the best of our knowledge, our chaotic cipher implementation is the fastest reported in the literature. Full article

Robustness in networks plays a vital role in mitigating the effects of failures caused by nodes or links, which can disrupt essential services. Among the various vulnerability parameters in graph theory, such as connectivity and integrity, their applications to fuzzy graphs remain underexplored, despite fuzzy graphs being a powerful tool for modeling uncertainty. In this paper, we introduce the parameter ’fuzzy node integrity’, which considers both the number of disrupted elements and the strength of residual connections. We derive general formulas for different types of symmetric and asymmetric fuzzy graph structures, including cycle graphs, wheel graphs, and star graphs, to systematically demonstrate the utility of this parameter. The proposed parameter is then applied to a military logistics problem to gain insights into the identification of critical nodes and route optimization under uncertainty. This study bridges an important gap in fuzzy graph theory by redefining node integrity through the inclusion of connection strength, offering a promising tool for assessing network vulnerability. These findings lay the foundation not only for theoretical research but also for practical improvements in transportation, disaster management, and communication networks. Full article

In this paper, motivated by the recently introduced topological indices—the Sombor index, Sombor coindex, and Lanzhou index, we define a new index—the Lanzhou coindex of a graph. Furthermore, we investigate the Sombor index (coindex) and the Lanzhou index (coindex) of tadpole graphs, wheel graphs, and two-dimensional grid graphs, as well as their paraline graphs. Full article

For an undirected graph G, a zero-sum flow is an assignment of nonzero integer weights to the edges such that each vertex has a zero-sum, namely the sum of all incident edge weights with each vertex is zero. This concept is an undirected analog of nowhere-zero flows for directed graphs. We study a more general one, namely constant-sum $\mathbb{A}$-flows, which gives edge weights using nonzero elements of an additive Abelian group $\mathbb{A}$ and requires each vertex to have a constant-sum instead. In particular, we focus on two special cases: $\mathbb{A}={\mathbb{Z}}_k$, the finite cyclic group of integer congruence modulo k, and $\mathbb{A}=\mathbb{Z}$, the infinite cyclic group of integers. The constant sum under a constant-sum $\mathbb{A}$-flow is called an index of G for short, and the set of all possible constant sums (indices) of G is called the constant sum spectrum. It is denoted by $I_k\left(G\right)$ and $I\left(G\right)$ for $\mathbb{A}={\mathbb{Z}}_k$ and $\mathbb{A}=\mathbb{Z}$, respectively. The zero-sum flows and constant-sum group flows for regular graphs regarding cases $\mathbb{Z}$ and ${\mathbb{Z}}_k$ have been studied extensively in the literature over the years. In this article, we study the constant sum spectrum of nearly regular graphs such as wheel graphs $W_n$ and fan graphs $F_n$ in particular. We completely determine the constant-sum spectrum of fan graphs and wheel graphs concerning ${\mathbb{Z}}_k$ and $\mathbb{Z}$, respectively. Some open problems will be mentioned in the concluding remarks. Full article

The primary objective of this study is the computation of the matching polynomials of a number of symmetric, semisymmetric, double group graphs, and solids in third and higher dimensions. Such computations of matching polynomials are extremely challenging problems due to the computational and combinatorial complexity of the problem. We also consider a series of recursive graphs possessing symmetries such as D_2h-polyacenes, wheels, and fans. The double group graphs of the Möbius types, which find applications in chemically interesting topologies and stereochemistry, are considered for the matching polynomials. Hence, the present study features a number of vertex- or edge-transitive regular graphs, Archimedean solids, truncated polyhedra, prisms, and 4D and 5D polyhedra. Such polyhedral and Möbius graphs present stereochemically and topologically interesting applications, including in chirality, isomerization reactions, and dynamic stereochemistry. The matching polynomials of these systems are shown to contain interesting combinatorics, including Stirling numbers of both kinds, Lucas polynomials, toroidal tree-rooted map sequences, and Hermite, Laguerre, Chebychev, and other orthogonal polynomials. Full article

To achieve optimal controllability in a dual steering tractor (a four-wheel, iso-diametric tractor equipped with a dual-hydraulic steering system), this study proposes a coordinated approach that combines experimental testing (using a special agricultural tractor) with numerical analysis of the entire vehicle, developed in Bond Graph-3D. For certain crops, a dual steering vehicle is used to meet the needs of professionals who require easy maneuverability in narrow spaces and/or reduced steering time. This study aims to explore the reasons behind the need for dual steering tractors, highlighting the advantages and disadvantages of these two different configurations and ultimately focusing on the combined benefits of both. Based on an extensive review of the literature and drawing from previous studies, this paper analyzes aspects such as the variation in noise levels (or comfort level) experienced at the steering wheel when switching from Ackermann steering to a dual steering system. After outlining the theoretical methodology used to describe the model, both experimental and numerical analyses of a vineyard tractor in operation are presented. The goal of this work is to provide guidance on design methods and, through the Bond Graph-3D model, suggest the best control algorithms to minimize steering noise and enhance driving comfort. This research aims to pave the way for future control strategies in electrohydraulic steering systems. Full article

This research introduces two novel topological indices, the entire Albertson index and the entire sigma index, as quantitative measures of molecular irregularity. The indices are defined by precise mathematical formulas and their behavior is analyzed across a diverse range of graph families. To evaluate the predictive capabilities of the proposed indices, we compare their performance with established irregularity indices in the modeling of molecular properties. Correlations with physicochemical properties, including the boiling point, melting point, and molecular volume, are investigated. Specific expressions for these indices are derived for various molecular structures, such as bridge molecules, polyomino chains of n-cycles, triangular benzenoid graphs, graphene, and dendrimer stars $D_3\left[n\right]$. The findings of this study contribute significantly to the field of chemical graph theory by providing novel tools to understand and predict molecular behavior. The entire irregularity indices have potential applications in drug discovery, materials science, and other areas where molecular properties are crucial. Full article

A graph, $G=(V,E)$, is edge odd graceful if it possesses edge odd graceful labeling. This labeling is defined as a bijection $g:E\left(G\right)\to \{1,3,\dots ,2m-1\}$, from which an injective transformation is derived, $g^{*}:V\left(G\right)\to \{1,2,3,\dots ,2m-1\}$, from the rule that the image of $u\in V\left(G\right)$ under $g^{*}$ is ${\sum }_{uv\in E\left(G\right)}g\left(uv\right)\mathrm{mod}\left(2m\right)$. The main objective of this manuscript is to introduce new classes of planar graphs, namely water wheel graphs, $W{W}_n$; triangulated water wheel graphs, $T{W}_n$; closed water wheel graphs, $C{W}_n$; and closed triangulated water wheel graphs, $C{T}_n$. Furthermore, we specify conditions for these graphs to allow for edge odd graceful labelings. Full article

Recent technological advancements and evolving regulatory frameworks are catalysing the integration of renewable energy sources in construction equipment, with the objective of significantly reducing greenhouse gas emissions. The electrification of non-road mobile machinery (NRMM), particularly self-propelled Rough-Terrain Variable Reach Trucks (RTVRT) equipped with telescopic booms, presents notable stability challenges. The transition from diesel to electric propulsion systems alters, among other factors, the centre of gravity and the inertial matrix, necessitating precise load capacity determinations through detailed load charts to ensure operational safety. This paper introduces a virtual model constructed through multiphysics modelling utilising the bond graph methodology, incorporating both scalar and vector bonds to facilitate detailed interconnections between mechanical and hydraulic domains. The model encompasses critical components, including the chassis, rear axle, telescopic boom, attachment fork, and wheels, each requiring a comprehensive three-dimensional treatment to accurately resolve spatial dynamics. An illustrative case study, supported by empirical data, demonstrates the model’s capabilities, particularly in calculating ground wheel reaction forces and analysing the hydraulic self-levelling behaviour of the attachment fork. Notably, discrepancies within a 10% range are deemed acceptable, reflecting the inherent variability of field operating conditions. Experimental analyses validate the BG-3D simulation model of the telehandler implemented in 20-SIM establishing it as an effective tool for estimating stability limits with satisfactory precision and for predicting dynamic behaviour across diverse operating conditions. Additionally, the paper discusses prospective enhancements to the model, such as the integration of the virtual vehicle model with a variable inclination platform in future research phases, aimed at evaluating both longitudinal and lateral stability in accordance with ISO 22915 standards, promoting operator safety. Full article

The crossing number $\mathrm{cr}\left(G\right)$ of a graph G is the minimum number of edge crossings over all drawings of G in the plane. The main aim of this paper is to give the crossing numbers of the join products $G^{*}+P_n$ and $G^{*}+C_n$ for the connected graph $G^{*}$ obtained by removing one edge (incident with the dominating vertex) from the wheel $W_5$ on six vertices, and where $P_n$ and $C_n$ are paths and cycles on n vertices, respectively. Finally, we also introduce four new conjectures concerning crossing numbers of the join products of $P_n$ and $C_n$ with $W_m\setminus e$ obtained by removing one edge (of both possible types) from the wheel $W_m$ on $m+1$ vertices. Full article

The presence of contaminants influences braking efficiency in the railway system because it alters the adhesion at the wheel–rail interface. It is essential to study this phenomenon, as contaminants reduce the friction between wheels and rails, which impacts braking and transport safety. In addition, these contaminants increase the risk of derailments. The objective of the research was to determine the impact of different contaminants and operating speeds on the critical braking system’s responses. Using the 3^k full factorial experimental design methodology, with analysis of variance (ANOVA) and linear and quadratic regressions, visualized using surface graphs, the effects of three operating conditions were studied: clean rails, with sand and sawdust, and driving the train at three operating speeds. These conditions gave rise to variations in braking distances, maximum creep, wheel slip times, and maximum peaks of electric current when braking in each experiment. The tests were carried out on the straight section of a β-shaped track and a railway vehicle, designed at a scale of 1:20. The analysis reveals that the braking distance increases significantly with surface roughness (clean track < sawdust < sand). At 0.75 m/s, the sawdust track reduces braking distance by 21% compared with the clean track; at 1.00 m/s, the reduction is 19%; and at 1.30 m/s, it is 35%. Full article

Graph theory is a crucial branch of mathematics in fields like network analysis, molecular chemistry, and computer science, where it models complex relationships and structures. Many indices are used to capture the specific nuances in these structures. In this paper, we propose a new index, the weighted asymmetry index, a graph-theoretic metric quantifying the asymmetry in a network using the distances of the vertices connected by an edge. This index measures how uneven the distances from each vertex to the rest of the graph are when considering the contribution of each edge. We show how the index can capture the intrinsic asymmetries in diverse networks and is an important tool for applications in network analysis, optimization problems, social networks, chemical graph theory, and modeling complex systems. We first identify its extreme values and describe the corresponding extremal trees. We also give explicit formulas for the weighted asymmetry index for path, star, complete bipartite, complete tripartite, generalized star, and wheel graphs. At the end, we propose some open problems. Full article