Atakan Altınkaynak

Classical variational formulations are typically presented for systems of constant total mass, which can obscure how to treat problems where a convenient subsystem gains or loses mass. We consider a guided ``falling chain'' variant in which a uniform chain of length L interacts with a horizontal disc rotating at constant angular speed ω. A single generalized coordinate r(t) describes the chain length on the disc while the remaining length L-r(t) hangs vertically. We derive the same equation of motion using fixed-mass Lagrangian, D’Alembert, variable-mass and Lagrange-multiplier formulations, thus comparing energy-based, force-based, subsystem-based and constraint-based viewpoints within a single problem. A compact nondimensional form shows that the dynamics depends on a single parameter β = ω2L/(2g), yields a closed-form equilibrium relation for the on-disc fraction, and allows a simple local analysis showing that this equilibrium is linearly unstable in the present idealized model. The example is intended as a short worked comparison problem for advanced analytical mechanics teaching, illustrating how subsystem choice, generalized forces, constraint reactions, and interface momentum flux must be handled in order for fixed-mass and variable-mass descriptions to remain consistent.

This brief note addresses a common confusion in continuum mechanics, particularly in axially moving beams, strings and plates, where certain terms arising from the material derivative are mistakenly labeled as “Coriolis acceleration” due to their mathematical similarity to the Coriolis expression. We clarify this misinterpretation using definitions of Coriolis, convective and gyroscopic terms, and show that these terms are not Coriolis accelerations when viewed in fixed reference frames. In addition, we briefly comment on the meaning of the Coriolis inertial force whether it performs mechanical work and how such mislabeling affects teaching, computational modeling and the interpretation of vibration problems.

This paper optimizes the geometry of a novel Delta mechanism via origami-inspired fabrication. The aim is to maximize workspace volume without increasing the mechanism’s footprint. Optimize the geometry to increase the limitation of the mechanism and experimentally test the optimized mechanism and compare the results with the original one. The Delta mechanism’s novelty altered fabrication and design parameters. A genetic algorithm, a common optimization method, was applied. Finite element analysis examined the impact of elastic joints. Experiments compared the kinematic model’s workspace trajectory between optimized and initial mechanisms. The paper reports a 35% increase in workspace volume over the initial mechanism while maintaining a constant footprint size. The optimized mechanism achieves sub-0.5 mm root mean square (RMS) accuracy in the X , Y , and Z directions, ensuring precise positioning within the calculated workspace using rigid kinematics. Despite the expanded workspace, the accuracy of reaching boundary points remains nearly constant compared to the initial model. This study covers only a specific type of parallel mechanism fabricated by the origami-inspired method. Therefore, researchers are encouraged to test and optimize different mechanisms with higher degree of freedom further. The paper discusses implications for advancing flexible mechanisms especially origami-inspired mechanisms, a widely studied type in recent research. Employing optimization techniques can enhance accuracy, reliability, and cost-effectiveness in the fabrication process for other types of mechanisms. This paper addresses the acknowledged requirement to delve into origami-inspired mechanisms, featuring distinctive design parameters and fabrication methods when compared to conventional mechanisms. The significance of this inquiry is heightened by the existing dearth of design optimization in flexible parallel mechanisms.

Complex numbers and complex functions are frequently utilized in solving equations of motion in free and harmonic responses of vibration systems. However, certain fundamental details are sometimes overlooked and many books and articles may present differential equations with inconsistencies, which can confuse meticulous readers. This confusion often arises because one side of the equations is in real form, while the other side is expressed in complex form. To address this issue, the present article offers examples from literature to highlight the perplexing situation and provides a didactic methodology, aimed at enhancing clarity and ensuring that readers are left with a thorough understanding of the subject matter.

Bu çalışmada, ağsız yöntemler için radyal özelliğe sahip yeni bir temel fonksiyon önerilmiştir. Önerilen fonksiyon, iki boyutta, dört farklı problemde, ağsız yöntemlerde sıklıkla kullanılan Ters Multikuadrik ve Gauss fonksiyonlarıyla birlikte test edilmiştir. Test problemlerinin üç tanesi 2. mertebeden mühendislik problemlerini içerirken son test problemi 4. mertebeden bir mühendislik problemi uygulaması olmuştur. 2. mertebeden test problemlerinde farklı sınır koşulları ve problem türleri incelenmiştir. Yapılan sayısal deneyler, önerilen fonksiyonun Ters Multikuadrik ve Gauss fonksiyonlarına kıyasla daha az nokta sayılarında benzer mertebedeki hatalara ulaşabildiğini göstermiştir. Ayrıca nokta sayısının artmasıyla aynı mertebedeki hatalar için kullanılabilecek şekil/ölçek parametresinin (epsilon) diğer iki fonksiyona kıyasla daha geniş bir aralıkta seçilebildiği gösterilmiştir. Dolayısıyla, önerilen fonksiyon, ağsız yöntem uygulamalarında bir alternatif olarak kullanılabilecektir.