In this paper, we analyze involutes of pseudo-null curves in Lorentz–Minkowski 3-space. Pseudo-null curves are spacelike curves with null principal normals, and their involutes can be defined analogously as for the Euclidean curves, but they exhibit...
We introduced the concept of involute partner-ruled surfaces, which are formed by the involutes of spacelike curves and additional conditions ensuring the presence of definite surface normals in Minkowski three-space. First, we provided the criteria...
A rectifying curve is a twisted curve with the property that all of its rectifying planes pass through a fixed point. If this point is the origin of the Cartesian coordinate system, then the position vector of the rectifying curve always lies in the...
Recently, extensive research has been done on evolute curves in Minkowski space-time. However, the special characteristics of curves demand advanced level observations that are lacking in existing well-known literature. In this study, a special kind...
In this paper, novel non-involute cylindrical gears are designed based on a curved path of contact. Firstly, a parabolic curve is predesigned as the contact path of novel gears. Then, the tooth profiles of the novel gears are calculated using differe...
Willmore defined embedded surfaces on
In this paper, the quasi-frame and quasi-formulas are introduced in Galilean three-space. In addition, the quasi-Bertrand and the quasi-Mannheim curves are studied. It is proven that the angle between the tangents of two quasi-Bertrand or quasi-Mannh...
A twisted surface is a type of mathematical surface that has a nontrivial topology, meaning that it cannot be smoothly deformed into a flat surface without tearing or cutting. Twisted surfaces are often described as having a twisted or Möbius-li...
Let X be a compact Riemann surface of genus
We propose a new hierarchy of the vector derivative nonlinear Schrödinger equations and consider the simplest multiphase solutions of this hierarchy. The study of the simplest solutions of these equations led to the following results. First, the...
This paper investigates the design methodologies of pure rolling helical gear pumps with various tooth profiles, based on the active design of meshing lines. The transverse active tooth profile of a pure rolling helical gear end face is composed of v...
In this paper, the fixed points of involutions on the moduli space of principal
To meticulously examine the repercussions of nonlinear vibrations on fretting damage within aero-engine involute spline pairs, a dynamic model was constructed rooted in well-established theories and methodologies. MATLAB was engaged to resolve the mo...
In this paper, the authors present the design of a suitable gear transmission with the continuously changing gear ratio in the range from 0.5 through 1.0 to 2.0 and back during one revolution of intermeshing gears, according to demands specified for...
Form grinding is a precision machining method for the modified ZI worms, and the grinding accuracy mainly depends on the dressing accuracy of the grinding wheel’s profile. A mathematical model of the modified involute helicoid of ZI worms is es...
Currently, in nonlinear optics, models associated with various types of the nonlinear Schrödinger equation (scalar (NLS), vector (VNLS), derivative (DNLS)), as well as with higher and mixed equations from the corresponding hierarchies are usually stu...
Lines of curvatures (LoCs) are curves on a surface that are derived from the first and second fundamental forms, and have been used for shaping various types of surface. In this paper, we investigated the LoCs of two types of log aesthetic (LA) surfa...
Helical gears are widely used in powertrain systems. The computerized design of a new type of non-generated external helical gears based on critical control points at the transverse tooth profile is presented. The entire tooth profile is divided into...
In his 1842 lectures on dynamics C.G. Jacobi summarized difficulties with differential equations by saying that the main problem in the integration of differential equations appears in the choice of right variables. Since there is no general rule for...
To solve the design problem of non-circular gears with cusp pitch curves, this paper proposed a new variable-involute and incomplete variable-cycloid composite tooth profile (VIIVC-CTF), deduced the new VIIVC-CTF mathematical model, and constructed t...
In part II of this group of papers, the control of the gait of a biped robot during rectilinear walk was considered. The modeling approach and simulation, using Kane’s method with implementation leveraged by Autolev, a symbolic computational environm...
The tooth flank distortion error occurring during the form-grinding (FG) of an involute helical gear can significantly compromise transmission performance. Conventional research approaches often focus on single-parameter optimization—either the...
A widespread distribution of gas-regulating stations creates challenges in energy recovery during pressure reduction. This study employs a scroll expander as a central mechanism to enhance the efficiency of residual gas pressure recovery, demonstrati...
Traditional involute gear pumps find it difficult to meet the requirements of miniaturization and high performance because of the undercutting, trapped oil, and flow pulsation. To eliminate the phenomenon of trapped oil and reduce flow pulsation in t...
Recently, with policies aimed at strengthening domestic manufacturing and technological innovation, the robotics industry has been growing rapidly, and its applications are expanding across various industrial fields. Accordingly, the importance of hi...
Due to the dense crop residue in the Huang-Huai-Hai region, challenges such as large resistance, increased power consumption, and straw backfilling arise in the process of no-till seeding under the high-speed operations. This paper presents the desig...