—This paper studies the control motion of a single link flexible joint robot by using a hierarchical non-singular terminal sliding mode controller (HNTSMC). In comparison to the conventional sliding mode controller (CSMC), the proposed algorithm (NTSMC) not only can conserve characteristics of the convention CSMC, such as easy implementation, guaranteed stability and good robustness against system uncertainties and external disturbances, but also can ensure a faster convergence rate of the systems states to zero in a finite time and singularity free. The flexible joint robot (FJR) is a two degree of freedom (2DOF) nonlinear and underactuated system. The system here is modeled as a fourth order system by using Lagrangian method. Based on t

Background/Aim: Knee osteoarthritis is a frequently crippling chronic condition. Numerous pharmacological medications have been successfully utilised to treat knee osteoarthritis. This research aimed to compare the efficiency of metformin and serratiopeptidase in treating and preventing osteoarthritis development via distinct mechanisms. Methods: Between 1 January and 30 May 2019, a randomised-clinical-trial was done at Al-Kindy Hospital on 80 osteoarthritis patients, divided in two groups. Group I was given metformin 850 mg orally, whereas Group II was given serratiopeptidase 20 mg and metformin 850 mg orally. Parameters in these groups were compared with forty healthy normal controls. Results: Following treatment, patients in Grou

The current study executes a fully coupled thermomechanical simulation of friction stir welding (FSW) process of aluminum 6061-T6 alloy T-joint type using finite element method. The analysis simulation accounts for the three steps of the FSW process which includes: plunging, dwelling, and moving stages. The temperature history, associated stresses and strains generated through the FSW phases, tool reaction force, and time-dependence of the energy dissipation were evaluated. To overcome the shortcomings of purely Lagrangian and Eulerian descriptions, Arbitrary Lagrangian Eulerian (ALE) formulation, adaptive meshing, and the mass scaling were used as techniques to improve sequence modeling of the friction stir welding process. Coulomb’s fri

In this paper, a single link flexible joint robot is used to evaluate a tracking trajectory control and vibration reduction by a super-twisting integral sliding mode (ST-ISMC). Normally, the system with joint flexibility has inevitably some uncertainties and external disturbances. In conventional sliding mode control, the robustness property is not guaranteed during the reaching phase. This disadvantage is addressed by applying ISMC that eliminates a reaching phase to ensure the robustness from the beginning of a process. To design this controller, the linear quadratic regulator (LQR) controller is first designed as the nominal control to decide a desired performance for both tracking and vibration responses. Subsequently, discontinuous con

Nonlinear differential equation stability is a very important feature of applied mathematics, as it has a wide variety of applications in both practical and physical life problems. The major object of the manuscript is to discuss and apply several techniques using modify the Krasovskii's method and the modify variable gradient method which are used to check the stability for some kinds of linear or nonlinear differential equations. Lyapunov function is constructed using the variable gradient method and Krasovskii’s method to estimate the stability of nonlinear systems. If the function of Lyapunov is positive, it implies that the nonlinear system is asymptotically stable. For the nonlinear systems, stability is still difficult even though

In this paper, the construction of Hermite wavelets functions and their operational matrix of integration is presented. The Hermite wavelets method is applied to solve nth order Volterra integro diferential equations (VIDE) by expanding the unknown functions, as series in terms of Hermite wavelets with unknown coefficients. Finally, two examples are given

In this paper, a new analytical method is introduced to find the general solution of linear partial differential equations. In this method, each Laplace transform (LT) and Sumudu transform (ST) is used independently along with canonical coordinates. The strength of this method is that it is easy to implement and does not require initial conditions.

This paper deals with the thirteenth order differential equations linear and nonlinear in boundary value problems by using the Modified Adomian Decomposition Method (MADM), the analytical results of the equations have been obtained in terms of convergent series with easily computable components. Two numerical examples results show that this method is a promising and powerful tool for solving this problems.