The inverse kinematic equation for a robot is very important to the control robot’s motion and position. The solving of this equation is complex for the rigid robot due to the dependency of this equation on the joint configuration and structure of robot link. In light robot arms, where the flexibility exists, the solving of this problem is more complicated than the rigid link robot because the deformation variables (elongation and bending) are present in the forward kinematic equation. The finding of an inverse kinematic equation needs to obtain the relation between the joint angles and both of the end-effector position and deformations variables. In this work, a neural network has been proposed to solve the problem of inverse kinematic equation. To feed the neural network, experimental data were taken from an elastic robot arm for training the network, these data presented by joint angles, deformation variables and end-effector positions. The results of network training showed a good fit between the output results of the neural network and the targets data. In addition, this method for finding the inverse of kinematic equation proved its effectiveness and validation when applying the results of neural network practically in the robot’s operating software for controlling the real light robot’s position.
In this paper, the methods of weighted residuals: Collocation Method (CM), Least Squares Method (LSM) and Galerkin Method (GM) are used to solve the thin film flow (TFF) equation. The weighted residual methods were implemented to get an approximate solution to the TFF equation. The accuracy of the obtained results is checked by calculating the maximum error remainder functions (MER). Moreover, the outcomes were examined in comparison with the 4th-order Runge-Kutta method (RK4) and good agreements have been achieved. All the evaluations have been successfully implemented by using the computer system Mathematica®10.
In this paper, three approximate methods namely the Bernoulli, the Bernstein, and the shifted Legendre polynomials operational matrices are presented to solve two important nonlinear ordinary differential equations that appeared in engineering and applied science. The Riccati and the Darcy-Brinkman-Forchheimer moment equations are solved and the approximate solutions are obtained. The methods are summarized by converting the nonlinear differential equations into a nonlinear system of algebraic equations that is solved using Mathematica®12. The efficiency of these methods was investigated by calculating the root mean square error (RMS) and the maximum error remainder (𝑀𝐸𝑅n) and it was found that the accuracy increases with increasi
... Show MoreIn this paper, we study the growth of solutions of the second order linear complex differential equations insuring that any nontrivial solutions are of infinite order. It is assumed that the coefficients satisfy the extremal condition for Yang’s inequality and the extremal condition for Denjoy’s conjecture. The other condition is that one of the coefficients itself is a solution of the differential equation .
There are many different methods for analysis of two-way reinforced concrete slabs. The most efficient methods depend on using certain factors given in different codes of reinforced concrete design. The other ways of analysis of two-way slabs are the direct design method and the equivalent frame method. But these methods usually need a long time for analysis of the slabs.
In this paper, a new simple method has been developed to analyze the two-way slabs by using simple empirical formulae, and the results of final analysis of some examples have been compared with other different methods given in different codes of practice.
The comparison proof that this simple proposed method gives good results and it can be used in analy
... Show MoreInvestigation regarding queue length dynamics have been explored using various kinds of models including ordinary differential equations (ODEs). ODEs possess the advantageous property of having a continuous-time representation of queue length dynamics, thus its adoption in this article in modelling various scenarios as system of first-order ODEs. Specifically, a multi-server queue is considered and a numerical approach for solving first-order ODEs using MATLAB is adopted to obtain approximate solutions of the resultant models. The results display the dynamics of the queue length in each scenario, thus showing the usefulness of ODEs in analysing the behaviour of queues using system of ODEs.
In this paper, our aim is to study variational formulation and solutions of 2-dimensional integrodifferential equations of fractional order. We will give a summery of representation to the variational formulation of linear nonhomogenous 2-dimensional Volterra integro-differential equations of the second kind with fractional order. An example will be discussed and solved by using the MathCAD software package when it is needed.
This study is considered to be the first on this sector of Tigris River after 2003, to evaluate the effect of Tharthar Arm on the composition and diversity of Copepoda in Tigris River. Six sampling sites were selected; two on the Tharthar Arm and four sites along the Tigris River, one before the confluence as a control site and the others downstream the confluence; thirty-five copepod taxa were recorded, 34 taxa in the Tigris River and 25 taxa in the Tharthar Arm.
The highest density of Copepoda was in site 2 at Tharthar Arm was 265584.2 Ind./m3 lead to an increasing in Copepoda density in Tigris River from 63878.2 Ind./m3 in site 1 before the confluence to 127198.3 Ind./m3 in site 4 immediately downstream the confluence. Also, the me
The research aims to find approximate solutions for two dimensions Fredholm linear integral equation. Using the two-variables of the Bernstein polynomials we find a solution to the approximate linear integral equation of the type two dimensions. Two examples have been discussed in detail.
Purpose To test the effect of strategic Supremacy on strategic success A case study in Thi Qar Governorate, methodology/approach – this is a mandatory entry.
a case study was used and applied to the Department managers of Government of the province of Thi Qar, Research limitations/implications – It is clear that the strategic Supremacy variable is not being used effectively to achieve strategic success.
Practical implications – use strategic supremacy positively to Support for strategic success. implementing and monitoring ignorance of them in how to use thi
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