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The purpose of this paper is to develop two types of simple jerk circuits and to carry out their dynamical analyses using a unified mathematical model.

Two types of simple jerk circuits only involve a nonlinear resistive feedback channel composited by a nonlinear device and an inverter. The nonlinear device is implemented through parallelly connecting two diode-switch-based series branches. According to the classifications of switch states and circuit types, a unified mathematical model is established for these two types of simple jerk circuits, and the origin symmetry and scale proportionality along with the origin equilibrium stability are thereby discussed. The coexisting bifurcation behaviors in the two types of simple jerk systems are revealed by bifurcation plots, and the origin symmetry and scale proportionality are effectively demonstrated by phase plots and attraction basins. Moreover, hardware experimental measurements are performed, from which the captured results well validate the numerical simulations.

Two types of simple jerk circuits are unified through parallelly connecting two diode-switch-based series branches and a unified mathematical model with six kinds of nonlinearities is established. Especially, the origin symmetry and scale proportionality for the two types of simple jerk systems are discussed quantitatively. These jerk circuits are all simple and inexpensive, easy to be physically implemented, which are helpful to explore chaos-based engineering applications.

Unlike previous works, the significant values are that through unifying these two types of simple jerk systems, a unified mathematical model with six kinds of nonlinearities is established, upon which symmetrically scaled coexisting behaviors are numerically disclosed and experimentally demonstrated.

The nonlinear jerk equation is a third-order nonlinear equation that describes some physical phenomena and in general form is given by: x = J (x, x, x). The purpose of this paper is to employ the modified (MDTM) differential transform method (DTM) to obtain approximate periodic solutions of two cases of nonlinear jerk equation.

The approach is based on MDTM that is developed by combining DTM, Laplace transform and Padé approximant.

Comparison of results obtained by MDTM with those obtained by numerical solutions indicates the excellent accuracy of solution.

The MDTM is extended to determining approximate periodic solution of third-order nonlinear differential equations.

The purpose of this paper is to analyze the impact of the torque, power, jerk and energy consumed constraints on the generation of minimum time collision‐free trajectories for industrial robots in a complex environment.

An algorithm is presented in which the trajectory is generated under real working constraints (specifically torque, power, jerk and energy consumed). It also takes into account the presence of obstacles (to avoid collisions) and the dynamics of the robotic system. The method solves an optimization problem to find the minimum time trajectory to perform the tasks the robot should do.

Important conclusions have been reached when solving the trajectory planning problem related to the value of the torque, power, jerk and energy consumed and the relationship between them, therefore enabling the user to choose the most efficient way of working depending on which parameter he is most interested in optimizing. From the examples solved the authors have found the relationship between the maximum and minimum values of the parameters studied.

This new approach tries to model the real behaviour of the actuators in order to be able to upgrade the trajectory quality, so a lot of work has to be done in this field.

The algorithm solves the trajectory planning problem for any industrial robot and the real characteristics of the actuators are taken into account, which is essential to improve the performance of it.

This new tool enables the performance of the robot to be improved by combining adequately the values of the mentioned parameters (torque, power, jerk and consumed energy).

The purpose of this paper is to propose a new acceleration/deceleration (acc/dec) algorithm for motion profiles. The motion efficiency, flexibility of the motion profiles and the residual vibration of the movement are discussed in this paper.

A dynamics model is developed to assess the residual vibration of these two kinds of motion profile. And a Simulink model is created to assess the motion efficiency and flexibility of the motion profiles with the proposed acc/dec algorithm.

Considering the flexibility of trigonometric motion profiles and the higher motion efficiency of S-curve motion profiles, the authors add the polynomial parts into the jerk profile of the cosine function acc/dec algorithm to hold the jerk when it reaches the maximum so that the motion efficiency can increase and decrease residual vibration at the same time. And the cyclical parameter k shows the decisive factor for the flexibility of trigonometric motion profiles.

Comparing with the traditional motion profiles, the proposed motion profiles have higher motion efficiency and excite less residual vibration. The acc/dec algorithm proposed in this paper is useful for the present motion control and servo system.

The purpose of this paper is to present, an optimization problem based on the imperialistic competitive algorithm (ICA) approach for optimizing the needle velocity and variation of needle acceleration in a link drive mechanism of a sewing machine. The optimal geometry of the link drive has been achieved using a non-linear optimization procedure.

As an important study in this case, the authors might refer to a previous work in which they introduced the possibility of replacing the slider-crank mechanism, that is typically used in sewing machines, with a link drive mechanism. The authors regenerate the optimization problem by modifying the objective function and follow a novel optimization method based on the ICA to overcome the drawbacks of that work. In addition, further modification of the objective function with respect to the variation of needle acceleration is applied to assure smooth movement of the needle during sewing process.

The results showed a significant improvement with respect to the optimization of needle velocity and variation of needle acceleration in comparison to that previous work. This clearly justifies the efficiency and reliability of the optimization formulation based on the ICA approach.

Needle temperature is considered as an effective parameter on sewing process efficiency and stitch quality. Needle heat generated during sewing process is directly related to needle velocity in penetration zone which in turn depends on the needle driver mechanism of sewing machine. According to literature survey, few researches have focussed to design a driver mechanism of the sewing machine to reduce the generated needle heat. This mechanism has the ability of reducing the penetration velocity of the needle without affecting sewing speed which consequently can reduce the needle heat generated during needle penetration. The work here is novel regarding implementation of optimization algorithm for this mechanism.

This paper aims to present a technique for optimal trajectory planning of industrial robots that applies a new harmony search (HS) algorithm.

The new HS optimization algorithm adds one more operation to the original HS algorithm. The objective function to be minimized is the trajectory execution time subject to kinematical and mechanical constraints. The trajectory is built by quintic B‐spline curves and cubic B‐spline curves.

Simulation experiments have been undertaken using a 6‐DOF robot QH165. The results show that the proposed technique is valid and that the trajectory obtained using quintic B‐spline curves is smoother than the trajectory using cubic B‐spline curves.

The proposed new HS algorithm is more efficient than the sequential quadratic programming method (SQP) and the original HS method. The proposed technique is applicable to any industrial robot and yields smooth and time‐optimal trajectories.

The glass substrate transfer robot uses flexible arm and fork to transport the glass substrate which will generate vibration. To reduce the settling time and increase productivity, the authors proposed a vibration suppression method that integrated the continuous input shaping into the S-curve feedrate profiling.

The quasi-optimal S-curve feedrate profiling is achieved by the robot model. Then the outputs of the S-curve are shaped by the continuous input shaper, which can greatly lower the vibration and shorten the settling time.

The robot produces vibrations because of the flexibility of the belt system and the forks; the vibration of the robot is especially obvious in the acceleration and deceleration stage and the low-speed operation stage. Because the fork fingers are flexible, vibration at the end of the fork is enlarged.

The effectiveness of the proposed method is verified by the comparative experiments conducted on a glass substrate transfer robot.

This paper aims to show that the variational iteration method (VIM) and the homotopy perturbation method (HPM) are powerful and suitable methods to solve the Fornberg‐Whitham equation.

Using HPM the explicit exact solution is calculated in the form of a quickly convergent series with easily computable components. Also, by using VIM the analytical results of this equation have been obtained in terms of convergent series with easily computable components.

Numerical solutions obtained by these methods are compared with the exact solutions, revealing that the obtained solutions are of high accuracy.

Also the results show that the introduced methods are efficient tools for solving the nonlinear partial differential equations.

Rosenau‐Hyman equation was discovered as a simplified model to study the role of nonlinear dispersion on pattern formation in liquid drops. Also, this equation has important roles in the modelling of various problems in physics and engineering. The purpose of this paper is to present the solution of Rosenau‐Hyman equation.

This paper aims to present the solution of the Rosenau‐Hyman equation by means of semi‐analytical approaches which are based on the homotopy perturbation method (HPM), variational iteration method (VIM) and Adomian decomposition method (ADM).

These techniques reduce the volume of calculations by not requiring discretization of the variables, linearization or small perturbations. Numerical solutions obtained by these methods are compared with the exact solutions, revealing that the obtained solutions are of high accuracy. These results reveal that the proposed methods are very effective and simple to perform.

Efficient techniques are developed to find the solution of an important equation.

An iteration technique has been developed based on the Mickens iteration method to obtain approximate angular frequencies. This technique also offers the periodic solutions to the nonlinear free vibration of a conservative, coupled mass–spring system having linear and nonlinear stiffnesses with cubic nonlinearity. Two real-world cases of these systems are analysed and introduced.

In this paper, the truncated terms of the Fourier series have been used and utilized in every step of the iteration.

The obtained results are valid for whole ranges of vibration amplitude of the oscillations. The approximated results are compared with existing and corresponding numerical (considered to be exact) results which show excellent agreement. The error analysis has been carried out and shown acceptable results for the proposed iteration technique.

Effectiveness of the proposed iteration technique is found in comparison with other existing methods. The method is demonstrated by examples.