In this paper, the graph models of planar frame structures with different symmetries are decomposed and appropriate processes are designed for their healing in order to form the corresponding factors. The eigenvalues and eigenvectors of the entire structure are then obtained by evaluating those of its factors. The methods developed in this article simplify calculation of the natural frequencies and natural modes of the planar frames with different types of symmetry.

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In this paper, a simple method for the discretization of planar continuous current sources is presented. First, the planar current distribution is determined by the Fourier and Inverse Hankel Transforms. Then it is discretized for the design of a planar array. The radiation pattern of the array of discrete elements will be quite different from that of the planar continuous current source. Therefore, for the improvement of its radiation characteristics, such as side-lobe level and ripple in the pattern, the iterative method of least squares is used. The desired radiation characteristics of the array, such as​ ​ the side-lobe level and ripple of pattern, are achieved by an iterative algorithm of the method of least squares together with the array element excitations. Indeed, first, in each iteration, in order to properly adjust the radiation pattern, the values of radiation pattern at the maximum points of the side-lobes and at the maximum and minimum points of the main-lobe, are replaced with the desired values. Then, by sampling of the adjusted radiation pattern, a linear equation system is obtained which by solving this linear equation system by using the method of least squares, the excitation currents of array elements are determined. The proposed method can be used to optimize any array with arbitrary configuration. Several examples of simulations have been presented to verify the efficacy of the proposed method.

The Recent development of 2-DOF electrical machines leads to increasing need for 2-DOF position sensors. Using a planar sensor instead of two linear ones decreases the complexity, and cost of the employed drive. Therefore, in this paper a new slotless configuration is proposed for the planar resolver, that simplifies the manufacturing of the sensor. Then, the optimal combination of the stator/mover number of coils is determined based on the proposed analytical model. Finally, to reduce the number of integrated parts of the proposed resolver, a new configuration with skewed coils is proposed. The success of the developed model and the presented configuration is validated using three-dimensional finite element analysis.

The Recent development of 2-DOF electrical machines leads to increasing need for 2-DOF position sensors. Using a planar sensor instead of two linear ones decreases the complexity, and cost of the employed drive. Therefore, in this paper a new slotless configuration is proposed for the planar resolver, that simplifies the manufacturing of the sensor. Then, the optimal combination of the stator/mover number of coils is determined based on the proposed analytical model. Finally, to reduce the number of integrated parts of the proposed resolver, a new configuration with skewed coils is proposed. The success of the developed model and the presented configuration is validated using three-dimensional finite element analysis.

Decoupling of dynamic equations in robotic mechanisms has attracted many researchers in the recent years. This kind of decoupling can be achieved by modifying the original kinematic structure through the use of counterweights attached to the moving links. Therefore, the robotic control becomes easier due to reducing the coupling disturbances. In this paper, different methods of decoupling including the static balancing, Coriolis and centripetal force eliminating and dynamic balancing are introduced and their concepts are described based on Lagrange-Euler equations. The systematic adaptive approach is proposed for any open-chain planar robots whose links are connected by revolute joints. The method is tested for two-link and three-link manipulator. The results indicate that the system is fully-decoupled and simple classical approach is sufficient to control it.