• Korean Journal of Computational Design and Engineering
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• v.14 no.1
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• pp.18-24
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• 2009

This paper proposes an analytical method of evaluating the maximum error by modeling the exact tool path for the tool traverse singular region in five-axis machining. It is known that the NC data from the inverse kinematics transformation of 5-axis machining can generate singular positions where incoherent movements of the rotary axes can appear. These lead to unexpected errors and abrupt operations, resulting in scoring on the machined surface. To resolve this problem, previous methods have calculated several tool positions during a singular operation, using inverse kinematics equations to predict tool trajectory and approximate the maximum error. This type of numerical approach, configuring the tool trajectory, requires much computation time to obtain a sufficient number of tool positions in a region. We have derived an analytical equation for the tool trajectory in a singular area by modeling the tool operation into a linear and a nonlinear part that is a general form of the tool trajectory in the singular area and that is suitable for all types of five-axis machine tools. In addition, we have evaluated the maximum tool-path error exactly, using our analytical model. Our algorithm can be used to modify NC data, making the operation smoother and bringing any errors to within tolerance.

• International Journal of Control, Automation, and Systems
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• v.5 no.1
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• pp.86-92
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• 2007

In this paper, we first establish $D_L$-admissibility and $D_R$-admissibility conditions for singular systems. The admissibility conditions expressed as Lyapunov type inequalities extend the existed results of normal systems to singular systems. As special cases the admissibility conditions of the continuous-time and the discrete-time singular systems can be obtained directly. The results established in this paper can be applied to solve the problems of eigenvalue assignment, regional pole-placement and robust control etc.

• The Journal of Korea Robotics Society
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• v.4 no.2
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• pp.88-96
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• 2009

In this paper, we present a linear controller for attitude of aircraft. We use a rotational matrix in one approach and a quaternion in the other approach. We also find some interesting mathematical properties concerning a symmetric rotational matrix and we use these properties to analyze the stability of the proposed control law. We find that the quaternion approach is better than rotational matrix approach because there exists no singular region problem in quaternion approach. On the other hand, singular region problem may happens in rotational matrix approach. The controller structure of the quaternion is also very simple compared with the one proposed by using a rotational matrix approach. We make use Matlab Simulink to simulate and illustrate the theoretical claims. The graphic animation program is developed based on Open-GL for the computer simulation of the proposed control algorithm.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.11 no.5
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• pp.997-1003
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• 2007

In this paper, we propose a global approach for automatic inspection of defects in the polarizer film image. The proposed method does not rely on local feature of the defect. It is based on a global image reconstruction scheme using the singular value decomposition(SVD). SVD is used to decompose the image and then obtain a diagonal matrix of the singular values. Among the singular values, the first singular value is used to reconstruct a image. In reconstructed image, the normal pixels in background region have a different characteristics from the pixels in defect region. It is obtained the ratio of pixels in the reconstructed image to ones in the original image and then the defects are detected based on the the statistical process of the ratio. The experiment results show that the proposed method is efficient for defect inspection of polarizer lam image.

• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.937-948
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• 2011

The method of Asymptotic Inner Boundary Condition for Singularly Perturbed Two-Point Boundary value Problems is presented. By using a terminal point, the original second order problem is divided in to two problems namely inner region and outer region problems. The original problem is replaced by an asymptotically equivalent first order problem and using the stretching transformation, the asymptotic inner condition in implicit form at the terminal point is determined from the reduced equation of the original second order problem. The modified inner region problem, using the transformation with implicit boundary conditions is solved and produces a condition for the outer region problem. We used Chawla's fourth order method to solve both the inner and outer region problems. The proposed method is iterative on the terminal point. Some numerical examples are solved to demonstrate the applicability of the method.

• Structural Engineering and Mechanics
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• v.44 no.4
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• pp.487-499
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• 2012

Dynamic instability of beams subjected to periodic axial forces is studied using the discrete singular convolution (DSC) method with the regularized Shannon's delta kernel. The principal regions of dynamic instability under different boundary conditions are examined in detail, and the non-stationary vibrations near the stability-instability critical regions have been investigated. It is found that the results obtained by using the DSC method are consistent with the analytical solutions, which shows that the DSC algorithm is suitable for the problems considered in this study. It was found that there is a narrow region of beat vibration existed in the vicinity of one side (${\theta}/{\Omega}$ > 1) of the boundaries of the instable region for each condition.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.11 no.2
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• pp.49-57
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• 2007

In fingerprints, singular regions including core or delta points have different directional characteristics from non-singular regions. Generally, the ridges of singular regions change more abruptly than those of nonsingular areas, thus in order to effectively enhance fingerprint images regardless of region, local ridge curvature information needs to be used. In this paper, we present an improved Directional Filter Bank (DFB)-based fingerprint image enhancement method that effectively takes advantage of such ridge curvature information. The proposed method first decomposes a fingerprint image into 8 directional subbands using the DFB and then classifies the image into background, low curvature, and high curvature regions using the directional energy estimates calculated from the subbands. Thereafter, the weight values for directional subband processing are determined using classification information and directional energy estimates. Finally, the enhanced image is obtained by synthesizing the processed subbands. The experimental results show that the proposed approach is effective in enhancing both singular and non-singular regions.

• Bulletin of the Korean Chemical Society
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• v.14 no.1
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• pp.95-100
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• 1993

A noise-induced transition is presented for a bistable system subjected to a multiplicative random force, which is singular at the unstable state. The stationary probability distribution is obtained from the Fokker-Planck equation and the effects of the singularity is analyzed. On the basis of noise-induced phase transition with Gaussian white noise, the relaxation time and the transition rate of the system are evaluated up to the first order correction of D. In the parameter region v < l, the transition rates decrease as the exponent v goes to 1 and as the coefficient of the linear term of the kinetic equation increases.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.39 no.6
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• pp.631-637
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• 1990

It is well-known that the redundancy can be exploited to avoid the singular regions of the redundant manipulators by increasing the manipulability. The method, however, requires excessive energy and gives rather large tracking errors since the manipulability is increased rapidly so that the manipulator avoids the singular region quickly. In this paper, a new method is proposed in which the increasing speed of the manipulability is confined to a certain bound. Therefore, in the proposed method, the movement energy and the tracking errors are reduced. The computer simulation studies are performed to show the validity of the method.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.14 no.3
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• pp.381-390
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• 2001

In this paper, a new improved crack analysis technique by Element-Free Galerkin(EFG) method is proposed, in which the singularity and the discontinuity of the crack successfully described by adding enrichment terms containing a singular basis function to the standard EFG approximation and a discontinuity function implemented in constructing the shape function across the crack surface. The standard EFG method requires considerable addition of nodes or modification of the model. In addition, the proposed method significantly decreases the size of system of equation compared to the previous enriched EFG method by using localized enrichment region near the crack tip. Numerical example show the improvement and th effectiveness of the previous method.