Corner Curve Research Articles

Determination of Forces and Moments Per Unit Length in Symmetric Exponential FG Plates with a Quasi-Triangular Hole

In this study, the resultant forces and moments acting on infinite symmetric FGPs with a triangular hole subject to uniaxial tensile load were examined via an analytical method using the complex variable approach. The mechanical properties of graded plates are hypothesized to vary throughout the thickness exponentially. The impact of various factors, namely hole orientation, hole aspect ratio as well as the hole corner curve on stress distribution and moment resultants is considered. In order to approve the credibility of the analytical approach, its outcomes are compared to numerical results acquired from ABAQUS finite element modeling. This comparison showed a favorable agreement level among the acquired analytical and numerical outcomes. Based on these results, the mentioned factors entail a considerable effect on the distribution of resultant forces and moments at the proximity of the hole and the load bearing tolerance of functional grated plates with holes may be enhanced by suitable selection of the aforementioned parameters.

Determination of the Effective Parameters for Perforated Functionally Graded Plates with Polygonal Cutout by Analytical Solution

This paper investigates the moments and stress resultants from infinite FG laminates with different polygonal cutouts subject to uniaxial tensile load. The analytical solution used for the calculation of stress resultants and moments is the basis of the complex-variable method and conformal mapping function. The impact of various factors, namely cutout orientation angle, cutout aspect ratio as well as the cutout corner curve on stress distribution and moment resultants is studied. The effect of the aforementioned parameters around triangular, square, pentagonal and hexagonal cutout is analyzed. The mechanical characteristics of the graded plates are hypothesized to vary throughout the thickness exponentially. Finite element numerical solution is employed to examine the results of the present analytical solution. This comparison showed a favorable agreement level among the acquired analytical and numerical outcomes.

Optimization of Corner Blending Curves

The blending or filleting of sharp corners is a common requirement in geometric design applications — motivated by aesthetic, ergonomic, kinematic, or mechanical stress considerations. Corner blending curves are usually required to exhibit a specified order of geometric continuity with the segments they connect, and to satisfy specific constraints on their curvature profiles and the extremum deviation from the original corner. The free parameters of polynomial corner curves of degree ≤6 and continuity up to G3 are exploited to solve a convex optimization problem, that minimizes a weighted sum of dimensionless measures of the mid-point curvature, maximum deviation, and the uniformity of parametric speed. It is found that large mid-point curvature weights result in undesirable bimodal curvature profiles, but emphasizing the parametric speed uniformity typically yields good corner shapes (since the curvature is strongly dependent upon parametric speed variation). A constrained optimization problem, wherein a particular value of the corner curve deviation is specified, is also addressed. Finally, the shape of Pythagorean-hodograph corner curves is compared with that of the optimized “ordinary” polynomial corner curves.

Uyghur Off-line Signature Verification Based on Modified Corner Line Features

A modified corner line features based off-line signature verification method proposed for Uyghur handwritten signature in this paper. The signature images were preprocessed according to the nature of Uyghur signature. Then 3 types of corner line features and modified corner curve features were extracted separately. Experiments were performed using Euclidean distance classifier and non-linear SVM classifier for Uyghur signature samples from 150 genuine signatures, 72 random and skilled forgeries are selected from our Uyghur handwritten signature database. Experiments indicate that the MCLF-48 with training 75 samples has obtained 2.16% of FRR and 2.27% of FAR with none-linear SVM classifier. It was concluded that modified corner line features based verification method can capture the nature of Uyghur signature and its writing style more efficiently.

Yawning Detection Based on Mouth Feature Points Curve Fitting

A yawning detection method which can be used in drivers’ fatigue monitoring is proposed. To adapt to the variance in different mouth shapes and sizes, it based on mouth inner contour corner detection and curve fitting. First, the Harris corner detection algorithm was used to detect inner mouth feature points. Second, we established the open mouths’ mathematical model by curve fitting those points, calculated the degree of mouth openness using the mouth model, and generated the real-time M-curve. Third, the duration of big openness in successive images is divided into levels for further judgment. The validation results show that the method can obtain more precise mouth parameters and distinguish yawn from complex mouth activities. So the method achieves a higher level of accuracy.

Corner Curve Transition Interpolation Algorithm for High Speed Machining of Micro-line Segment

The existing micro-line block interpolation algorithm can not meet the need of high speed machining.Through building the vector model of corner curve transition,the relation between contour machining accuracy,adjacent line segment length and included-angle,transition curve arc length and maximum curvature is given.Based on them,a micro-line segment interpolation algorithm based on corner curve transition is proposed.According to this algorithm,the transition curve parameterized by path distance is used to connect adjacent micro-line segment with continuous curvature.At the same time,the maximum allowable velocity limited by chord error and mechanical property of machine tool is calculated and automatically adjusted.So the machining efficiency can be improved while the machining accuracy and quality ensured.The experimental results show that the proposed algorithm can efficiently improve transition speed and dramatically reduce machining time.It is successfully applied in NC systems of high speed engraving and milling machines.

Fundamental Analysis of a Linear Type Trochoidal Gear (3rd Report)

To realize a positioning with high accuracy for straight-corner slide system, the internal gear type trochoidal corner curve rack system has been developed. This system consists of a straight trochoidal rack, a corner curve rack with internal gear type trochoidal cam tooth, a roller pinion and a linear-corner slide system. Also the tooth profile is generated using trochoidal curve loci. In this report, the motion principle is analyzed using the polar complex vectors analysis which is similar to the linear motion type cam rack. And to eliminate a backlash on the connecting section of a straight rack and a corner rack, the conditions to modify the teeth profile are shown. It is proved that a reduction ratio and a tooth height are limited to keep the non-backlash meshing for the straight-corner slide system. Also the combination of each profile shifting coefficient of the straight rack and the corner curve rack is limited.