• Title/Summary/Keyword: saddle points

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Development of An User-Friendly Integrated Program and Teaching System for Automatic Polishing Robot System (자동 연마 시스템의 사용자 지향형 통합 프로그램 및 자동 교시 시스템 개발)

  • Go, Seok-Jo;Lee, Min-Cheol;Lee, Man-Hyeong;An, Jung-Hwan;Jeon, Cha-Su;Lee, Don-Jin
    • Journal of Institute of Control, Robotics and Systems
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    • v.7 no.4
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    • pp.334-343
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    • 2001
  • Polishing a die that has free-form surfaces is a time-consuming and tedious job, and requires a considerable amount of high-precision skill. Some workers tend to gradually avoid the polishing work because of the poor environment caused by dust and noise. In order to reduce the polishing time and cope with the shortage of skilled workers, a user-friendly automatic polishing system was developed in this research. The polishing system with five degrees of freedom is able to keep the polishing tool normal to the die surface. The polishing system is controlled by a PC-NC controller. To easily operate the developed polishing robot system, this study developed an integrated program in the Windows environment. This program consists of four modules: the polishing module, the graphic simulator, the polishing data generation module, and the teaching module. Also, the automatic teaching system was developed to easily obtain teaching data and it consists of a three dimensional joystick and a proximity sensor. The joystick is used to simultaneously drive the polishing system to an arbitrary orientation and the proximity sensor is used to obtain teaching points precisely. Also, to evaluate the stability of the driving program and the teaching system, polishing experiments of a die of saddle shape were carried out.

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Optimization of Cultivational Conditions of Rice(Oryza sativa L.) by a Central Composite Design Applied to an Early Cultivar in Southern Region (중심합성계획법에 의한 남부 조생벼 재배요인의 최적조건 구명)

  • Shon, Gil-Man;Kim, Jeung-Kyo;Choe, Zhin-Ryong;Lee, Yu-Sik;Park, Joong-Yang
    • KOREAN JOURNAL OF CROP SCIENCE
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    • v.34 no.1
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    • pp.60-73
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    • 1989
  • Two field experiments were carried out to assess the applicability of a central composite design (CCD) in determining optimum culture condition of an early rice cultivar, Unbongbyeo in southern Korea. A central composite design with two replicates was applied to five levels of five factors such as the number of hills per 3.3m2, the number of seedlings per hill, the levels of nitrogen, the transplanting date and the seedling age (Experiment 1). The levels of planting density were ranged from 30 hills to 150 hills per 3.3m2 ; the number of seedlings per hill from 1 seedling to 9 seedlings per hill; the levels of nitrogen application from 1 kg/l0a to 21 kg/l0a; the transplanting date from June 15 to July 5; the seedling age from 25 days to 45 days. A fractional factorial design was applied to three levels of five factors tested in CCD (Experiment 2). Yield per hill and per unit area were examined and the results obtained from both experiments were compared. The benefits from the central composite design were discussed. Maximum yield of brown rice per unit area was obtained at the combination of the central levels of one of five factors when the other four factors were fixed at central point. Furthermore, brown rice yield per unit area affected by interaction of two factors was maximized at the central point when the remain three factors being fixed at the central level. The responses of five factors to brown rice yield per hill and unit area were found to be a saddle point in both designs. Actual values of the stationary points were 107 hills per 3.3 m2, 4 seedlings per hill, 10 kg nitrogen per l0a, transplanting date of rice on June 26 and 33 days of seedling age in the central composite design. Brown rice yield per unit area at the stationary points were estimated 439 kg/l0a in the central composite design and 442 kg/l0a in the fractional factorial design. Considering the number of experimental treatment combinations, the central composite design was rather convenient in reducing the number of treatment combinations for similar information. It was more convenient for an experimenter to present the results from the central composite design than those from the fractional factorial design. Considering the optimum yields of brown rice per unit area at the stationary points being verified as saddle points in both designs. inter-heterogeneity of each of the factors should be avoided in setting up factors in pursuit of inducing unidirectional response of the factors to yield. Even though both the lower and higher levels in the central composite design being beyond the region of an experimenter's interest. they were considered highly valued in interpretation of the results. Conclusively. the central composite design was found to be more beneficial to optimize culture condition of paddy rice even with several levels of various factors were involved.

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A FINITE ELEMENT ANALYSIS ON THE 3-UNIT FIXED PROSTHESIS SUPPORTED WITH A NATURAL TOOTH AND ANGLE VARIABLE IMPLANT (고정성 보철치료에서 골유착성 임프란트의 경사도변화에 따른 변위와 응력에 관한 유한요소적 연구)

  • Ko Hyun;Woo Yi-Hyung;Park Nam-Soo
    • The Journal of Korean Academy of Prosthodontics
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    • v.31 no.4
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    • pp.580-610
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    • 1993
  • The purpose of this study was to analyse the deflection and stress distribution at the supporting bone and it's superstructure by the alteration of angulation between implant and it's implant abutment. For this study, the free-end saddle case of mandibular first and second molar missing would be planned to restore with fixed prosthesis. So the mandibular second premolar was prepared for abutment, and the cylinder type osseointegrated implant was placed at the site of mandibular second molar for abutment. The finite element stress analysis was applied for this study. 13 two-dimensional FEM models were created, a standard model at $0^{\circ}$ and 12 models created by changing the angulation between implant and implant abutment as increasing the angulation mesially and distally with $5^{\circ}$ unittill $30^{\circ}$. The preprocessing decording, solving and postprocessing procedures were done by using FEM analysis software PATRAN and SUN-SPARC2GX. The deflections and von Mises stresses were calculated under concentrated load (load 1) and distributed load(load 2) at the reference points. The results were as follows : 1. Observing at standard model, the amount of total deflection at the distobuccal cusp-tip of pontic under concentrated load was largest of all, and that at the apex of implant was least of all, and the amount of total deflection at the buccal cusp-tip of second premolar under distributed load was largest of all, and that at the apex of implant was least of all. 2. Increasing the angulation mesially or distally, the amounts of total deflection were increased or decreased according to the reference points. But the order according to the amount of total deflection was not changed except apex of second premolar and central fossa of implant abutment under concentrated load during distal inclination. 3. Observing at standard model, the von Mises stress at the distal joint of pontic under concentrated load was largest of all, and that at the apex of implant was least of all. The von Mises stress at the distal margin of second premolar under distributed load was largest of all, and that at the apex of Implant was least of ail. 4. Increasing the angulation of implant mesially, the von Mises stresses at the mesial crest of implant were increased under concentrated load and distributed load, but those were increased remarkably under distributed load and so that at $30^{\circ}$ mesial inclination was largest of all. 5. Increasing the angulation of implant distally, the von Mises stresses at the distal crest of implant were increased remarkably under concentrated load and distributed load, and so those at $30^{\circ}$ distal inclination were largest of all.

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Optimization of the Addition of Garlic in Cheonggukjang using Response Surface Methodology (반응표면분석을 이용한 청국장 제조시 마늘의 첨가조건 최적화)

  • Hwang, Cho-Rong;Sim, Hye-Jin;Kim, Gyeong-Min;Cho, Kye-Man;Kim, Jeong-Hwan;Shin, Jung-Hye
    • Korean journal of food and cookery science
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    • v.29 no.6
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    • pp.661-669
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    • 2013
  • This study was performed to determine the optimal composition of Cheonggukjang added with garlic. The experiment utilized a central composite design (CCD). The evaluation was carried out by means of response surface methodology (RSM), which included 18 experimental points with three independent variables : the content of the garlic (1.3~9.7%, $X_1$), the steaming time of garlic (0~15.1 min, $X_2$), and the fermentation time of Cheonggukjang (48.2~71.8 h, $X_3$). The viscous substance ($Y_1$), acidity ($Y_2$), amino-type nitrogen ($Y_3$), ${\gamma}$-GTP activity ($Y_4$) and ABTS radical scavenging activity ($Y_5$). were assessed in four replicates with five dependent variables. The maximum content of the viscous substance was 13.02% at 6.53% ($X_1$), 6.81 min ($X_2$) and 55.18 h ($X_3$). The acidity was increased when the fermentation time was longer, and the minimum acidity point was 0.50% at 7.75% ($X_1$), 3.42 min ($X_2$) and 58.60 h ($X_3$), respectively. The content of the amino-type nitrogen at the experimental range studied was was 80.58~158.82 mg%, and the stationary point was at saddle point. Using ridge analysis, the maximum point was 156.97 mg% at 6.21% ($X_1$), 14.85 min ($X_2$) and 58.04 h($X_3$). The optimum conditions of ${\gamma}$-GTP activity was 5.73% ($X_1$), 6.99 min ($X_2$) and 57.96 h($X_3$), respectively, at the maximum point was 353.66 mU/mL. The maximum point of ABTS radical scavenging activity was 76.43% at 3.78% ($X_1$), 14.28 min ($X_2$) and 57.99 h($X_3$) at the saddle point, when the garlic steaming time was longer.

Optimization for the Physical Properties of Steamed Foam Cakes Prepared with Single-stage Method by Response Surface Methodology (반응표면 분석법에 의한 단단계법 거품형 찜 케이크의 물리적 특성의 최적화)

  • Kwhak, Sung-Ho;Jang, Myung-Sook
    • Journal of the Korean Society of Food Science and Nutrition
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    • v.34 no.4
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    • pp.557-566
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    • 2005
  • In preparation of steamed foam-cakes, effects of whipping time, amount of wheat flour, and amounts of emulsifier on physical properties of the steamed foam cakes were investigated using RSM (response surface methodology). The three independent variables selected for the RSM experiment were whipping time $(X_1)$, amount of wheat flour $(X_2)$, and amounts of wheat flour $(X_2)$, and concentration of emulsifier $(X_3)$ were set for single-stage mixing, respectively. A rotatable central composite design was used for treatment arrangement. The responses from the product for loaf volume, color values and textural properties were analysed. In the analysis of variance for the foam cakes prepared by single-stage method, significant interactions were observed between independent variables (experimental factors) and physical property like loaf volume (p<0.05); textural properties like hardness, gumminess, and chewiness (p<0.05). Among independent variables, concentration of emulsifier had the most effects on physical properties while whipping time. The ordinary points in surface response showed maximal points with physical property like colorimetric b value while other properties revealed saddle points. The 3-dimensional response surface graphs of the predicted regression models displayed decreasing loaf volumes with increasing whipping times and emulsifier concentrations beyond optimum levels. The optimum conditions for best loaf volume and textural property (hardness, gummimess and chewiness) of the products selected by extracting intersectional areas of the contour maps that commonly overlapped all characteristics were; $11\~13$ min whipping time, $470\~486\;g$ amount of wheat flour, and $19\~20\;g$ emulsifier concentration, in case of single-stage method. The median values extracted from the RSM experimental results for optimum manufacturing conditions for single-stage method, i.e., 12 min whipping time, 478 g amount of wheat flour, and 20 g emulsifier concentration were empirically proven to fit the predicted levels of physical properties from the final foam cakes.

Inspection of the Nuclear Fuel Rod Deformation using an Image Processing (영상처리를 이용한 핵연료봉의 변형 검사)

  • Cho, Jai-Wan;Choi, Young-Soo
    • Journal of the Institute of Electronics Engineers of Korea SP
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    • v.47 no.1
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    • pp.91-96
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    • 2010
  • In this paper, a deformation measurement technology of the nuclear fuel rod is proposed. The deformation measurement system include high definition CCD or CMOS image sensor, lens, semiconductor laser line beam marker, and optical & mechanical accessories. The basic idea of the deformation measurement is to illuminate the outer surface of the fuel rod with collimated laser line beam at an angle of 45 degrees or higher. The relative motion of the fuel rod in the horizontal direction causes the illuminated laser line beam to move vertically along the surface of the fuel rod. The resulting change of laser line beam position in the surface of the fuel rod is imaged as the parabolic beam in the high definition CCD or CMOS image sensor. From the parabolic beam pattern, the ellipse model is extracted. And the slope of the long and the short axis of the ellipse model is found. The crossing point between the saddle point of the parabolic beam and the long & short axis of the ellipse model is taken as the feature of the deformed fuel rod. The vertical offset between feature points before and after fuel rod deformation is calculated. From the experimental results, $50\;{\mu}m$ inspection resolution is acquired using the proposed method, which is three times enhanced than the conventional criterion ($150\;{\mu}m$) of the guide for the inspection of the nuclear fuel rod.

Three body problem in early 20th century (20세기초의 삼체문제에 관해서)

  • Lee, Ho Joong
    • Journal for History of Mathematics
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    • v.25 no.4
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    • pp.53-67
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    • 2012
  • Today, it is necessary to calculate orbits with high accuracy in space flight. The key words of Poincar$\acute{e}$ in celestial mechanics are periodic solutions, invariant integrals, asymptotic solutions, characteristic exponents and the non existence of new single-valued integrals. Poincar$\acute{e}$ define an invariant integral of the system as the form which maintains a constant value at all time $t$, where the integration is taken over the arc of a curve and $Y_i$ are some functions of $x$, and extend 2 dimension and 3 dimension. Eigenvalues are classified as the form of trajectories, as corresponding to nodes, foci, saddle points and center. In periodic solutions, the stability of periodic solutions is dependent on the properties of their characteristic exponents. Poincar$\acute{e}$ called bifurcation that is the possibility of existence of chaotic orbit in planetary motion. Existence of near exceptional trajectories as Hadamard's accounts, says that there are probabilistic orbits. In this context we study the eigenvalue problem in early 20th century in three body problem by analyzing the works of Darwin, Bruns, Gyld$\acute{e}$n, Sundman, Hill, Lyapunov, Birkhoff, Painlev$\acute{e}$ and Hadamard.

Optimization of Soy Sauce Production Conditions with Black Garlic Extract by Response Surface Methodology (반응표면 분석법에 의한 흑마늘 추출물이 첨가된 간장의 제조 조건 설정)

  • Shim, Hye-Jin;Kang, Min-Jung;Kim, Gyeong-Min;Lee, Chang-Kwon;Kim, Jeong-Hwan;Shin, Jung-Hye
    • Korean journal of food and cookery science
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    • v.32 no.3
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    • pp.307-315
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    • 2016
  • Purpose: The central composition design was used to optimize the mixture conditions of black garlic extract. Methods: The response surface methodology (RSM) was carried out from concentration of black garlic extract ($X_1$) and the amount of the black garlic extract ($X_2$) as independent variables, and salts ($Y_1$), reducing sugars ($Y_2$), the content of total phenolic compounds ($Y_3$) and ABTS radical scavenging activity ($Y_4$) as dependent variables. We confirmed the conditions that salinity was minimized and reducing sugar, total phenolic compounds and ABTS radical scavenging activity had maximum values through the response surface analysis. Results: All results had saddle points in originally set up conditions hence, ridge analysis was carried out for narrowing the experimental area. The minimum salt concentration was 16.03% at black garlic extract concentration of $14.84^{\circ}brix$ and contents of 9.26%. Reducing sugar content had maximum of value 7.30 g/mL at $24.58^{\circ}brix$ and contents of 8.08%. Total phenolic compounds contents and ABTS radical scavenging activity had maximum values at black garlic extract concentration of 20.33 and $25.02^{\circ}brix$. The results indicate that addition of black garlic extract contributed to increased reducing sugar, phenolic compounds contents and antioxidant activity of the soy sauce, but the salt concentration was not significantly affected. Conclusion: Based on the results of RSM, the optimum ranges of addition conditions for lowering the salt concentration and, increasing the sensory and functional ability of soy sauce were as follows: black garlic extract concentration of $15-25^{\circ}brix$ and content of 7.8-9.3%.