• Title/Summary/Keyword: Non-convex Polygon

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A Study on the Irregular Nesting Problem Using Genetic Algorithm and No Fit Polygon Methodology (유전 알고리즘과 No Fit Polygon법을 이용한 임의 형상 부재 최적배치 연구)

  • 유병항;김동준
    • Journal of Ocean Engineering and Technology
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    • v.18 no.2
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    • pp.77-82
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    • 2004
  • The purpose of this study is to develop a nesting algorithm, using a genetic algorithm to optimize nesting order, and modified No Fit Polygon(NFP) methodology to place parts with the order generated from the previous genetic algorithm. Various genetic algorithm techniques, which have thus far been applied to the Travelling Salesman Problem, were tested. The partially mapped crossover method, the inversion method for mutation, the elitist strategy, and the linear scaling method of fitness value were selected to optimize the nesting order. A modified NFP methodology, with improved searching capability for non-convex polygon, was applied repeatedly to the placement of parts according to the order generated from previous genetic algorithm. Modified NFP, combined with the genetic algorithms that have been proven in TSP, were applied to the nesting problem. For two example cases, the combined nesting algorithm, proposed in this study, shows better results than that from previous studies.

THE LOWER BOUND OF THE NUMBER OF NON-OVERLAPPING TRIANGLES

  • Xu, Changqing;Ding, Ren
    • Journal of applied mathematics & informatics
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    • v.11 no.1_2
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    • pp.283-290
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    • 2003
  • Andras Bezdek proved that if a convex n-gon and n points are given, then the points and the sides of the polygon can be renumbered so that at least[${\frac{n}{3}}$] triangles spanned by the ith point and the ith side (i = 1,2,...n) are mutually non-overlapping. In this paper, we show that at least [${\frac{n}{2}}$] mutually non-overlapping triangles can be constructed. This lower bound is best possible.

Development on the Automated Process System for Cold Forging of Non-axisymmetric Parts (비축대칭 제품의 냉간단조 공정설계 시스템 개발)

  • 이봉규;조해용;권혁홍
    • Proceedings of the Korean Society of Precision Engineering Conference
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    • 1997.10a
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    • pp.527-530
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    • 1997
  • An automated process planning system for cold forging of non-axisymmetric parts of comparatively simple shape was developed in this study. Programs for the system have been written with Visual LISP in the AutoCAD using a personal computer and are composed of four main modules such as input module, shape cognition and shape expression module, material diameter determination module and process planning module. The design rules and knowledges for th system are extracted from the plasticity theories. handbook, relevant reference and empirical knowledge of field experts. Generally, in forging, only front view is needed for expression of axisymmetric parts, but non-axisymmetric parts are needed both front view and plane. At the plane, this system cognizes the external shape of non-axisymmetric parts - number of sides of regular polygon and radius of a circle circumscribing the polygon of n sides. At the front view, the system perceives diameter of axisymmetric portions and hight of primitive geometries such as polygon, cylinder, cone, concave, convex, etc.

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A Study on the Automated Process Planning System for Cold Forging of Non-axisymmetric Parts (비축대칭 제품의 냉간단조 공정설계시스템에 관한 연구)

  • Lee, Bong-Gyu;Jo, Hae-Yong;Gwon, Hyeok-Hong
    • Journal of the Korean Society for Precision Engineering
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    • v.19 no.2
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    • pp.195-202
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    • 2002
  • An automated process planning system for cold forging of non-axisymmetric parts of comparatively simple shape was developed in this study. Programs for the system have been written with Visual LISP in the AutoCAD using a personal computer and are composed of four main modules such as input module, shape cognition and shape expression module, material diameter determination module and process planning module. The design rules and knowledges for the system are extracted from the plasticity theories, handbook, relevant reference and empirical knowledge of field experts. Generally, in forging, only front view is needed for expression of axisymmetric parts, but non-axisymmetric parts need front and plane view. At the plane, this system cognizes the external shape of non-axisymmetric, parts - number of sides of regular polygon and radius of a circle circumscribing the polygon of n sides. At the front view, the system perceives diameter of axisymmetric portions and height of primitive geometries such as polygon, cylinder, cone, concave, convex, etc.

Development of Process Planning System for Cold Forging of Non-axisymmetric Parts (비축대칭 제품의 냉간단조 공정설계시스템의 개발)

  • 이봉규;권혁홍;조해용
    • Transactions of Materials Processing
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    • v.11 no.5
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    • pp.405-413
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    • 2002
  • A process planning system for cold forging of non-axisymmetric parts of comparatively simple shape was developed in this study. Programs for the system have been written with Visual LISP in AutoCAD. Shape of the product must be drawn with the solid line and the hidden line, and with the plane and front view, as well. At the plane, the system recognizes the external shape of non-axisymmetric portions - the number of the sides of the regular polygons and the radii of circles inscribing and circumscribing the polygon. At the front view, the system cognizes the diameter of axisymmetric portions and the height of the primitive geometries such as polygon, cylinder, cone, concave, convex, etc. The system perceives that the list developed from the solid line must be formed by the operation of forward extrusion or upsetting, and that the list developed from the hidden line must be formed by the operation of backward extrusion. The system designs the intermediate geometries again by considering clearance between workpiece and die, and then finally the billet diameter, in reverse order from the finished product, on the basis of volume constancy and using the operations, the forming sequence, the number of operations and the intermediate geometries which were already designed. The design rules and knowledges for the system were extracted from the plasticity theories, handbook, relevant reference and empirical knowledge of field experts. Suitability of the process planning was analyzed using SuperForge of FVM simulation package. The results of analysis showed good formability.

Synthesis of Automatically Path-Generating Four-Bar Linkage Using NURBS (NURBS를 이용한 4절 링크의 자동 경로 생성)

  • Hwang, Deuk-Hyun;Yang, Hyun-Ik
    • Journal of the Korean Society of Manufacturing Technology Engineers
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    • v.18 no.6
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    • pp.576-584
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    • 2009
  • Up to now, it has been said that no satisfactory computer solution has been found for synthesizing four-bar linkage based on the prescribed coupler link curve. In our study, an algorithm has been developed to improve the design synthesis of four bar linkage based on the 5 precision points method. The suggested algorithm generates the desired coupler curve by using NURBS, and then the generated curve approximates as closely as possible to the desired curve representing coupler link trajectory. Also, when comparing each generated curve by constructing the control polygon, rapid comparison is easily achieved by applying convex hull of the control polygon. Finally, an optimization process using ADS is incorporated into the algorithm based on the 5 precision point method to reduce the total optimization process time. As for examples, two four bar linkages were tested and the result well demonstrated the effectiveness of the algorithm.

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