• Proceedings of the Korean Society of Precision Engineering Conference
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• 2001.04a
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• pp.979-982
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• 2001

In CNC machining, demands on precision machining of free formed surface model are increasing. Most of the CAD/CAM systems provide the NURBS(Non-Uniform Rational B-Spline) interpolator. NURBS is defined with NURBS parameter by control point, weight value and knot value. This paper shows the realtime NURBS interpolation algorithms and compared with each other. One is based on the equal length of curve segments rather than equal increment of the parameter Δu. The other is to limit the interpolation error to any desired level by adjusting the feedrate considering the curvature of the shape and sampling time.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2002.10a
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• pp.784-787
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• 2002

The NURBS surfaces are widely employed for exchanging geometric models between different CAD/CAE systems. However if the input NURBS surfaces are poorly parameterized, most surface meshing algorithms may fail or the constructed meshes can be ill-conditioned. In this paper presents a new method is presented that can generate well conditioned meshes even on poorly parameterized NURBS surfaces by regenerating NURBS surfaces. To begin with, adequate Points are sample on original poorly parameterized surfaces and new surfaces are created by interpolating these points. And then. mesh generation is performed on new surfaces. With this method, models with poorly parameterized NURBS surfaces can be meshed successfully.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2000.05a
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• pp.1032-1035
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• 2000

Increasing demands on precision machining with computerized numerical control (CNC) machines have necessitated that the tool to move not only position error as small as possible, but also with smoothly varying feedrates in space. This paper presents a new high precision interpolation algorithm for 3-dimensional (3D) Non-Uniform Rational B-Spline (NURBS) curve in the reference-pulse CNC technique. Based on the minimum path error strategy, real-time NURBS interpolator was developed in software and this was implemented with a PC-NC milling machine. The several experimental results have shown that the proposed NURBS interpolator is useful for the high precision machining of complex shapes. It is expected that this algorithm can be applied to the CNC machines for the machining of 3D free-form surfaces.

• Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
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• 2002.10a
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• pp.181-185
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• 2002

The modeling of realistic water-jet geometry is needed in order to facilitate the design modifications. The present paper proposes a method of generating inlet geometry. Inlet duct was represented by NURBS method which utilized the skinning and local cubic interpolation scheme. Three test examples are presented demonstrating the effectiveness of the methods of skinning and local cubic interpolation. Computational examples associated with practical configurations have shown the usefulness of the present method.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 2002.04a
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• pp.227-232
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• 2002

This paper presents an algorithm for general 2D and 3D NURBS interpolation and deals with command generation for 3 axes milling machining, including the feedrate control in order to meet two limitations, a geometrical accuracy and a dynamic restriction. Both of the maximum chordal error and the maximum acceleration specified by machine parameter lead to limit the allowable feedrate on the curvature of NURBS tool path. So, motion commands at every sampling time are continuously generated by those two limitations and programmed feedrate. Simulation results of interpolating several NURBS curves show that proposed NURBS algorithm is favorable in the machining free-form curve

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.20 no.4
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• pp.369-375
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• 2011

Design is important in the IT, digital appliance, and auto industries. Aesthetic and art images are being applied for better quality of the products. Most image patterns are complex and much lead-time is required to implement them to the product design process. A precise reverse engineering method generating 2.5D engraving models from 2D artistic images is proposed through the image processing, NURBS interpolation and 2.5D reconstruction methods. To generate 2.5D TechArt models from the art images, boundary points of the images are extracted by using the adaptive median filter and the novel MBF (modified boundary follower) algorithm. Accurate NURBS interpolation of the points generates TechArt CAD models. Performance of the developed system has been confirmed through the quick turnaround 2.5D engraving simulation linked with the commercial CAD/CAM system.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.20 no.2
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• pp.181-190
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• 2007

The linkage framework of surface geometric modeling based on the NURBS and shell finite element analysis is developed in this study. In the geometrically exact shell finite element analysis, the accuracy of the analysis strongly depends upon the accurate computation of the surface geometric quantities. Therefore if we obtain the necessary geometric quantities from the NVRBS surface equation, it's possible to construct the effective linkage framework of surface modeling in the CAD systems and shell finite element analysis using geometrically exact shell finite element. Besides, the linkage framework can be applied to the analysis of general and complex surfaces as well as simple surfaces. In this study, the shell surfaces are generated by interpolating given set of data points based on the NURBS surfaces. These data points usually can be obtained from surface scanning. But the representations of the generated NURBS surface are not same to one another. The accuracy depends on the chosen parameterization methods used in NURBS. Therefore, it is needed to select the suitable parameterization method according to the geometry of the surfaces. To verify the performance and accuracy of our developed linkage framework, we solve several well-known benchmark problems and assess the performance of the developed method.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 2004.04a
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• pp.323-328
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• 2004

Finish machining of a curved surface is often carried out by an NC system with curved interpolation in a high speed machining strategies. This study aims to develop the NURBS interpolator for the PC-NC based machine tools. In the case of a finish cut using a ball-end mill in high speed machining, low machinability at the bottom of a tool produces a harmful effect on surface roughness. The developed interpolator considers the relation between inclined angle, surface roughness, and feed rate, and adjusts real-time feed rate in order to generate surfaces which have isotropic surface roughness. The proposed interpolator is fully implemented and an experimental results are shown.

• 한국HCI학회:학술대회논문집
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• 2006.02a
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• pp.480-485
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• 2006

본 논문에서는 사용자가 NURBS 곡면을 다양한 형태로 변형을 손쉽게 할 수 있는 수정된 유한요소법을 이용한 곡면 변형의 방법을 제시한다. 수정된 유한요소법은 NURBS 기저함수를 전통적 유한요소법의 형상함수를 대신하여 유한요소해석을 한다. 모델링된 객체는 NURBS 곡면으로 이루어져 있고, 각각의 세그먼트별로 나누어진 기저함수와 제어점으로 구성되어있기 때문에 번거롭게 요소와 형상함수를 따로 구하지 않아도 되며, 자체 보간 방식이므로 기존의 유한요소법에 비해 적은 요소와 절점으로 곡면을 해석 할 수 있다. NURBS 곡면 변형은 각각의 제어점에 의해 구역이 나눠지고 각 구역은 변형될 지점과 가장 가까운 제어점으로 구성된 구역의 제어점들을 변형시킬 지점과 각 제어점의 거리 비례에 따라서 제어점 들의 속도가 지정되어 변형을 완성한다. 제시된 변형 방법은 다른 변형들과 같이 초기 입력에 의해 변형이 한 순간에 진행되는 것이 아니라 점진적 변형이 일어나며, NURBS 의 특징인 전체 제어점 변형으로 인해 의도하지 않은 변형이 일어나는 것을 변형 중간에 각각의 제어점의 속도를 제어함으로써 사용자의 의도한 변형으로 빠른 시간에 완성할 수 있게 된다.

• Journal of the Korean Society for Precision Engineering
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• v.23 no.9 s.186
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• pp.156-163
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• 2006

The purpose of this study is to improve the machining of free-formed NURBS surfaces using newly defined G-codes which can directly deal with shapes defined from CAD/CAM programs on a surface basis and specialize in rough and finish cut. To this purpose, a NURBS surface interpolation system is proposed in this paper. The proposed interpolation system includes online tool-path planning, real-time interpolation and feedrate regulation considering an effective machining method and minimum machining time all suitable for unit NURBS surface machining. The corresponding algorithms are simultaneously executed in an online manner. The proposed NURBS surface interpolation system is integrated and implemented with a PC-based 3-axis CNC milling system. A graphic user interface (GUI) and a 3D tool-path viewer which interprets the G-codes for NURBS surfaces and displays whole tool-paths are also developed and included in our real-time control system. The proposed system is evaluated through actual machining in terms of size of NC data, machining time, regulation of feedrate and cutting force focused on finish cut in comparison with the existing method.