Parametric NURBS Curve Interpolators: A Review

Mohan, Sekar,Kweon, Sung-Hwan,Lee, Dong-Mok,Yang, Seung-Han Korean Society for Precision Engineering 2008 International Journal of Precision Engineering and Vol.9 No.2

Free-form shapes which were once considered as an aesthetic feature are now an important functional requirement. CNC industries are looking for a compact solution for reproducing free-form shapes as conventional interpolation models are inadequate, The parametric curve interpolator developed in the last decade has clearly emerged as favorite among its contemporaries in recent years, At present intense research has been done on parametric curve interpolators and interesting developments are reported. Out of the various parametric representations for curves and surfaces, NURBS has been standardized and widely used in free-form shape design. This paper presents a review of various methods of parametric interpolation for NURBS and discusses the salient features, problems and solutions. Recent approaches on variable feedrate interpolation, parameter compensation are also reviewed and research trends are addressed finally.

매개변수를 이용한 3축 CSARA 로봇의 이종모션 블랜딩

주지훈,정원지,이기상 제어로봇시스템학회 2008 제어로봇시스템학회 국내학술대회 논문집 Vol.2008 No.10

In order to implement continuous-path motion on a robot, it is necessary to blend one joint motion to another joint motion near a via point in a trapezoidal form of joint velocity. First, the velocity superposition using parametric interpolation is proposed. Hybrid motion blending is defined as the blending of different two type’s motions such as blending of joint motion with linear motion, in the neighborhood of a vis point. Second, hybrid motion blending algorithm is proposed based on velocity superposition using parametric interpolation. By using a 3-axis SCARA (Selective Compliance Assembly Robot Arm) robot with LabVIEWⓡ controller [2], the velocity superposition algorithm using parametric interpolation is shown to result in less vibration, compared with PTP(Point-To-Point) motion and Kim’s algorithm [1]. Moreover, the hybrid motion algorithm is implemented on the robot using LabVIEWⓡ [2] programming, which is confirmed by showing the end-effector path of joint-linear hybrid motion.

매개변수를 이용한 Labview<SUP>®</SUP>기반의 3축 SCARA로봇의 이종모션 제어 알고리즘

정원지(Won-Jee Chung),주지훈(Ji-Hun Ju),이기상(Kee Sang Lee) 한국생산제조학회 2009 한국생산제조학회지 Vol.18 No.2

In order to implement continuous-path motion on a robot, it is necessary to blend one joint motion to another joint motion near a via point in a trapezoidal form of joint velocity. First, the velocity superposition using parametric interpolation is proposed. Hybrid motion blending is defined as the blending of different two type’s motions such as blending of joint motion with linear motion, in the neighborhood of a via point. Second, hybrid motion blending algorithm is proposed based on velocity superposition using parametric interpolation. By using a 3-axis SCARA (Selective Compliance Assembly Robot Arm) robot with LabVIEW<SUP>®</SUP> controller(1), the velocity superposition algorithm using parametric interpolation is shown to result in less vibration, compared with PTP(Point-To-Point) motion and Kim’s algorithm(2). Moreover, the hybrid motion algorithm is implemented on the robot using LabVIEW<SUP>®</SUP>(1) programming, which is confirmed by showing the end-effector path of joint-linear hybrid motion.

모드선택기법을 이용한 보간법 기반 파라메트릭 차수축소모델의 개선

이재훈(Jaehun Lee),조맹효(Maenghyo Cho) 대한기계학회 2017 대한기계학회 춘추학술대회 Vol.2017 No.11

In this study, we enhanced the performance of the interpolation-based parametric reduced order model (IB-PROM) by employing the mode selection method to the domain of design parameters. For the conventional IB-PROM combined with component mode synthesis, substructural modes are selected by using the frequency cut-off method. However, if the value of the system parameter changes during the design optimization procedure, the order of important substructural mode can be switched. In other words, if we keep using the modes selected during the sampling process even though the design variables are changing, the accuracy of the ROM decreases. To improve the performance of the IB-PROM combined with the component mode synthesis for various design parameters, we adapted the mode selection method based on the moment-matching (CMSχ). Various numerical examples are studied to demonstrate the efficiency and accuracy of the proposed method.

보간법 기반의 파라메트릭 차수축소모델을 이용한 구조최적설계

이재훈(Jaehun Lee),조맹효(Maenghyo Cho) 대한기계학회 2016 대한기계학회 춘추학술대회 Vol.2016 No.12

In this study, design optimizations for structural parameters have been conducted by using the interpolation-based parametric reduced order model (IBPROM). In particular, the substructuring scheme was selectively employed for a certain type of design parameters to enhance the efficiency of the optimization. For the design optimization of size parameters, the parameters are affinely decomposed from the system matrices. Therefore, it is easy to reduce the full order model by using various reduction techniques, i.e., proper orthogonal decomposition. On the other hand, the shape parameters cannot be exactly decomposed due to the non-affine characteristics. In this case, we need to apply the congruence transformation in order to interpolate the each reduction mode in Euclidean space. Various design optimization examples are studied to demonstrate the efficiency and accuracy of the proposed IBPROM.

Fast and Precision NURBS Interpolator for CNC Systems

백대균,양승한,고태조 한국정밀공학회 2012 International Journal of Precision Engineering and Vol.13 No.6

This paper presents a performance evaluation of a NURBS interpolator that uses not Taylor’s expansion method but the recursive characteristics of NURBS. Taylor’s expansion has mostly been used for NURBS interpolation. However, it is very complicated and gives an indispensable truncation error. A fast and precision NURBS interpolator replacing Taylor’s expansion is presented for CNC systems in robots and CNC machine tools. The presented interpolation algorithm uses the recursive equation of the NURBS formula rather than Taylor’s expansion. A simulation study is conducted to demonstrate the advantages of this proposed interpolator compared with those using Taylor’s equation. The feedrate error and calculation time are simulated in the performance evaluation. The recursive method of NURBS interpolation is faster and more accurate than Taylor’s expansion.

CNC 공작기계에서 상호결합제어기를 위한 새로운 윤곽오차모델

이재하,양승한 韓國工作機械學會 2000 한국생산제조학회지 Vol.9 No.6

In the control of CNC machine tools, it is significant for precise machining to reduce the contour error. The object of servo-control is reduction of contour error and necking error. In past studies, there were two approaches to control a servo-system. One was to eliminate axial tracking errors, and the other was to control contour errors. The Cross-coupled con-troller(CCC) was introduced from a viewpoint of contour errors. For constructing CCC, it is necessary to make the contour error model. Recently, for machining part with free form surfaces, we propose a new contour error model based on curve interpolator. It is presented here that performance of CCC using proposed model is enhanced. Therefore, we can make more precise parts with the curve interpolator and the new contour error model.

Parametric NURBS Curve Interpolators

Sekar Mohan,Sung-Hwan Kweon,Dong-Mok Lee,Seung-Han Yang 한국정밀공학회 2008 International Journal of Precision Engineering and Vol.9 No.2

Free-form shapes which were once considered as an aesthetic feature are now an important functional requirement. CNC industries are looking for a compact solution for reproducing free-form shapes as conventional interpolation models are inadequate. The parametric curve interpolator developed in the last decade has clearly emerged as favorite among its contemporaries in recent years. At present intense research has been done on parametric curve interpolators and interesting developments are reported. Out of the various parametric representations for curves and surfaces, NURBS has been standardized and widely used in free-form shape design. This paper presents a review of various methods of parametric interpolation for NURBS and discusses the salient features, problems and solutions. Recent approaches on variable feedrate interpolation, parameter compensation are also reviewed and research trends are addressed finally.

CAD/CAM 시스템에서 媒介變數形 曲線補間器에 關한 硏究

김희송,오선 한국공작기계학회 1996 한국생산제조학회지 Vol.5 No.4

The interpolator is very important in CNC machines. This study proposed a parametric curve interpolator(PCI) which can be used for machining nay sculptured surface represented in a parametric form and generates commands for tool motion between CAD data points according to given accuracy demands. The proposed interpolator is superior to the existing linear interpolator in accuracy, feed rate and acceleration continuity. Moreover in comparison to the recently developed cubic spline interpolator, the PCI has the capability of handling higher order parametric curves and also ensures precise tracking in the velocity domain. Results from real time simulations and experiments on open architecture CNC machines equipped with the proposed interpolator are presented to show its practical capability. It is believed that the combination of the proposed interpolator and the open architecture machine controller further advances the area of command generation which is an important aspect of CAD/CAM.

Utility of Parametric Curves in Image Processing Applications

Manish Dixit,Sanjay Silakari 보안공학연구지원센터 2015 International Journal of Signal Processing, Image Vol.8 No.7

Image Processing is dealing with images containing lots of points. By Interpolation of these points to form different curves are taken under consideration in this paper. The curve modification and fitting in image processing can use Bezier Curve applications in various ways and by modifying these curves better result are generated. Bezier curve and its applications have vast scope for research in image processing like curve fitting algorithm, pattern recognition and computer aided geometric design. Application of Bezier curve are widely implemented in face detection, smile detection, hand writing and digit recognition which give wide view of Bezier curves. In this paper we go through various concepts and its application which can be used in image processing for providing extra edge in this field.