• Journal of the Korean Society for Precision Engineering
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• v.17 no.1
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• pp.192-197
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• 2000

In CNC machining, a free curve is cut into small linear segments using the linear interpolation(G01) method. Therefore, the interpolation error along the curve is not constant due to the changing curvature. This paper presents a NURBS (Non-Uniform Rational B-Spline) interpolation algorithm for machining free curves with high precision and high speed. The proposed NURBS interpolation defines the tool path with NURBS parameters and limits the interpolation error to any desired level by adjusting the feed rate considering the curvature of the shape and sampling time. Both linear and NURBS interpolations are compared to show the validity of the proposed algorithm.

• Journal of the Korean Society for Precision Engineering
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• v.17 no.12
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• pp.115-120
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• 2000

Increasing demands on precision machining of free-form surface have necessitated that the tool to move not only position error as small as possible, but also with smoothly varying feedrates. This paper presents new algorithm for high precision 3D(3-dimensional) NURBS(Non-Uniform Rational B-Spline) interpolation in the reference-pulse technique. Based o the minimum path error strategy, interpolation algorithm was designed to follow the NURBS curve. Using this algorithm a real-time 3D NURBS interpolator was developed in software. The algorithm implemented in a PC showed promising results in interpolation error and speed performance. It is expected that this can be applied to the CNC systems for the high precision machining of complex shapes.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10b
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• pp.656-659
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• 1996

An universal NURBS interpolation for an open architectured CNC controller is proposed in order to unify internal data structure and algorithm of different interpolations such as linear, circular and spline, and to intelligently interface CAD database of the various workpiece contour. Furthermore, NURBS interpolation may result in better surface roughness and high speed machining due to the continuous generation of cutter movement. The mathematical manipulation of NURBS is presented and the practical implementation on the CNC controller of a lathe is discussed for real machining. The comparison between a computer design and workpieces machined on a lathe shows the feasibility of the NURBS interpolation format as an universal interpolation scheme.

• International Journal of CAD/CAM
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• v.11 no.1
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• pp.27-32
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• 2011

The increase in the productivity and the assurance of quality machining on the NC machines depends on, amongst other things, the perfection of the programming using adequate methods of interpolation. The programming language is until now based on the code ISO 6983 which defines the principles of the code G. This latter is not well adapted to the new strategies of machining imposed by the machining of complex surfaces and machining at high speed with the increasingly more severe requirements of precision. The CNC which adopt the interpolation of NURBS (Non Uniform Rational B-spline) are very rare (FANUC Siemens${\ldots}$). Based on the advantages of NURBS (continuity, flexibility, smoothing$.{\ldots}$), new formats G are currently developed but their use is still very limited. Our work consists on putting forward these new approaches of programming using the interpolation of NURBS. For this reason, a program capable to trace NURBS trajectories under Visual BASIC 6.0 was developed. This program was used thereafter in CAM software for the generation of NURBS formats like their new formats NC.

• Transactions of the Korean Society of Machine Tool Engineers
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• v.13 no.6
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• pp.56-63
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• 2004

The real-time NURBS interpolation method using 2-stage interpolation is studied. The 2-stage interpolation method that compensates for interpolation errors within machine BLU is proposed. The interpolation result was filtered by an Acceleration/Jerk limitation equation. Through this 2-stage interpolation, both the interpolation error condition and the motion kinematics could be satisfied. Using computer simulation in which interpolation results are evaluated by a numerical iteration method, it is shown that the 2-stage interpolation algerian could interpolate target curves precisely with geometric and dynamic contentment. The proposed algorithm was implemented in the CNC simulator system and an experimental un was conducted to identify the real-time adaptation.

• Korean Journal of Computational Design and Engineering
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• v.2 no.4
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• pp.237-243
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• 1997

A new method is introduced for the interpolation in NURBS Surface. This method uses the basis functions to assign the parameter values to the arbitrary set of geometric data and uses the iteration method to compute the control net. The advantages of this method are the feasible transformation of the data set to the matrix form and the effective surface generation as a result, especially to the design engineer.

• 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.

• Journal of the Korean Society for Precision Engineering
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• v.33 no.9
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• pp.745-751
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• 2016

This paper presents the acceleration and deceleration control of free-form surfaces. A rapid variation of acceleration (or Deceleration) drives the system into a machine shock, resulting in the inaccuracy of the path control of the NURBS curve. The pattern of acceleration control can be established using the curvature of the NURBS curve. The curvature can be easily calculated from the first and second derivative of the NURBS curve used in Taylor's expansion for NURBS interpolation. However, the derivatives are not used in the recursive method for NURBS interpolation. Hence, we attempted the difference-derivatives for calculating the NURBS curvature. Both, Taylor's expansion and the recursive method, are used jointly for controlling the acceleration in the same interpolation algorithm.

• Korean Journal of Computational Design and Engineering
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• v.3 no.4
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• pp.243-250
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• 1998

In parametric surface interpolation, the choice of the parameter values to the set of scattered points makes a great deal of difference in the resulting surface. A new method is developed and tested for the parametrization in NURBS surface global interpolation. This method uses the parameter value at the maximal value of relevant rational basis function, to assign the parameter values to the arbitrary set of design data. This method gives us several important advantages in geometric modeling, the freedom of the selection of knot values, the feasible transformation of the data set to the matrix, the possibility of affinite transformation between the design data and generated surface, etc.

• Journal of the Korean Society for Precision Engineering
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• v.19 no.5
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• pp.89-94
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• 2002

Increasing demands on precision machining using CNC machines have necessitated that the tool to move with a position error as small as possible in 3-dimensional (3D) space. This paper presents the simultaneous 3D machining with a retrofitted PC-NC milling machine. To achieve the simultaneous 3-axis motions, a new precision interpolation algorithm for 3D Non-Uniform Rational B-Spline(NURBS) curve is used. With this accurate and efficient algorithm for the generation of complex. 3D shapes, a real-time NURBS interpolator was developed using a PC and the simultaneous 3D machining is accomplished.