• Journal of the Korean Society for Precision Engineering
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• v.16 no.9
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• pp.172-178
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• 1999

3D linear and circular interpolations are a basic part for the machining of complex shapes. Until now, because of the absence of appropriate algorithms for the generation of 3D lines and circles, a full accomplishment for available machine tool resolution is difficult. this paper presents new algorithms for 3D linear and circular interpolation in the reference pulse technique. In 3D space, the line or circle is not expressed as an implicit function, it is only defined as the intersection of two surfaces. A 3D line is defined as the intersection of two planes, and a 3D circle is defined as the intersection of a plane and the surface of a sphere. Based on these concepts, interpolation algorithms are designed to follow intersection curves in 3D space, and a real-time 3D linear and circular interpolator was developed in software using a PC. The algorithm implemented in a PC showed promising results in interpolation error and speed performance. It is expected that it can be applied to the next generation computerized numerical control systems for the machining of 3D lines, circles and some other complex shapes.

• Transactions of the Korean Society of Mechanical Engineers
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• v.6 no.4
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• pp.341-345
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• 1982

The interpolator is usually built in hardware (logic circuitry), and the interpolator fabricated in a single LSI chip is recently made use of in most NC controllers, making the system more compact. However, the LSI interpolator not only has the technical difficulties but also requires high cost, in its fabrication. To solve these problems, we tried to find the method of interpolation by software, and succeeded in developing a program which, executed by INTEL's 8085 microprocessor, can distribute the input pulses of up to 4.0 [Kpps] for the linear interpolation and 3.0 [Kpps] for the circular interpolation. This paper presents the algorithm used to reduce the execution time and the flow chart of the interpolation program, and also shows the possibility of software interpolation. The interpolation program designed in assembly language is presented in the appendix.

• Transactions of the Korean Society of Mechanical Engineers
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• v.12 no.5
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• pp.968-975
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• 1988

The maximum feedrate generated from the hardware DDA is closely related to its calculation efficiency. The smaller interpolation span results in the lower calculation efficiency. This paper presents the method to improve the calculation efficiency for the smaller interpolation span. For the linear interpolation the higher calculation efficiency can be achieved by putting biggest value that the interpolation DDA can hold. for the circular interpolation, however, the scheme used for linear interpolation does not work since arbitrary change of value in the interpolation DDA changes the radius of the circle. The bit length of the hardware DDA is adjusted instead of adjusting the value in DDA, which results in the every same effect on calculation efficiency for the circular interpolation. The hardware circuit and supporting software are designed, and tested by two axis step motor driven milling machine. The experimental results show that the proposed method drastically increases the maximum feedrate even for the smaller interpolation span.

• Journal of Korea Society of Industrial Information Systems
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• v.12 no.1
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• pp.46-53
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• 2007

NC (Numerical Control) code for the tool path needs to be generated efficiently for machining of free form pockets with arbitrary wall geometry on a three axis CNC machine. The unified rough and finish cut algorithm and the tool motion is graphically simulated in Part 1. In this paper, a grid based 3D navigation algorithm simulated in Part 1 for generating NC tool path data for both linear interpolation and a combination of linear and circular interpolation for three-axis CNC milling of general pockets with sculptured bottom surfaces is experimentally performed and verified.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 2001.04a
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• pp.399-404
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• 2001

In CNC machining, a 3D(3-dimension) linear segment and a 2D(2-dimension) circular arc are general forms given by CAD/CAM system. Generally, the 2D circular arc machining is processed using dividing into some linear segments. A 3D circular arc also don't exist in the standard form of NC data. This paper present a algorithm and method for real-time machining of a circular arc(not only the 2D one, but also the 3D one). The 3D circular arc machining is based on the 2D circular arc machining. It only needs making a new coordinate system, converting given 3D points(a start point, a end point, and a center point of a 3D circular arc) into points of the new coordinate system, and processing a inverse transformation about a interpolated point. The proposed algorithm was implemented and simulated on PC system. It was confirmed to give a gcod result.

• 한국전산유체공학회:학술대회논문집
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• 2010.05a
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• pp.397-403
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• 2010

The Immersed boundary method(IBM) is one of CFD techniques which can simulate flow field around complex objectives using simple Cartesian grid system. In the previous studies the IBM has mostly been implemented to fractional step method based Navier-Stokes solvers. In these cases, pressure buildup near IB was found to occur when linear interpolation and stadard mass conservation is used and the interpolation scheme became complicated when higher order of interpolation is adopted. In this study, we implement the IBM to an incompressible Navier-Stokes solver which uses SIMPLE algorithm. Bi-linear and quadratic interpolation equations were formulated by using only geometric information of boundary to reconstruct velocities near IB. Flow around 2D circular cylinder at Re=40 and 100 was solved by using these formulations. It was found that the pressure buildup was not observed even when the bi-linear interpolation was adopted. The use of quadratic interpolation made the predicted aerodynamic forces in good agreement with those of previous studies.

• Journal of Korea Society of Industrial Information Systems
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• v.9 no.1
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• pp.7-16
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• 2004

The tool path needs to be determined in an efficient manner to generate the final NC (numerical control) code for efficient machining. This is particularly important in machining free form pockets with an arbitrary wall geometry on a three-axis CNC machine. Many CAD/CAM systems use linear interpolation to generate NC tool paths for curved surfaces. However, this needs to be modified to improve the smoothness of the machined bottom surface, reduce machining time and CL (cutter location) file size. Curved machining can be a solution to reduce these problems. The unified rough and finish cut algerian and the tool motion is graphically simulated. In this paper, a grid based 3D navigation algorithm for generating NC tool path data for both linear interpolation and a combination of linear and circular interpolation for three-axis CNC milling of general pockets with sculptured bottom surfaces is developed.

• Proceedings of the KIEE Conference
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• 2003.11c
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• pp.596-599
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• 2003

In this paper, we designed the digital pulse motor control chip including a circular interpolation function. The proposed algorithm in this paper is a nonparametric cure generation algorithm (Jordan's algorith) and a very simple algorithm. So the design for this algorithm used a small number of gates. Also an average error is fairly low. The max output speed is 4Mpps(Pulse per second), the max input frequency is 16MHz and the chip is useful for the stepping and servo motors. The software contains one or two, and many axes linear interpolation algorithm and two axes circular interpolation algorithm.

• 제어로봇시스템학회:학술대회논문집
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• 1987.10b
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• pp.228-231
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• 1987

Microprocessor-based software DDA interpolator is developed and applied to two axis contouring control of X-Y table. Developed assembly program is composed of feedrate, linear and circular DDA interpolation routines. Reference-pulse type of open-loop stepping motor control system in which the micro-computer produces a sequence of reference pulses for each axis of motion is adopted. To test performance of the developed program, X-Y table drive system based on stepping motor and shaft encoder is designed. Contouring error of the system in linear and circular path is within .+-.0.2 mm.

• Transactions of the Korean Society of Mechanical Engineers
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• v.12 no.2
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• pp.389-396
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• 1988

Microprocessor-based software DDA interpolator is developed and applied to two axis contouring control of X-Y table. Developed assembly program is composed of feedrate, linear and circular DDA interpolation routines. Reference-pulse type of open-loop stepping motor control system in which the micro-computer produces a sequence of reference pulses for each axis of motion is adopted. To test performance of the developed program, X-Y table drive system based on stepping motor and shaft encoder is designed. Conturing error of the system in linear and circular path is within .+-. 0.2mm under start stop pulse rate of stepping motor.