• 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.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2002.10a
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• pp.570-575
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• 2002

This paper presents a new circular curve fitting approach of articulated manipulators, based on pseudoinverses. The paper aims at gaining the interpolation of circle from n data points, under the condition that the fitted circle should pass both a start point and an end point. In this paper, two algorithms of circular interpolation are presented. Prior to circular interpolation, are a spherical fitting should be performed, using least squares. In the first algorithm, the relationship between point data and normal vector on the sphere is used. In the second algorithm. the equation of plane which can be obtained from 3 points, i.e., a start point, an end point, and center of a sphere. The proposed algorithms are show to be efficient by using MATLAB-based simulation.

• Journal of the Korean Society for Precision Engineering
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• v.14 no.11
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• pp.77-83
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• 1997

This work is concerned with the algorithm of generating a new circular are interpolation. This research presents a new biarc curve fitting that is a circular interpolation method based on a triarc curve fitting. The triarc method, where a segment span is composed of three circular arcs, using maximum error estimation has the advantage of generating arc splines easily to a given tolerance. The new biarc method is called when the adjacent radii are the same in the same in the triarc method. In generating the machining data for various cam curves in CNC machining with the biarc method and the new biarc method, the latter accomp- lished faster NC-code generation, shorter NC-code block formation and machined the same cam profile more efficiently.

• 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.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2005.06a
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• pp.1678-1681
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• 2005

The disk cam mechanism cam produce a positive motion with a relatively few components. In the present paper a shape design of cam using the relative velocity method and the machining information analysis using the circular interpolation are introduced. In the first part of the paper a machining information at each point using the circular interpolation is taken. This study purposes the analysis method of the cutting error due to the moving path of the cutter, so that we can lead to the optimum design in a disk cam mechanism..

• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 2000.04a
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• pp.624-628
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• 2000

The performance of machine tools is qualified by many test procedures given by the national/international standards or respected organisations. Among them, test regarding circular-interpolation accuracy is getting to be one of the important acceptance tests at the production level. Machine tool systems are composed of many mechanical and electronical sub-systems so that it is not easy to improve dynamic performance by examining only one particular part. Instead, overall systematic approach encompassing all the contributing elements is necessary to achieve good results. In this study, measures taken in circular accuracy improvements will be explained case by case.

• 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.

• 제어로봇시스템학회:학술대회논문집
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• 1993.10a
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• pp.830-835
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• 1993

The errors in machining process by CNC machining center are due to many elements, such as the delay of the servo drivers, friction and the gain mismatch between x-axis and y-axis motors and so on. We made a counter circuit to measure the output of motor encoders for the motion error analysis of a CNC machining center, and have measured the errors experimentally when the CNC performs a circular interpolation. We have also used an iterative learning method to reduce the radius errors and stick motion errors generated by the CNC machining center performing a circular interpolation. The proposed learning scheme worked well and the circle obtained has smaller error.

• 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.

• 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.