• Journal for History of Mathematics
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• v.25 no.4
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• pp.37-51
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• 2012

By comparing the development history of rectangular coordinate system in Cartography and Mathematics, we assert in this manuscript that the rectangular coordinate system is not so much related to analytic geometry but comes from the space perceiving ability inherent in human beings. We arrived at this conclusion by the followings: First, although the Cartography have much influenced to various area of Mathematics such as trigonometry, logarithm, Geometry, Calculus, Statistics, and so on, which were developed or progressed around the advent of analytic geometry, the mathematical coordinate system itself had not been completely developed in using the origin or negative axis until 100 years and more had passed since Descartes' publication. Second, almost mathematicians who contributed to the invention of rectangular coordinate system had not focused their studying on rectangular coordinate system instead they used it freely on solving mathematical problem.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.6
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• pp.1545-1553
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• 1995

For general geometry of Coordinate Measuring Machine (CMM), volumetric error equation including 21 systematic error components was showed using vector expression. Different types of CMM listed on an international standard (BS 6808) were classified according to their geometry, and the general volumetric error equation was used for the CMMs. Application of volumetric error equation was also introduced, such as position error compensation, error equation of CNC-machine and parametric error analysis, etc.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2000.11a
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• pp.76-80
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• 2000

This paper describes a coordinate measuring technique based on optical triangulation using the two images. To overcome the defect of structured light system which measures coordinate point by point, light source is replaced by CCD camera. Pixels in CCD camera were considered as virtual light source. The overall geometry including two camera images is modeled. Using this geometry, the formula for calculating 3D coordinate of specified point is derived. In a word, the ray from a virtual light source was reflected on measuring point and the corresponding image point was made on the other image. Through the simulation result, validation of formula is verified. This method enables to acquire multiple points detection by photographing.

• Bulletin of the Korean Chemical Society
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• v.18 no.4
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• pp.406-409
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• 1997

The various cobalt(Ⅱ) complexes were synthesized and characterized using tris-(2-benzimidazolylmethyl)amine (ntb) as a ligand where the ntb plays as a tripodal tetradentate ligand to form complexes with a trigonal pyramidal geometry. The complexes have 5 and 6 coordinate cobalt(Ⅱ) ions depending on the additional ligand used. In each complex the additional ligand, chloride anion, or acetate anion occupies the "open" site trans to the apical tertiary nitrogen atom of ntb ligand. Complex 1, [Co(Ⅱ)(ntb)Cl]Cl has a trigonal bipyramidal geometry. This geometry was easily constructed using ntb as a tetradentate ligand and chloride as a monodentate ligand. The complex is isostructural to the corresponding manganese(Ⅱ) complex. Crystal data are as follows: [Co(Ⅱ)(ntb)Cl]Cl·MeOH, 1. triclinic space group P1; a=13.524(2) Å, b=14.037(2) Å, c=17.275(1) Å; α=78.798(9), β=84.159(8)°, γ=65.504(9)°; V=2929.6(6) Å3; Z=4; R1=0.0715, wR2=0.1461 for reflections of I > 2σ(I). Six coordinate complex 2 [Co(ntb)(OAc)](OAc) was synthesized using ntb as a tetradentate ligand and acetate as a bidentate chelating ligand.

• Tribology and Lubricants
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• v.16 no.6
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• pp.432-439
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• 2000

The present work is an attempt to calculate the steady state pressure and perturbed pressure of herringbone grooved journal bearings. A generalized coordinate system is introduced to handle the complex bearing geometry. The coordinates are fitted to the groove boundary and the Reynold's equation is transformed to be fitted to this coordinate system using the Gauss divergence theorem. This method makes it possible to deal with an arbitrary configuration of a lubricated surface. The caharacteristics of finite herringbone groove journal bearing are well calculated using this method.

• Transactions of the Korean Society of Mechanical Engineers
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• v.15 no.2
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• pp.668-676
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• 1991

Turbulent flows around tube banks and in the diffuser were studied using a non-orthogonal boundary fitted coordinate system and the modified K-.epsilon. turbulence model. In these cases, many problems emerge which stem from the geometrical complexity of the flow domain and the physical complexity of turbulent flow itself. To treat the complex geometry, governing equations were reformulated in a non-orthogonal coordinate system with Cartesian velocity components and discretised by the finite volume method with a non-staggered variable arrangement. The modified K-.epsilon. model of Hanjalic and Launer was applied to solve above two cases under the condition of strong and mild pressure gradient. The results using the modified K-.epsilon. model results in both test cases.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.8
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• pp.1666-1671
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• 2002

A lane sensing algorithm using vision sensors is developed based on lane geometry models. The parameters of the lane geometry models are estimated by a Kalman filter and utilized to reconstruct the lane geometry in the global coordinate. The inverse perspective mapping from image plane to global coordinate assumes earth to be flat, but roll and pitch motions of a vehicle are considered from the perspective of the lane sensing. The proposed algorithm shows robust lane sensing performance compared to the conventional algorithms.

• Proceedings of the Korean Society of Tribologists and Lubrication Engineers Conference
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• 1999.06a
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• pp.317-324
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• 1999

The present work is an attempt to calculate the steady state pressure and perturbed pressure of herringbone grooved journal bearings. A generalized coordinate system is introduced to handle the complex bearing geometry. The coordinates are fitted to the groove boundary and the Reynold's equation is transformed to be fitted to this coordinates system using the Gauss divergence theorem. This method makes it possible to deal with an arbitrary configuration of a lubricated surface. The characteristics of finite herringbone grooved journal are well calculated using this method.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.28 no.3
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• pp.230-237
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• 2004

Lane Sensing techniques based on vision sensors are regarded promising because they require little infrastructure on the highway except clear lane markers. However, they require more intelligent processing algorithms in vehicles to generate the previewed roadway from the vision images. In this paper, a lane sensing algorithm using vision sensors is developed to improve the sensing robustness. The parallel stereo-camera is utilized to regenerate the 3-dimensional road geometry. The lane geometry models are derived such that their parameters represent the road curvature, lateral offset and heading angle, respectively. The parameters of the lane geometry models are estimated by the Kalman filter and utilized to reconstruct the lane geometry in the global coordinate. The inverse perspective mapping from the image plane to the global coordinate considers roll and pitch motions of a vehicle so that the mapping error is minimized during acceleration, braking or steering. The proposed sensing system has been built and implemented on a 1/10-scale model car.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2002.05a
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• pp.546-550
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• 2002

This paper proposes an error compensation method that improves accuracy with geometry information of injection molding parts. Geometric information can give an improved accuracy in reverse engineering. Measuring data can not lead to get accurate geometric model, including errors of physical parts and measuring machines. Measuring data include errors which can be classified into two types. One is molding error in product, the other is measuring error. Measuring error includes optical error of laser scanner, deformation by probe forces of CMM and machine error. It is important to compensate these in reverse engineering. Least square method(LSM) provides the cloud data with a geometry compensation, improving accuracy of geometry. Also, the functional shape of a part and design concept can be reconstructed by error compensation using geometry information.