• Transactions of the Korean Society of Machine Tool Engineers
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• v.11 no.3
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• pp.80-85
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• 2002

The free curve gear is a non-circular gear without any relating center, which can perform free curve motion for complicated mechanisms, and minimize the work area. In this study, an algorithms for tooth profile generation of free curve involute gear is developed. The algorithm uses the involute gear creating principle in which a gear can be generated by rolling with another standard involute one. Cycloid me and third polynomial curve gears were designed and verified by computer graphics. These gears are manufactured in the wire-cut EDM and examined in engagement with a standard spur gear. The results showed that the proposed algorithm is successful to design and to manufacture the free curve gear with concave and convex profiles.

• Journal of the Korea Computer Graphics Society
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• v.6 no.4
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• pp.29-34
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• 2000

This paper classifies the structure of the intersection curve between a surface of extrusion and a free-form surface. Our algorithm computes the silhouette curve of the free-form surface with respect to the unique ruling direction of the surface of extrusion. By intersecting the silhouette curve and the base curve of the surface of extrusion, we can classify the topological structure of the intersection curve, and compute all singularities in the intersection curve. Moreover, we can determine which ruling lines of the surface of extrusion intersect the other free-form surface and how many times. This classification provides a robust and efficient method for computing the intersection curve.

• Journal of the Korean Mathematical Society
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• v.57 no.4
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• pp.809-823
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• 2020

In this article, we study the deformation theory of locally free sheaves and Hitchin pairs over a nodal curve. As a special case, the infinitesimal deformation of these objects gives the tangent space of the corresponding moduli spaces, which can be used to calculate the dimension of the corresponding moduli space. The deformation theory of locally free sheaves and Hitchin pairs over a nodal curve can be interpreted as the deformation theory of generalized parabolic bundles and generalized parabolic Hitchin pairs over the normalization of the nodal curve, respectively. This interpretation is given by the correspondence between locally free sheaves over a nodal curve and generalized parabolic bundles over its normalization.

• International Journal of Control, Automation, and Systems
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• v.2 no.1
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• pp.107-117
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• 2004

A new algorithm for planning a collision-free path based on an algebraic curve as well as the concept of path space is developed. Robot path planning has so far been concerned with generating a single collision-free path connecting two specified points in a given robot workspace with appropriate constraints. In this paper, a novel concept of path space (PS) is introduced. A PS is a set of points that represent a connection between two points in Euclidean metric space. A geometry mapping (GM) for the systematic construction of path space is also developed. A GM based on the 2$^{nd}$ order base curve, specifically Bezier curve of order two is investigated for the construction of PS and for collision-free path planning. The Bezier curve of order two consists of three vertices that are the start, S, the goal, G, and the middle vertex. The middle vertex is used to control the shape of the curve, and the origin of the local coordinate (p, $\theta$) is set at the centre of S and G. The extreme locus of the base curve should cover the entire area of actual workspace (AWS). The area defined by the extreme locus of the path is defined as quadratic workspace (QWS). The interference of the path with obstacles creates images in the PS. The clear areas of the PS that are not mapped by obstacle images identify collision-free paths. Hence, the PS approach converts path planning in Euclidean space into a point selection problem in path space. This also makes it possible to impose additional constraints such as determining the shortest path or the safest path in the search of the collision-free path. The QWS GM algorithm is implemented on various computer systems. Simulations are carried out to measure performance of the algorithm and show the execution time in the range of 0.0008 ~ 0.0014 sec.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10b
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• pp.896-899
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• 1996

A new algorithm for planning a collision free path is developed based on linear parametric curve. A collision-free path is viewed as a connected space curve in which the path consists of two straight curve connecting start to target point. A single intermediate connection point is considered in this paper and is used to manipulate the shape of path by organizing the control point in polar coordinate (.theta.,.rho.). The algorithm checks interference with obstacles, defined as GM (Geometry Mapping), and maps obstacles in Euclidean Space into images in CPS (Connection Point Space). The GM for all obstacles produces overlapping images of obstacle in CPS. The clear area of CPS that is not occupied by obstacle images represents collision-free paths in Euclidean Space. Any points from the clear area of CPS is a candidate for a collision-free path. A simulation of GM for number of cases are carried out and results are presented including mapped images of GM and performances of algorithm.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.57 no.6
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• pp.966-971
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• 2008

Free-piston engine system is a new type energy converter which uses a linear motion of piston by using linear generator. In free-piston engine system, the piston is not connected to a crank-shaft. The major advantages of free-piston engine system are high efficiency and low mechanical loss from the absence of motion conversion devices. Linear generator of free-piston engine system is used as generator and starting motor. In design step, considering of back-emf and detent force characteristics for generating mode and thrust and control characteristics for starting mode is needed. In this research, generating mode of flat-type linear generator and tubular-type linear generator is analyzed by finite element analysis method and starting mode of both type linear generators is analyzed by using capability curve. Capability curve is plotted from electrical parameters of both type linear generator and motion profile is calculated from mechanical parameters.

• The Transactions of the Korea Information Processing Society
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• v.7 no.4
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• pp.1271-1278
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• 2000

A general curve and surface is a basic method to generate Free-form object using the fundamental properties of blending function. In typical method, there is an overhead of calculating to present Free-form object with the line segments and interpolation algorithm, In this paper, for resolving this problem efficiently, it will propose the flexible Free-form curves/surfaces using Ball curve shape-preserving property. This method includes Geometric Continuity that is needed to design Free-form Surface of high degree consisted with many curves. Also, when lots of data are reduced using Geometric Property of Free-form curves, the shape-preserving property of resulting object can be maintained, then it can represent any Free-form object with less calculating .

• International Journal of Precision Engineering and Manufacturing
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• v.9 no.2
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• pp.84-92
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• 2008

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.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.8 no.5
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• pp.96-101
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• 1999

This study suggests an algorithm for tooth profile generation of free from curve involute gear, a special gear of which the pitch line is a free curve instead of a circular one. For the first, a methodology for calculation of the tooth curve is developed and formulated Then the formulated algorithm, is programmed for manufacturing and verified by computer graphics. Next the calculated results as changed in to NC codes to apply to wire electric discharge machine(WEDM). Finally, the machined gear is examined in engagement with a standard involute gear.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.12 no.1
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• pp.82-88
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• 2002

This paper deals with the free vibrations of horizontally curved beams with transition curve. Based on the dynamic equilibrium equations of a curved beam element subjected to the stress resultants and inertia forces, the governing differential equations are derived for the out-of-plane vibration of curved beam wish variable curvature. This equations are applied to the beam having transition curve in which the third parabolic curve is chosen in this study. The differential equations are solved by the numerical procedures for calculating the natural frequencies. As the numerical results, the various parametric studies effecting on natural frequencies are investigated and its results are presented in tables and figures. Also the laboratory scaled experiments were conducted for verifying the theories developed herein.