• Honam Mathematical Journal
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• v.30 no.3
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• pp.425-433
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• 2008

In this paper, we introduce the concept of p-preconvex sets on preconvexity spaces. We study some properties for p-preconvex sets by using the co-convexity hull and the convexity hull. Also we introduce and study the concepts of pc-convex function, $p^*c$-convex function, pI-convex function and $p^*I$-convex function.

• Journal of the Korean Society for Precision Engineering
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• v.23 no.1 s.178
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• pp.113-120
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• 2006

This paper proposed the control algorithm fur aspheric surface grinding and was verified by the experiment. The functions of the algorithm were simultaneous control of the position and interpolation of the aspheric curve. The non-linear formula of the tool position was derived from the aspheric equations and the shape of the tool. The function was partitioned by an certain interval and the control parameters were calculated at each control section. The movement in a session was interpolated with acceleration and velocity. The position error was feed-backed by rotary encorder. The concept of feedback algorithm was correcting position error by increasing or decreasing the speed. In the experiment, two-axis machine was controlled to track the aspheric surface by the proposed algorithm. The effect of the control and process parameters was monitored. The result showed that the maximum tracking error was under sub-micro level for the concave and convex surfaces.

• International Journal of Precision Engineering and Manufacturing
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• v.7 no.4
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• pp.51-56
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• 2006

This paper proposes a control algorithm, which is verified experimentally, for aspherical surface grinding and polishing. The algorithm provides simultaneous control of the position and interpolation of an aspheric curve. The nonlinear formula for the tool position was derived from the aspheric equation and the shape of the tool. The function was partitioned at specific intervals and the control parameters were calculated at each control section. The position, acceleration, and velocity at each interval were updated during the process. A position error feedback was introduced using a rotary encoder. The feedback algorithm corrected the position error by increasing or decreasing the feed speed. In the experimental verification, a two-axis machine was controlled to track an aspherical surface using the proposed algorithm. The effects of the control and process parameters were monitored. The results demonstrated that the maximum tracking error with tuned parameters was at the submicron level for concave and convex surfaces.

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.1
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• pp.31-40
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• 1992

This paper presents an automatic feature recognition system for recognizing and extracting feature information needed for the process planning input from a 3D CAD system. A given part is modeled by using the AutoCAD and feature information is automatically extracted from the AutoCAD database. The type of parts considered in this study is prismatic parts composed of faces perpendicular to the X, Y, Z axes and the types of features recognized by the proposed system are through steps, blind steps, through slots, blind slots, and pockets. Features are recognized by using the concept of convex points and concave points. Case studies are implemented to evaluate feasibilities of the function of the proposed system. The developed system is programmed by using Turbo Pascal on the IBM PC/AT on which the AutoCAD and the proposed system are implemented.