CURVAS PARALELAS EXPLÍCITAS DE LAS CURVAS CÓNICAS NO DEGENERADAS PARA EL TORNEADO CNC DE LENTES Y ESPEJOS ASFÉRICO-CÓNICOS (EXPLICIT PARALLEL CURVES OF NON-DEGENERATE CONIC CURVES FOR THE TURNED CNC OF ASPHERIC-CONIC LENSES AND MIRRORS)
CURVAS PARALELAS EXPLÍCITAS DE LAS CURVAS CÓNICAS NO DEGENERADAS PARA EL TORNEADO CNC DE LENTES Y ESPEJOS ASFÉRICO-CÓNICOS (EXPLICIT PARALLEL CURVES OF NON-DEGENERATE CONIC CURVES FOR THE TURNED CNC OF ASPHERIC-CONIC LENSES AND MIRRORS)
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Este artículo presenta el método para obtener, en coordenadas cartesianas, las líneas curvas paralelas de las curvas cónicas no degeneradas, por métodos analíticos y numéricos. Se define el offset como una función paralela a la función original a una distancia r. El offset de una cónica es importante para los procesos de fabricación de mecanismos, lentes, espejos y moldes; especialmente en el torneado con control numérico computarizado (CNC) de superficies de revolución con secciones cónicas, usando buriles de diamante con punta de radio r. También se presenta una técnica refinada usando interpolación circular segmentaria para construir numéricamente el offset de una parábola, que también puede usarse como modelo para determinar el offset de la elipse y de la hipérbola.
Abstract: This paper presents the method to obtain, in Cartesian coordinates, the parallel curve lines of non-degenerate conical curves, by analytical and numerical methods. Offset is defined as parallel function to the original function to a distance r. Offset of a conic is important for the manufacturing processes of mechanisms, lenses, mirrors, and molds; especially in the turning with computerized numerical control (CNC) of surfaces of revolution with conical sections, using diamond tools of radio r. Also a refined tip technique using segmental circular interpolation to numerically construct the parabola offset is presented, that also can be used as model to determine offsets of ellipse and hyperbola.
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