Offsetting NURBS curves and tool-path generation for pockets

• Main Authors: Jiunn-Long Shih, 施浚龍
• Other Authors: S.-H. Frank Chuang
• Format: Others
• Language: en_US
• Published: 2005
• Online Access: http://ndltd.ncl.edu.tw/handle/99318654650727965792

博士 === 國立中興大學 === 機械工程學系 === 93 === This research aims to develop an efficient and robust method for computing higher-degree continuity offsets of NURBS curves and to investigate its application on constructing NURBS-format tool paths for pocketing. The basic steps for offsetting freeform curves are: (1) computing the line-fitting curve of a given progenitor curve; (2) constructing a linear approximating offset by offsetting the line-fitting curve exactly; and (3) reconstructing a higher-degree continuous offset curve based on the offset line-fitting curve. Under different offsetting conditions, three kinds of offsetting results can be obtained using this proposed method. One of them will generate offset curves with G1 continuity using piecewise Bezier curves; another one will have offsets with C2 continuity in integral B-spline form; and the last one, which is a novel attempt for NURBS offsetting, will obtain one-sided offset approximations in form of C1 piecewise Bezier curves. Unlike previous offset computation methods, the proposed method can estimate the offset approximation errors with global accuracy based on the convex hull property of Bezier curves and the idea of cumulative position error. And since all operations involved in offsetting are linear geometric calculations, the method is very efficient and robust. In particular, this offsetting method is able to precisely provide a total solution to the complicated problem of NURBS-format tool path generation for pocketing. The enormous success behind this application is largely due to the fact that the method can obtain offset curves with globally controllable error and self-intersecting loops can be eliminated as early as when the initially linear approximation offsets are obtained. Hence, higher-degree continuous tool paths can be generated easily with no overcutting or cusps.