Generation of mechanizing trajectories with a minimum number of points

Abstract

A large number of coordinate points is available after digitizing a profile, a surface, or generating the points of the function that define the surface or the profile (if an equation to generate these points is available). These coordinate points are grouped according to the strategy followed for the digitization or the generation. But not all the coordinate points are equally important: More coordinate points are needed in the zones where the curvature is larger, in contrast to the zones where the curvature is smaller. A new selection method of coordinate points is presented in this study. It is based on the maximum allowed chord error. This method simplifies the selection of the important coordinate points for the shape reconstruction with a computer-aided design program or for the computer numerical control (CNC) mechanizing, using either less information, smaller number of points, or NC program lines. To accomplish this objective, any programming language can be applied. An Excel macro and MATLAB have been used in this study. This is interesting both in high-speed CNC machines and in old equipment. The first ones have “look ahead” benefits, because the number of blocks in the NC program are read in advance. Therefore, if a smaller number of lines are needed for the same required precision, the process speed will be higher. The use of old machines will also be improved by the smaller number of lines to process. It must be noted that this process is as fast as the slowest of its elements.