Mathematical basis for three dimensional circular interpolation on CNC machines

Abstract

The control units of numerically controlled manufacturing machines allow the programmer only a limited number of mathematical functions with which programmes can be written. Despite these limitations it is now possible to write programmes with which three dimensional (3D) circular interpolation can be performed directly on the .machines. The necessary mathematical techniques to perform 3D circular interpolation directly on the machines are deduced, although somewhat roundabout to overcome the programming limitations. The main programming limitations as well as cutter speed limitations are indicated.Die beheereenhede van numeriesbeheerde vervaardigingsmasjiene beskik:oor 'n beperkte aantal wiskundige funksies wat tot die beskikking van die programmeerder gestel word om programme mee te skryf. Selfs met .hierdie beperkings is dit nou moontlik om programme te skryf waarmee driedimensionele (3D) sirkelinterpolasie direk op die masjiene uitgevoer kan word. Die nodige wiskundige tegnieke waarmee 3D sirkelinterpolasie gedoen kan word, al is dit 'n effens omslagtige manier om die beperkings te oorkom, word afgelei. Die belangrikste programmeringsbeperkings asook snyspoedbeperkings word aangetoon.