A real-time CNC interpolator algorithm for trimming and filling planar offset curves

Tool paths for CNC machines must be offset from the desired part shape, in order to compensate for the tool radius. To avoid gouging the part geometry and to ensure continuous paths, the offset construction employs trimming and filling operations at tangent discontinuities and regions of high concave curvature on the part shape. Typically, offset paths are constructed offline in a CAM system - the resulting paths are inherently approximate, and must be re-generated when a different tool size is selected. To circumvent these shortcomings, an interpolator algorithm for real-time offset curve trimming and filling is developed and verified herein. Since the algorithm uses the exact part geometry, offset path approximation errors are completely eliminated. Circular fill arcs of the appropriate angular extent are automatically executed at convex tangent-discontinuous junctures of adjacent part boundary segments, and offset trimming operations are triggered by real-time point/curve distance computations, which determine footpoints of the instantaneous tool position on the part boundary. The algorithm also accommodates feedrates that correspond to a constant speed of either the tool/part contact point, or the tool center. The practical feasibility of the method is demonstrated by an implementation on a 3-axis CNC mill governed by an open-architecture software controller.