A locus tracing algorithm for cutter offsetting in CNC machining

Abstract This paper presents a new interpolation algorithm for tool motion generation along planar offset curves, an important manufacturing problem in CNC machining. The development of the algorithm is based on a locus tracing concept. The main advantage of the concept is the fact that is applicable not only when an analytic expression of the desired path is available but also in situations where, although the path is geometrically defined, its analytic description is either impossible to compute, or too cumbersome to work with. The presented locus tracing algorithm, uses the locus defining geometric property to generate a succession of points on the desired path (the offset), through repeated application of two analytically implemented construction operations. These operations are formulated on the basis of the direction and proximity criteria introduced by Danielson, which guarantee a locus position error of at most one step. The effectiveness and simplicity of the algorithm is demonstrated by two representative examples. The first example uses an ellipse as the generator curve while the second example treats with a more complex case such is the case of a free-form curve implemented in terms of a Bezier curve.