An algorithm for generating NC tool paths for arbitrarily shaped pockets with islands

Abstract

In this paper we describe algorithms for generating NC tool paths for machining of arbitrarily shaped 2 l/2 dimensional pockets with arbitrary islands. These pocketing algorithms are based on a new offsetting algorithm presented in this paper. Our offsetting algorithm avoids costly two-dimensional Boolean set operations, relatively expensive distance calculations, and the overhead of extraneous geometry, such as the Voronoi diagrams, used in other pocketing algorithms.

Polygon Offsetting by Computing Winding Numbers

“…The resulting curve is called a raw offset curve. A raw offset curve usually contains invalid loops, which must be removed to produce the offset polygon [2,[12][13][14][15]. In this paper we present a simple new algorithm to offset multiple, non-overlapping polygons with arbitrary holes using a variation of the traditional raw offset curve and calculating the winding numbers of its connected regions.…”

“…Beyond the use of offsets as design primitives, for manufacturing they are a critical tool for analysis and process planning. In order to generate tool paths for 2 1 2 D pocket machining, for example, the boundary of each pocket must first be offset inward by a distance equal to the radius of the cutting tool to avoid gouging [1][2][3][4][5]. For direction parallel tool path generation (see Figure 1(a)), the tool path includes the line segments inside the pocket generated by intersecting the offset boundaries with equidistant parallel lines; for contour-parallel tool path generation (see Figure 1(b)), the original boundaries are offset successively and the offset curves are chained together into the tool path [2,3,6].…”

A Novel Method of Offset Approximation along the Normal Direction with High Precision

“…Offset curves are widely used in various computer-aided design and manufacturing (CAD/CAM) areas, such as tool path generation [1,2], 3D numerical control (NC) machining [3,4], solid modeling [5], graphics [6], and so on. However, the offset curve usually cannot be represented in a polynomial or rational form, and thus is difficult to apply in CAD systems.…”

C1Continuous Toolpath Generation Toward 5-axis High Speed Machining

“…NC machining is one of the most common manufacturing scheme available nowadays [1][2][3], [10][11][12], [15], [17][18], [20]. For example, forming die-cavities [2] is one such application.…”

“…The second approach offsets the outline(s) of the pocket by equally spaced offset distances, and employs these successive offsets to derive a toolpath [3], [10], [15]. Offsets of a C 1 continuous outline can yield C 1 discontinuities in regions where the radius of curvature of the curve is smaller than the offset distance.…”