Nesting of a single shape on a strip

Abstract

This paper presents three approaches to minimize and eliminate scrap from stamping a single shape arranged in a single row or double rows on strip raw materials. In the first approach, interlocking shapes are generated. Although such shapes are scrap-free, they require congruent lines in the design. At the early stages of the design process, a skilful designer can compromise between functional features and symmetric features to improve nesting. The second approach is to characterize a shape by parallel lines bounding it. Specifically, the method to find a minimum area parallelogram that encloses a given convex shape is discussed. The result gives the optimum arrangement of a convex shape in single row. The third approach involves the nesting of a given shape in a specified pattern. Three computational algorithms for the single and double row arrangements are given. The double row arrangement includes a half-turn or a mirror reflection. The three approaches are all based on the concept of interlocking shapes and they can readily be implemented on a small computer. Depending on the design environment and the piece shape, one of the approaches can be used.