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The fold-and-cut theorem states that any shape with straight sides can be cut from a single (idealized) sheet of paper by folding it flat and making a single straight complete cut. [1] Such shapes include polygons, which may be concave, shapes with holes, and collections of such shapes (i.e. the regions need not be connected ).
The fold-and-cut problem asks what shapes can be obtained by folding a piece of paper flat, and making a single straight complete cut. The solution, known as the fold-and-cut theorem, states that any shape with straight sides can be obtained. A practical problem is how to fold a map so that it may be manipulated with minimal effort or movements.
Cutting-stock problems can be classified in several ways. [1] One way is the dimensionality of the cutting: the above example illustrates a one-dimensional (1D) problem; other industrial applications of 1D occur when cutting pipes, cables, and steel bars. Two-dimensional (2D) problems are encountered in furniture, clothing and glass production.
Cutting speed may be defined as the rate at the workpiece surface, irrespective of the machining operation used. A cutting speed for mild steel of 100 ft/min is the same whether it is the speed of the cutter passing over the workpiece, such as in a turning operation, or the speed of the cutter moving past a workpiece, such as in a milling operation.
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Surface feet per minute (SFPM or SFM) is the combination of a physical quantity (surface speed) and an imperial and American customary unit (feet per minute or FPM).It is defined as the number of linear feet that a location on a rotating component travels in one minute.
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Guillotine cutting is the process of producing small rectangular items of fixed dimensions from a given large rectangular sheet, using only guillotine-cuts. A guillotine-cut (also called an edge-to-edge cut) is a straight bisecting line going from one edge of an existing rectangle to the opposite edge, similarly to a paper guillotine.