This paper presents an analytical method for planning an efficient tool-path in machining free-form surfaces on 3-axis milling machines. This new approach uses a nonconstant offset of the previous tool-path, which guarantees the cutter moving in an unmachined area of the part surface and without redundant machining. The method comprises three steps: (1) the calculation of the tool-path interval, (2) the conversion from the path interval to the parametric interval, and (3) the synthesis of efficient tool-path planning.

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