The incremental sheet forming represents a relatively recent technology that guarantees high customization, thanks to the layered manufacturing principle typical of rapid prototyping, and cost-effectiveness, because it does not require dedicated equipment. Research has initially shown that this process is effective in metal materials capable of withstanding plastic deformation but, in recent years, the interest in this technique has been increasing for the manufacture of complex polymer sheet components as an alternative to the conventional technologies, based on heating-shaping-cooling manufacturing routes. Conversely, incremental formed polymer sheets can suffer from some peculiar defects, for example twisting. To reduce the risk of this phenomenon and the occurrence of failures, a viable way is to choose toolpath strategies that make the tool/sheet contact conditions less severe, and this represents the main goal of the present research. Polycarbonate sheets were worked by incremental forming; in detail, cone frusta with a fixed wall angle were manufactured with a reference and a stair toolpath strategy, and both the forming forces and the twist angle were monitored. The analysis of the results highlighted that a stair toolpath involving an alternation of diagonal up and vertical down steps represents a useful strategy to mitigate the forming forces and, with them, the occurrence of the twisting phenomenon in incremental formed thermoplastic sheets.

From an industrial point of view, the milling of 2.5D cavities is a frequent operation, 1 consuming time and presenting optimization potential, especially through a judicious choice of 2 the tool trajectory. Among the different types of trajectories, some have a general spiral-like aspect 3 and can potentially offer a reduced machining time. They are called curvilinear trajectories and are 4 obtained by interpolation between structure curves which are the numerical solutions of a partial 5 differential equation. In this case, the machine tool will connect points and the trajectory will be made 6 up of small segments. Even if, macroscopically, these trajectories have all the qualities to allow the 7 tool to move quickly, on a small scale, the discontinuities in tangency, inherent in the discretization, 8 significantly increase machining time. This article suggests to enhancing the continuity level of the 9 toolpath by rebuilding structure curves with a set of Hermite quartic spline patches connected in 10 tangency and curvature. Thanks to this, the tool will machine at an average feedrate closer to the 11 programmed one and will, de facto, reduce traveling time. 12 This article shows that the proposed method increases, on the two tested cavities, toolpath quality 13 indicators, reduces milling time from 10% to 18% for a curvilinear method without a filter and make 14 it possible to generalize the Bieterman and Sandström method for all non convex pockets.