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Origami is to transform a flat square sheet of paper into a finished sculpture through folding and sculpting techniques. It is widely used in many fields such as traditional art, furniture design, solar panels and medical devices. To address the problems of complex configuration of origami, uneasy folding, and the difficult process of establishing origami model, this paper proposes a digital origami representation and design optimization method with DAG (Directed Acyclic Graph) model and directional plane. Firstly, the DAG model is constructed, whose nodes and branches represent the paper states and folding behaviors respectively. Secondly, the constraint relations are defined and established between the point-line-surface geometric elements and the folding behaviors, making it feasible to conform to the paper folding process. Lastly, combined with DAG model, the folding design process, including similar folding, reasonable folding and fewer folding operations, can be optimized to improve the computational efficiency. The method provides a digital theory for origami and is validated and tested by the software Unity3d.

Although fused deposition modeling (FDM) can fabricate complex functional components with desired structures, various defects emerge due to the diverse process parameters used in the process, which have a substantial impact on the quality and mechanical properties of the manufactured FDM parts. Therefore, the selection of suitable process parameters is an important design consideration for improving component quality. In the proposed work, the Taguchi optimization approach was used to optimize FDM process parameters to eliminate warpage defects in 3D printed parts. Infill pattern, infill density, raster angle, printing speed, layer height, build plate temperature, and extruder temperature were selected as the process parameters. Polylactic acid (PLA) was used to make the specimens using the Creality Ender-3 3D printer. The entire fabrication process was remotely monitored by interfacing the Raspberry Pi controller and camera with the OctoPrint platform. The influence of selected factors on warpage defect was evaluated and optimized using Analysis of Variance (ANOVA), the signal-to-noise ratio (S/N ratio), and a linear regression model. The results were later experimentally validated. The applicability of the optimized 3D printed part was verified by subjecting them to tensile tests.