{"id":640,"date":"2022-12-04T17:30:49","date_gmt":"2022-12-04T17:30:49","guid":{"rendered":"https:\/\/ioannamitropoulouarch.com\/?p=640"},"modified":"2024-01-24T14:56:24","modified_gmt":"2024-01-24T14:56:24","slug":"nonplanar-3d-printed-shells","status":"publish","type":"post","link":"https:\/\/ioannamitropoulouarch.com\/index.php\/2022\/12\/04\/nonplanar-3d-printed-shells\/","title":{"rendered":"Vector-field-controlled 3D printing of shells, 2022"},"content":{"rendered":"\n

How can we approximate a shape using non-planar paths that conform to its geometric features?<\/p>\n\n\n\n\n\n\n\n

This work continues the research on the development of computational techniques to design non-planar print paths for robotic 3D printing. We control the paths using a parametrization function that is defined considering a tangent guiding vector field as its gradient. This provides more flexibility in the possible input constraints compared to the recently published boundary-controlled method<\/a>. <\/p>\n\n\n\n

We optimize the governing vector field considering properties desirable for fabrication, such as alignment to user-defined directions, smoothness, unit length, and integrability. The illustration below shows the resulting parametrization function controlled by a vector field aligned with principal curvature directions (left), boundaries (middle), and user-drawn directions (right)<\/p>\n\n\n\n

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Left: Vector field aligned to curvature directions. Middle: Vector field aligned to boundaries. Right: Vector field aligned to user-drawn directions. Top: Directional constraints. Middle: Optimized vector field. Bottom: Resulting parametrization.<\/figcaption><\/figure>\n\n\n\n

In addition, we optimize a second vector field orthogonal to the original field to create a 2D parametrization that can be integrated into two orthogonal strip networks that, when overlayed, form a strip-decomposable quad mesh. <\/p>\n\n\n\n

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2D parametrization function produced by optimizing two transversal vector fields. Left: Curvature aligned. Middle: Boundaries aligned. Right: Aligend to user-drawn directions.<\/figcaption><\/figure>\n\n\n\n

This discrete quad mesh representation is very handy for fabrication, as it can be used to edit the produced paths, partition them into singularity-free patches that can be fabricated in one go, and add fabrication details such as rigidifying ribs. <\/p>\n\n\n\n

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Top left: TPMS minimal surface printed with boundary-aligned paths, dimensions: 38 x 38 x 38 cm. Top right: Half-sphere model printed with paths aligned to user-drawn directions, dimensions: 30 x 30 x 15 cm. Bottom left: Enepper minimal surface printed with curvature-aligned paths, dimensions: 70 x 70 x 45 cm. Bottom right: Batwing minimal surface printed with curvature-aligned paths, dimensions: 76 x 76 x 76 cm.<\/figcaption><\/figure>\n\n\n\n

In addition, we can use the information from the two vector fields to print double-shell geometries with transversal path orientations on each side. This adds structural depth to the resulting object, thus improving stability. It also allows distributing imperfections more evenly along different directions on each side of the shell.<\/p>\n\n\n\n

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Costa minimal surface printed as a double shell using paths aligned to principal curvature directions, dimensions: 60 x 60 x 70 cm.<\/figcaption><\/figure>\n\n\n\n

The video below shows the entire process of creating a double shell print. <\/p>\n\n\n\n

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