3.1. Specification of the Explored Errors
The mold errors of interest for this study are coined in manufacturing engineering literature as pillows or bulges [38
]. They concern the bottom parts of the formed geometry and appear as zones with concave curvature. Such errors arise in a particular geometrical situation where curvature changes from steep to more flat. This geometrical condition generates material compression and local thickening of the material in flatter areas, elevating them as bulges. The effect is additionally amplified by the more steep and therefore stiffer neighboring zones, which push the less formed material towards the middle and then upwards [39
]. The mechanics of this phenomenon are not yet fully understood but its probable cause is the in-plane stresses, in horizontal plane perpendicular to the tool axis, generated during forming [40
The mathematical quantification of this error can be done in two ways, both of which require the reverse engineering of the physical model into a digital representation to compare the deviations between the original geometry and the physical version. One way is to express the error as orthogonal distance between the ideal geometry profile and the actual one [41
]. Another way is to calculate changes in principal curvature for local error quantification [42
] and aggregate normal vectors for global error quantification [43
In our case, however, we do not apply the numerical quantification of the error. Our approach to error exploration relies on the mean curvature analysis of the fabricated geometry using an existing software tool that is commonly available to architects. Therefore, we do not employ any numerical comparisons between the original and the manufactured model as this would require creating a new analysis tool. Nonetheless, such an approach could be implemented as an interesting further development of our current research.
3.2. Generalized Workflow for Framework Implementation
As introduction to the framework’s presentation, let us begin with an outline of a generalized workflow for the framework’s implementation. As presented in Figure 2
, such a workflow features a combination of physical and digital activities and is looped to facilitate design iteration.
The exploration process begins with the 3D modeling of a of a NURBS (non-uniform rational basis spline) patch surface representing the first mold design. Then, section NURBS curves are generated for the surface and approximated to define a single polyline toolpath for the robot using the workflow described in Section 4.3
. The mold design is then fabricated. In the next step, the fabricated mold is digitalized, i.e., reconstructed into a digital 3D representation using the photogrammetry technique. To enable digital photography for photogrammetry, one surface of the transparent and glossy polymer mold is coated with an opaque, matte, removable spray paint.
Once the photographs of the mold are complete, they are used by the photogrammetry software to generate a digital representation of the mold as a point cloud. Using in-built functions in the photogrammetry software, the point cloud is approximated into a triangular mesh representation using binary STL meshing with no decimation.
The resultant triangular mesh is imported into a 3D modeling software and its face count is reduced by 50% for faster processing. This reduced mesh is then subjected to a curvature analysis targeting the mean curvature in order to identify areas of abrupt surface curvature change and to locate mesh areas that are convex, flat, and concave. The curvature values are represented as a colored map on the mesh surface, which aids their intuitive perception.
In parallel, optionally, translucent pigmented material is cast into the mold. The translucent material’s varying accumulations indicating the erroneous features of the mold are then photographed using a digital camera.
An image representing the initial mold design, a digital photograph of the mold, a digital image of mesh analysis, and an optional digital photograph of the translucent pigmented cast are then used as bases for locally affecting the erroneous mold features through combined intuitive digital painting and computational explorations.
As a result of the process, an iteration of the first mold design is generated. This 3D model is used as a point of departure for a new robot toolpath generation. The second mold is fabricated based on the toolpath data. The process of iterating its erroneous geometry features is then repeated according to the looped procedure outlined above.
3.4. Digital Processes
The digital processes component contains the digital operations assisting the explorations of geometrical errors of the robotically formed molds. The operations embrace: Free-form modeling, explorative computational design, bitmap painting, photogrammetric 3D mesh reconstruction, mesh curvature analysis, robot process simulation, and programming. Table 1
summarizes the particular functionalities of the digital toolkit enabling these operations in relation to error exploration.
The first type of operation, embracing free-form modeling, supports the creation of the first design that underpins the erroneous feature explorations. Moreover, these operations allow for the processing of the meshes obtained through photogrammetry, the fine-tuning of the intentionally erroneous mesh deformations generated based on bitmap painting, and, finally, the creation of geometries used as bases for robot toolpath programming. All of these operations are enabled by a 3D modeler Rhinoceros®, featuring a wide array of relevant tools for geometry edition, such as NURBS surface generation, remodeling, slicing, and joining; mesh smoothing, reduction, and subdivision; as well as operations of NURBS-to-mesh conversions. The designer can carry out the operations from this group in an intuitive manner, even though in-built computation and automated algorithms of the 3D modeling software lie at their core.
The second type of operation—photogrammetric 3D mesh reconstruction—facilitates the creation of a digital representation of the physical mold. Such a representation can have several purposes. Firstly, it can enable digital comparisons between the geometry of the original 3D model and of the fabricated mold. Secondly, it can serve as input for further design iterations of the mold or as a visual guide for intuitive digital bitmap painting. In our framework, the digital representation of the mold is generated using the Autodesk® ReCap™ Photo software. A 3D mesh model of the mold is created from a series of digital photographs of the mold, taken at different distances, heights, and angles.
The operations of mesh curvature analyses aid the visual evaluations of the photogrammetrically digitalized molds, helping to locate their erroneous features. These operations additionally support the artistic assessment of mold fine-tuning results in each design iteration. They help to determine whether a particular fine-tuned geometry version is esthetically satisfactory or whether its fine-tuning should continue. The curvature analysis is enabled by an add-on for Grasshopper® called Mesh Curvature. The add-on visually evaluates approximate mesh curvatures—Gaussian, mean, minimum, maximum, absolute, and root mean square (RMS). The tool generates a color-coded visual representation directly on the evaluated surface, indicating which of its regions are synclastic, neutral, and anticlastic.
The operations of bitmap painting support the intuitive development of geometrical errors in the molds. Such operations feature imprecise and ambiguous error feature painting, enabled by a bitmap editing software Adobe Photoshop. The software lets the designer overlay digital photos of the casts and molds, as well as the digital images of mesh curvature distributions—as translucent layers. These overlaid images then serve as visual guides to artistically apply paint strokes that indicate the locations of the desired mold deformations. Importantly, the digital image overlaying, as well as the painting, can in this case be approximate, to create a condition resembling digital sketching instead of precise drafting, which assures that the spontaneous flow of the design process is not slowed down or distracted by precision-focused activities.
The explorative computational design operations are enabled by a visual programming editor, Grasshopper®, extending the functionalities of the Rhinoceros® 3D modeler by offering procedural parametric control of the 3D modeling operations applied in mold geometry creation, modification, and fine-tuning. This category of operations therefore gives designers the possibility to explore mold errors more systematically, using exact numerical control. At the same time, however, this working mode is not limited to the procedural and precision-oriented working style only. The environment offers a number of functions that can be made imprecise, intuitive, and explorative. Such functions include, for example, intentionally approximated sampling of bitmap paint strokes or arbitrary mesh point relocations done using randomized multipliers for movement vector magnitudes, or movement vector magnitude remapping based on intuitively chosen function graphs.
Finally, the operations of robot process simulation and programming facilitate the robotic fabrication of iterated mold designs. They embrace the creation of robot toolpaths, the definition of the digital and physical parameters for the robotic process, the visual simulation of the forming process for collision detection purposes, and the generation of robot-specific machine codes executing the forming process. Robot toolpath generation is done parametrically, through the visual programming medium Grasshopper®, while the robot process setup, simulation, and machine code generation are supported with the KUKA|prc add-on functions, also executed in Grasshopper®.
3.5. Physical Processes
The physical processes component of the framework enables the inclusion of physical feedback in the digital explorations of erroneous mold features. It produces various digital representations of the physical results, which enables their utilization in the digital part of the framework. It is instrumental in the robotic fabrication of the initial and iterated mold designs, in the digitalization of the physical results and in the qualitative selection of erroneous mold features for exploration purposes. The operations in this component embrace: Robotic forming of molds, mold coating, digital photography of molds, translucent pigmented material casting, digital photography of casts, and visual analysis, identification, and selection of erroneous mold features.
The first category of operation relates to the robotic SPIF of molds, which produces input in the form of physical molds. Not only the molds, but also the entire course of the forming process is instrumental in error feature exploration. That is to say, the thorough observation of material behaviors during forming promotes a deeper understanding of how and why the erroneous features emerge. In particular, the understanding of the relationships between the features of a particular geometrical design and their effect on material behaviors causing errors. For best results and recollection, we recommend recording the forming process using a digital camera. The material behaviors in forming are very sensitive to even minor local changes in shape. As generalized conclusions are difficult to be drawn from this sensitive and failure-prone process, each forming occasion needs to be carefully observed and thoroughly registered.
The operations of mold coating with removable rubber paint produce an opaque, matte surface finish. Such a finish is essential for the mold to be photographable using a digital camera. It is best if the coating is removable, to enable unaffected casting of materials into the molds.
The operations of digital photography of molds produce images that can be used as inputs for photogrammetric 3D reconstruction and for the digital painting process. These photographs are also indispensable for the qualitative erroneous feature identification and ocular comparisons between the physical mold and its digital version. A dispersed lighting setup for photography is favorable for the photogrammetry photographs, while a setup featuring direct illumination generating shadows that underline the geometrical irregularities is favorable for the other types of photographs.
Finally, the operations of translucent pigmented material casting and its photography have a twofold purpose. Firstly, they produce silicone casts featuring material accumulations underlining the erroneous geometry of the mold, which aids the process of ocular error identification. Secondly, once captured in digital form through photography and overlaid with digital images of mesh curvature analysis and photographs of the coated mold, they serve as underlays for the bitmap painting process, visually guiding the process.