dropped. The generated design space cannot be larger than the maximum fingertip design space of the finger base. 4) Afterward, all points of the manipulation object point cloud, located within this design space volume, are extracted (Figure 3, Base process 4). 5) These extracted points are then the basis for the previously mentioned projected surface representation approach. The method preserves form details to maximize the form-closure factor but can leak chamfered edge characterizations, which can make the centering and receiving more difficult in the context of position offsets. The surface representation is achieved by conducting a systematic voxelization of the design space with the extracted object points to a uniformly Base Process 1 23 distributed grid (Figure 3, Finger designs A and B 5). We define the finger base surface on which the fingertip will be later printed on as our design plane with a regular grid pattern. We then generate and stack voxels for each designplane grid coordinate until the manipulation object is reached. This is evaluated by checking if the points of the object are located within the voxel space. If this is the case, the middle point of the voxel is stored and the voxel stacking stopped for the current design-plane coordinate. The same process is repeated for the next design-plane coordinate until all coordinates have been covered. Finally, the mid-points of all voxels having contact with the object point cloud are stored as a resulting projected surface point cloud. 5 4 (5) Finger-Design A: Projected Surface Representation a1 a2 (5) b1 d_i Finger-Design B: Bezier Surface Fit b2 b3 FIGURE 3. Automatic fingertip design pipeline steps: Base process 1: Point cloud import of object and finger base. Base process 2: Positioning of object and finger base. Base process 3: Design space generation. Base process 4: Extraction of points located within the design space. Finger designs A and B 5: Projection surface representation via voxelization and voxel point approximation. (a1 and b2) Surface transfer to closed volume and STL file. (a2 and b3) Printed fingertip prototype. 50 IEEE ROBOTICS & AUTOMATION MAGAZINE JUNE 2023