Efficient geometric algorithms for workpiece orientation in 4- and 5-axis NC-machining

In 4- and 5-axis NC-machines, the time to dismount, recalibrate, and remount the workpiece after each set of accessible faces of the workpiece has been machined can be considerable in comparison to the actual machining time. Unfortunately, the problem of minimizing the number of setups is NP-hard. In this paper, efficient algorithms are given for a greedy heuristic, where the goal is to find an orientation for the workpiece which maximizes the number of faces that can be machined in a single setup---using either a ball-end or a fillet-end cutter. The algorithms are based on geometric duality, topological sweep, interesting new properties concerning intersection and covering on the unit-sphere, and on techniques for efficiently constructing and searching an arrangement of polygons on the unit-sphere. The results imply that the optimal number of setups can be approximated to within a logarithmic factor. Evidence is also provided that it may not be possible to improve substantially on the..

Process planning for the subtractive rapid manufacturing of heterogeneous materials: Applications for automated bone implant manufacturing

This research presents a subtractive rapid manufacturing process for heterogeneous materials, in particular for custom shaped bone implants. Natural bone implants are widely used in the treatment of severe fractures or in tumor removal. In order for the human body to accept the bone implant material and heal properly, it is essential that the bone implant should be both mechanically and biologically compatible. Currently, the challenge of having correctly shaped natural bone implants created from an appropriate material is met through hand-shaping done by a surgeon. CNC-RP is a rapid machining method and software that can realize a fully automated Subtractive Rapid Prototyping (RP) process, using a 3-axis milling machine with a 4th axis indexer for multiple setup orientations. It is capable of creating accurate bone implants from different clinically relevant material including natural bone. However, there are major challenges that need to be overcome in order to implement automated shape machining of natural bones. They are summarized as follows: (1) Unlike homogeneous source materials for which a part can be machined from any arbitrary location within the original stock, for the case of donor bones, the site and orientation of implant harvest need to consider the nature of the heterogeneous internal bony architecture. (2) For the engineered materials, the source machining stock is in the convenient form of geometrically regular shapes such as cylinders or rectangular blocks and the entities of sacrificial supports can connect the part to the remaining stock material. However, irregularly-shaped bones and the heterogeneity of bone make the design of a fixture system for machining much more complicated. In this dissertation, two major areas of research are presented to overcome these challenges and enable automated process planning for a new rapid manufacturing technique for natural bone implants. Firstly, a new method for representing heterogeneous materials using nested STL shells is proposed. The nested shells model is called the Matryoshka mode, based in particular on the density distribution of human bone. The Matryoshka model is generated via an iterative process of thresholding the Hounsfield Unit (HU) data from a computed tomography (CT) scan, thereby delineating regions of progressively increasing bone density. Then a harvesting algorithm is developed to determine a suitable location to generate the bone implant from within the donor bone is presented. In this harvesting algorithm, a density score and similarity score are calculated to evaluate the overall effectiveness of that harvest site. In the second research area, an automated fixturing system is proposed for securing the bone implant during the machining process. The proposed method uses a variant of sacrificial supports (stainless surgical screws) to drill into appropriate locations and orientations through the free-form shaped donor bone, terminating at proper locations inside the solid part model of the implant. This automated fixturing system has been applied to machine several bone implants from surrogate bones to 3D printed Matryoshka models. Finally, the algorithms that are developed for setup planning are implemented in a CAD/CAM software add-on called CNC-RPbio . The results of this research could lead to a clinically relevant rapid machining process for custom shaped bone implants, which could create unique implants at the touch of a button. The implication of such high accuracy implants is that patients could benefit from more accurate reconstructions of trauma sites, with better fixation stability; leading to potentially shorter surgeries, less revisions, shorter recovery times and less likelihood of post-traumatic osteoarthritis, to name a few