Geometric process planning in rough machining

This thesis examines geometric process planning in four-axis rough machining. A review of existing literature provides a foundation for process planning in machining; efficiency (tool path length) is identified as a primary concern. Emergent structures (thin webs and strings) are proposed as a new metric of process robustness. Previous research efforts are contrasted to establish motivation for improvements in these areas in four-axis rough machining. The original research is presented as a journal article. This research develops a new methodology for quickly estimating the remaining stock during a plurality of 2 y D cuts defined by their depth and orientation relative to a rotary fourth axis. Unlike existing tool path simulators, this method can be performed independently of (and thus prior to) tool path generation. The algorithms presented use polyhedral mesh surface input to create and analyze polygonal slices, which are again reconstructed into polyhedral surfaces. At the slice level, nearly all operations are Boolean in nature, allowing simple implementation. A novel heuristic for polyhedral reconstruction for this application is presented. Results are shown for sample components, showing a significant reduction in overall rough machining tool path length. The discussion of future work provides a brief discussion of how this new methodology can be applied to detecting thin webs and strings prior to tool path planning or machining. The methodology presented in this work provides a novel method of calculating remaining stock such that it can be performed during process planning, prior to committing to tool path generation

Exact Geosedics and Shortest Paths on Polyhedral Surface

We present two algorithms for computing distances along a non-convex polyhedral surface. The first algorithm computes exact minimal-geodesic distances and the second algorithm combines these distances to compute exact shortest-path distances along the surface. Both algorithms have been extended to compute the exact minimalgeodesic paths and shortest paths. These algorithms have been implemented and validated on surfaces for which the correct solutions are known, in order to verify the accuracy and to measure the run-time performance, which is cubic or less for each algorithm. The exact-distance computations carried out by these algorithms are feasible for large-scale surfaces containing tens of thousands of vertices, and are a necessary component of near-isometric surface flattening methods that accurately transform curved manifolds into flat representations.National Institute for Biomedical Imaging and Bioengineering (R01 EB001550

Multi-Scale Free-Form Surface Description and Curvature Estimation

A novel technique for multi-scale smoothing of a free-form 3-D surface is presented. Complete triangulated models of 3-D objects are constructed at our center [4] and using a local parametrization technique, are then smoothed using a 2-D Gaussian filter. Our method for local parametrization makes use of semigeodesic coordinates as a natural and efficient way of sampling the local surface shape. The smoothing eliminates the surface noise together with high curvature regions such as sharp edges, therefore, sharp corners become rounded as the object is smoothed iteratively. Our technique for free-form 3-D multi-scale surface smoothing is independent of the underlying triangulation. It is also argued that the proposed technique is preferrable to volumetric smoothing or level set methods since it is applicable to incomplete surface data which occurs during occlusion. The technique was applied to simple and complex 3-D objects and the results are presented here

A New Contour Reconstruction Approach from Dexel Data in Virtual Sculpting

This paper presents a novel method of contour reconstruction from dexel data solving the shape anomalies for the complex geometry in virtual sculpting. Grouping and traversing processes are developed to find connectivity between dexels along every two adjacent rays. After traveling through all the rays on one slice, sub-boundaries are connected into full boundaries which are desired contours. The complexity of the new method has been investigated and determined as O(n). We also demonstrate the ability of the described method for viewing a sculpted model from different directions

Globally Optimal Surfaces By Continuous Maximal Flows

In this paper we consider the problem of computing globally minimal continuous curves and surfaces for image segmentation and 3D reconstruction. This is solved using a maximal flow approach expressed as a PDE model. Previously proposed techniques yield either grid-biased solutions (graph based approaches) or sub-optimal solutions (active contours and surfaces). The proposed algorithm simulates the flow of an ideal fluid with a spatially varying velocity constraint derived from image data. A proof is given that the algorithm gives the globally maximal flow at convergence, along with an implementation scheme. The globally minimal surface may be obtained trivially from its output. The new algorithm is applied to segmentation in 2D and 3D medical images and to 3D reconstruction from a stereo image pair. The results in 2D agree remarkably well with an existing planar minimal contour algorithm and the results in 3D segmentation and reconstruction demonstrate that the new algorithm is free from grid bias

Multi-scale 3-D Surface Description: Open and Closed Surfaces

A novel technique for multi-scale smoothing of a free-form 3-D surface is presented. Complete triangulated models of 3-D objects are constructed automatically and using a local parametrization technique, are then smoothed using a 2-D Gaussian filter. Our method for local parametrization makes use of semigeodesic coordinates as a natural and efficient way of sampling the local surface shape. The smoothing eliminates the surface noise together with high curvature regions such as sharp edges, therefore, sharp corners become rounded as the object is smoothed iteratively. Our technique for free-form 3-D multi-scale surface smoothing is independent of the underlying triangulation. It is also argued that the proposed technique is preferrable to volumetric smoothing or level set methods since it is applicable to incomplete surface data which occurs during occlusion. Our technique was applied to closed as well as open 3-D surfaces and the results are presented here

Advanced Process Planning for Subtractive Rapid Prototyping

This paper presents process planning methods for Subtractive Rapid Prototyping, which deals with multiple setup operations and the related issues of stock material management. Subtractive Rapid Prototyping (SRP) borrows from additive rapid prototyping technologies by using 2½D layer based toolpath processing; however, it is limited by tool accessibility. To counter the accessibility problem, SRP systems (such as desktop milling machines) employ a rotary fourth axis to provide more complete surface coverage. However, layer-based removal processing from different rotary positions can be inefficient due to double-coverage of certain volumes. This paper presents a method that employs STL models of the in-process stock material generated from slices of the part along the rotation axis. The developed algorithms intend to improve the efficiency and reliability of these multiple layer-based removal steps for rapid manufacturing.Mechanical Engineerin