Ordered point cloud (top) and unordered (bottom) 

Ordered point cloud (top) and unordered (bottom) 

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The paper presents a tool path generation methodology for roughing operation based on the oriented graph theory. The cutting areas are identified using an original method that is based on a bicolor and binary map. The toolpath is generated using the searching Dijkstra algorithm inside a graph in order to find the single-source shortest path. The me...

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... surface of Figure 8 was machined on CNC equipment and it was validated in terms of shape deviations by point by point measuring and comparing with the CAD model using a multisensor CMM. After the validation, the surface was digitized, Figure 9, using the contact and non-contact methods in order to obtain ordered and unordered point clouds (Figure 1). After the digitization the ordered cloud point contains 47817 points while the unordered one contains196057 points. For the segmentation on the Z axis a pitch of 0.5 mm was chosen, that corresponds to the depth of cut, thus resulting 25 layers. The distance between two consecutive trajectories is 1⁄2 of tools were used: ball mill and end mill having diameters of 4 mm with two cutting areas (flutes). After calculating the trajectory, the NC program is generated directly in Mathematica according to the requirements of ISO 6983-1 regarding program format and definitions of address words. Using the same parameters for segmentation (both Z axis and the plane XOY) 36763 program lines were obtained in case of the ordered point cloud and 38411 lines in case of the unordered point cloud. The Figure 10 shows the result of machining with two different mills (a, b, c and d) in case of using a distance of ...
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... and more researchers are studying the problem of direct tool path generation from point clouds because the devices capable of creating such geometry are becoming more efficient. These point clouds can be generated by 3D scanning of a real object (contact or non-contact) using Computer Tomography (CT) or by using photogrammetry. Machining toolpath generation directly on point cloud shortens the reverse engineering cycle of a component and can reduce costs by eliminating the scan processing costs. Thus, the filtering stage, the mesh generation stage and the surface generation stage can be completely eliminated. Usually the software of the scanning equipment (either by palpation, or laser, or optical) allows a primary processing of the point cloud so that it can be filtered or cropped to remove unwanted points. As show in [1], rapid generation of contour from massive point cloud data is the crucial step for feature-based model reconstruction. Based on the outline of a point cloud a clear distinction can be made between the area where the material is to be chipped and the area where it must remain intact. In [2] the authors propose an algorithm for generating roughing and finishing tool paths on measured data directly by using Moving Least-Squares (MLS) method. In their algorithm the roughing is performed in a slice-by-slice manner to remove material rapidly. They generate an offset point cloud for machining allowance, and slicing data points were fitted by using MLS method to generate offset curve for ball-end cutter. Using the same technique for slicing the cloud point in order to extract the machining regions (contour curves and their inclusion relationships), [3] uses a boundary extraction algorithm for determining the machining region. To avoid the computational difficulties, they develop an algorithm to calculate the finishing tool-path based on well-known 2D geometric algorithms, such as 2D curve offsetting and polygonal chain intersection algorithms. In [4] the authors present a strategy for direct tool path generation based on B-spline surfaces constructed using extracted point data form initial cloud as control points. They generate the adaptive (region-based) tool paths that overcome the inherent drawback (redundant tool paths). In [5] the authors present a method based on generating iso-planar piecewise. The primary direction of the generated iso-planar tool paths is derived from the projected boundary of the discrete points. A projected cutter location net (CL-net) is then created, which groups the data points according to the intended machining error and surface finish requirements. In [6] a point-based conformal map is employed to build the parameterization cloud point based on discrete Laplace equation. They use also Iso-parametric curve determined in base of normal curvature. Surfel is the term used by [7] to describe the association of rendering the scanned data. Direct tool path generation is made using a point-based model which is created using an elliptical Gaussian re-sampling filter that is based on a signal re-sampling algorithm. They use a re-sampling filter based on Nyquist criterion to transform the input data (random cloud point) into a continuous surface and then re-sample the continuous surface. Because the re-sampled data can accurately represent the original surface, tool paths can be generated using CL. The CL point is found by lowering the cutter in the direction normal to the projection plane until contacts with the re-sampled points are made. Using an algorithm based on 3D biarc fitting technique it is possible to generate a 5-axis machining tool-path as shown in [8]. They construct a three-dimensional (3D) triangular mesh from the digitizing data with the mesh points considered as the tool contact locations. The tool axis orientations which must be determined in 5-axis tool-path are calculated using 3D biarc fitting. [9] Since such planning falls into the iso-parametric category, it intrinsically depends on the parameterization of point clouds. Accordingly, a point-based conformal map is employed to build the parameterization. Based on it, formulas of computing path parameters are derived, which are much simpler than the conventional ones. By regularizing parameter domain and on the basis of the previous formulas, boundary conformed tool-path can be generated with forward and side step calculated against specified chord deviation and scallop height, respectively. Experimental results are given to illustrate the effectiveness of the proposed methods. As shown in the literature, it has not been reported yet any research aimed directly at tool path generation based on graph theory. The majority of developed methodologies use slicing and various algorithms and methods to reduce the number of points and to generate the tool path. Current digitization technology allows scanning free form type surfaces and directly obtaining the point cloud, Fig. 1, or in some cases directly obtaining the 3D meshes [10, 11]. The algorithm presented in this paper can be applied in case of roughing and finishing with commercial milling tools in case of both ordered point clouds and unordered point clouds. Starting from the point cloud direct tool path generation is done by following the steps below (Fig. 2): 1. Alignment of the point cloud: its orientation in space, establishing the axes system and determining the upper and lower limits on the Z axis. 2. Cloud segmentation on Z axis: it is done by slicing on perpendicular planes to the Z axis, the slicing pitch is determined taking into account the parameters of the cutting operation (tool geometry, material, feed rates, etc.) and the geometry of the component that will be cut. 3. Point recovery: beginning with the second segmentation plane all points that are found above the sectioning plane in which the tool path is calculated are projected on that plane from top to bottom. This operation aims ...

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