Material Removal Optimization Strategy of 3D Block Cutting Based on Geometric Computation Method

During the material removal stage in stone rough processing, milling type has been widely explored, which, however, may cause time and material consumption, as well as substantial stress for the environment. To improve the material removal rate and waste reuse rate in the rough processing stage for three-dimensional stone products with a special shape, in this paper, circular saw disc cutting is explored to cut a convex polyhedron out of a blank box, which approaches a target product. Unlike milling optimization, this problem cannot be well solved by mathematical methods, which have to be solved by geometrical methods instead. An automatic block cutting strategy is proposed intuitively by considering a series of geometrical optimization approaches for the first time. To obtain a big removal block, constructing cutting planes based on convex vertices is uniquely proposed. Specifically, the removal vertices (the maximum thickness of material removal) are searched based on the octree algorithm, and the cutting plane is constructed based on this thickness to guarantee a relatively big removal block. Moreover, to minimize the cutting time, the geometrical characteristics of the intersecting convex polygon of the cutting plane with the convex polyhedron are analyzed, accompanied by the constraints of the guillotine cutting mode. The optimization algorithm determining the cutting path is presented with a feed direction accompanied by the shortest cutting stroke, which confirms the shortest cutting time. From the big removal block and shortest cutting time, the suboptimal solution of the average material removal rate (the ratio of material removal volume to cutting time) is generated. Finally, the simulation is carried out on a blank box to approach a bounding sphere both on MATLAB and the Vericut platform. In this case study, for the removal of 85% of material with 19 cuts, the proposed cutting strategy achieves five times higher the average material removal rate than that of one higher milling capacity case

Algorithmic and Combinatorial Results on Fence Patrolling, Polygon Cutting and Geometric Spanners

The purpose of this dissertation is to study problems that lie at the intersection of geometry and computer science. We have studied and obtained several results from three different areas, namely–geometric spanners, polygon cutting, and fence patrolling. Specifically, we have designed and analyzed algorithms along with various combinatorial results in these three areas. For geometric spanners, we have obtained combinatorial results regarding lower bounds on worst case dilation of plane spanners. We also have studied low degree plane lattice spanners, both square and hexagonal, of low dilation. Next, for polygon cutting, we have designed and analyzed algorithms for cutting out polygon collections drawn on a piece of planar material using the three geometric models of saw, namely, line, ray and segment cuts. For fence patrolling, we have designed several strategies for robots patrolling both open and closed fences

Polygons Cuttable by a Circular Saw

We introduce and characterize a new class of polygons that models wood, stone, glass, and ceramic shapes that can be cut with a table saw, lapidary trim saw, or other circular saw. In this model, a circular saw is a line segment (in projection) that can move freely in empty space, but can only cut straight into a portion of material. Once a region of material is separated from the rest, it can be picked up and removed to allow the saw to move more freely. A polygon is called cuttable by a circular saw if it can be cut out of a convex shape of material by a sufficiently small circular saw. We prove that a polygon has this property precisely if it does not have two adjacent reflex vertices. 1 Introduction There are many saw tools 1 for cutting a desired shape out of material ranging from soft wood to brittle ceramic, glass, and stone. Cutting out a complex nonconvex shape requires careful maneuvering of the saw, and for many devices is simply impossible because turns cannot be made. ..

Modelling, Monitoring, Control and Optimization for Complex Industrial Processes

This reprint includes 22 research papers and an editorial, collected from the Special Issue "Modelling, Monitoring, Control and Optimization for Complex Industrial Processes", highlighting recent research advances and emerging research directions in complex industrial processes. This reprint aims to promote the research field and benefit the readers from both academic communities and industrial sectors