Tool Sequence Selection for 2.5D Pockets with Uneven Stock

2006 ◽  
Vol 6 (1) ◽  
pp. 33-39 ◽  
Author(s):  
Roshan M. D’Souza
Keyword(s):  
Shortest Path ◽  
Directed Acyclic Graph ◽  
Milling Process ◽  
Shortest Path Problem ◽  
Selection Problem ◽  
Single Source ◽  
Flat Bottom ◽  
Acyclic Graph ◽  
Sequence Selection ◽  
Selection For

This paper describes an algorithm to select the cheapest tool sequence for machining 2.5D pockets using the milling process when the stock is uneven (noncylindrical). Uneven stock is generated when multiple setups are used to machine a prismatic part. Even though the pockets have flat bottom faces, the amount of material to be removed will vary along the depth of the pocket. This research has developed algorithms for finding accessible areas for tools, and pocket decomposition when the stock is uneven. Finally, it is shown that tool sequence selection problem can be formulated as the shortest path problem in a single-source, single-sink directed acyclic graph.

Tool Sequence Selection for 2.5-D Pockets With Uneven Stock

2004 ◽  
Author(s):  
Roshan M. D’Souza
Keyword(s):  
Shortest Path ◽  
Directed Acyclic Graph ◽  
Milling Process ◽  
Shortest Path Problem ◽  
Selection Problem ◽  
Single Source ◽  
Flat Bottom ◽  
Acyclic Graph ◽  
Sequence Selection ◽  
Selection For

This paper describes an algorithm to select the cheapest tool sequence for machining 2.5-D pockets using the milling process when the stock is uneven (non cylindrical). Uneven stock is generated when multiple setups are used to machine a prismatic part. Even though the pockets have flat bottom faces, the amount of material to be removed will vary along the depth of the pocket. This research has developed algorithms for finding accessible areas for tools, and pocket decomposition when the stock is uneven. Finally, it is shown that tool sequence selection problem can be formulated as the shortest path problem in a single-source, single-sink directed acyclic graph.

Handling Tool Holder Collision in Optimal Tool Sequence Selection for 2.5-D Pocket Machining

2002 ◽  
Author(s):  
Roshan M. D’Souza ◽  
Paul K. Wright ◽  
Carlo Se´quin
Keyword(s):  
Shortest Path ◽  
Directed Acyclic Graph ◽  
Single Source ◽  
Time Saving ◽  
Pocket Machining ◽  
Tool Holder ◽  
Sequence Selection ◽  
Novel Method ◽  
Selection For ◽  
The Cost

Significant cycle time saving can be achieved in 2.5-D milling by intelligently selecting tool sequences. The problem of finding the optimal tool sequence was reduced to finding the shortest path in a single-source single-sink directed acyclic graph. The nodes in the graph represented the state of the stock after the tool named in the node was done machining and the edges represented the cost of machining. In this paper a novel method for handling tool holder collision in the graph-based algorithm for optimal tool sequence selection has been developed. The method consists of iteratively solving the graph for the shortest path, validating the solution by checking for tool holder collisions and eliminating problematic edges in the graph. Also described is a method to intelligently build the graph such that in presence of tool holder collisions, the complexity of building the graph is greatly reduced.

Handling Tool Holder Collision in Optimal Tool Sequence Selection for 2.5-D Pocket Machining

2002 ◽  
Vol 2 (4) ◽  
pp. 345-349 ◽  
Author(s):  
Roshan M. D’Souza ◽  
Paul K. Wright ◽  
Carlo Se´quin
Keyword(s):  
Shortest Path ◽  
Directed Acyclic Graph ◽  
Time Saving ◽  
Pocket Machining ◽  
Tool Holder ◽  
Sequence Selection ◽  
Sequence Graph ◽  
Novel Method ◽  
Selection For ◽  
The Cost

Significant cycle time saving can be achieved in 2.5-D milling by intelligently selecting tool sequences. The problem of finding the optimal tool sequence was formulated as finding the shortest path in a single-source single-sink directed acyclic graph. The nodes in the graph represented the state of the stock after the tool named in the node was done machining and the edges represented the cost of machining. In this paper a novel method for handling tool holder collision in the graph-based algorithm for optimal tool sequence selection has been developed. The method consists of iteratively solving the graph for the shortest path, validating the solution by checking for tool holder collisions and eliminating problematic edges in the graph. Also described is a method to reduce the complexity of building the tool sequence graph in case there are tool holder collisions.

Optimal Boundary Triangulations of an Interpolating Ruled Surface

2005 ◽  
Vol 5 (4) ◽  
pp. 291-301 ◽  
Author(s):  
Charlie C. L. Wang ◽  
Kai Tang
Keyword(s):  
Shortest Path ◽  
Geometric Modeling ◽  
Search Space ◽  
Shortest Path Problem ◽  
Ruled Surface ◽  
Search Problem ◽  
Combinatorial Search ◽  
Single Source ◽  
Cad Cam ◽  
Optimal Triangulation

We investigate how to define a triangulated ruled surface interpolating two polygonal directrices that will meet a variety of optimization objectives which originate from many CAD/CAM and geometric modeling applications. This optimal triangulation problem is formulated as a combinatorial search problem whose search space however has the size tightly factorial to the numbers of points on the two directrices. To tackle this bound, we introduce a novel computational tool called multilayer directed graph and establish an equivalence between the optimal triangulation and the single-source shortest path problem on the graph. Well known graph search algorithms such as the Dijkstra’s are then employed to solve the single-source shortest path problem, which effectively solves the optimal triangulation problem in O(mn) time, where n and m are the numbers of vertices on the two directrices respectively. Numerous experimental examples are provided to demonstrate the usefulness of the proposed optimal triangulation problem in a variety of engineering applications.

A System for Multi-Passenger Urban Ridesharing Recommendations with Ordered Multiple Stops

2019 ◽  
Vol 63 (5) ◽  
pp. 657-687
Author(s):  
Eleonora D’Andrea ◽  
Beatrice Lazzerini ◽  
Francesco Marcelloni
Keyword(s):  
Air Pollution ◽  
Recommender Systems ◽  
Shortest Path ◽  
Directed Acyclic Graph ◽  
Matching Criterion ◽  
Acyclic Graph ◽  
Ordering Constraints ◽  
The City

Abstract Traffic and air pollution caused by the increasing number of cars have become important issues in nowadays cities. A possible solution is to employ recommender systems for efficient ridesharing among users. These systems, however, typically do not allow specifying ordered stops, thus preventing a large amount of possible users from exploiting ridesharing, e.g. parents leaving kids at school while going to work. Indeed, if a parent desired to share a ride, he/she would need to indicate the following constraint in the path: the stop at school should precede the stop at work. In this paper, we propose a ridesharing recommender, which allows each user to specify an ordered list of stops and suggests efficient ride matches. The ride-matching criterion is based on a dissimilarity between the driver’s path and the shared path, computed as the shortest path on a directed acyclic graph with ordering constraints between the stops defined in the single paths. The dissimilarity value is the detour requested to the driver to visit also the stops of the paths involved in the ride-share, respecting the visiting order of the stops within each path. Results are presented on a case study involving the city of Pisa.

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