Lattice Tool Paths for High-Curvature Surface Machining
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Solution Overview
Problem
Current tool path generation systems for numerically controlled machines often result in suboptimal paths that are impractically slow and may reject high-curvature parts of CAD models, leading to surface errors and artifacts due to limitations in precision and computational resources.
Innovation Solution
The system uses Diophantine approximations to identify a subset of admissible lattice coordinates and dynamic programming to generate an optimal tool path that conforms tightly to the target surface without gouging, reducing computational load and improving precision.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If brute force dynamic programming is used to find the optimal path over all possible lattice coordinates, then manufacturing precision is improved, but computing time becomes impractically long
Solution Approach 1:
The patent segments the continuous target surface into discrete lattice coordinates that are admissible (on or above the surface). By dividing the problem space into discrete, manageable coordinate points and using dynamic programming to select the optimal sequence, the method achieves high precision while avoiding the computational intractability of brute force approaches over all possible coordinates.
Solution Approach 2:
The patent transforms the continuous coordinate space into a discrete lattice coordinate system with specific constraints (admissible points). By changing the parameter representation from continuous floating-point coordinates to discrete lattice coordinates and imposing the admissibility constraint, the problem becomes computationally tractable while maintaining manufacturing precision.
2Ease of operation
If resampling and smoothing methods are used to limit velocity and acceleration ranges, then ease of operation is improved, but manufacturing precision deteriorates due to rejection of high-curvature parts
Solution Approach 1:
The patent employs dynamic programming to dynamically select the optimal sequence of lattice coordinates, adapting the path to the local geometry of the surface. This dynamic approach allows the tool path to accurately follow high-curvature regions while maintaining feasible velocity and acceleration profiles, unlike static resampling methods that uniformly smooth the path and lose geometric fidelity.
Solution Approach 2:
The patent replaces traditional mechanical smoothing approaches (which physically limit velocity and acceleration) with a computational optimization approach. Instead of mechanically constraining the tool motion and accepting the resulting geometric loss, the system uses dynamic programming to computationally determine the optimal path that satisfies both geometric fidelity and motion constraints.
Data Source
AI summary
A data conversion system includes an interface to receive path data, a memory to store a computer-executable program including a lattice full algorithm and a dynamic programming algorithm, a processor, in connection with the memory, configured to execute the computer-executable program. The processor is configured to perform steps including providing a coordinate system including admissible points, forming, from the path data, a target polyline on the coordinate system, wherein the target polyline represents an approximated surface line of an object, dividing the target polyline into line segments, generating a set of rational vectors by approximating slopes of the line segments based on the lattice full algorithm, arranging the rational vectors to form lower convex hull lines arranged on or above corresponding line segments, wherein the lower convex hull lines are arranged onto the admissible points, wherein the admissible points are on or above the corresponding line segments, selecting a set of endpoints of the lower convex hull lines, and forming a final polyline by merging the endpoints based on the dynamic programming algorithm, wherein the final polyline is arranged to lay on or above the target polyline.