Steepest-Directed Tool Paths of Sculptured Parts: The Most Efficient Local Scheme in 3-Axis CNC Machining and its Mathematical Proof
Bibliographic record
Abstract
Abstract Three-axis CNC milling is often used in sculptured parts machining. Due to the complex shape of the part surfaces, optimal tool path planning can significantly improve machining efficiency. In this work the mechanism of 3-axis CNC machining is examined. The generic formulae of steepest direction of sculptured surface are derived. A mathematical proof of the highest machining efficiency of steepest-directed tool path is provided. The most efficient local scheme, steepest-directed tool path in tool path planning, is proposed. This scheme serves as a theoretical base for applying steepest-directed tool path in tool path generation algorithms for 3-axis CNC machining. The tool path has been used to develop the steepest-directed and iso-cusped (SDIC) tool path generation algorithm. An example of SDIC tool paths of a half-cylinder part illustrates the application of steepest-directed tool path.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".