A Real-Time C3 Continuous Local Corner Smoothing and Interpolation Algorithm for CNC Machine Tools
Bibliographic record
Abstract
Linear tool path segments of computer numerical control (CNC) machine tools need to be smoothed and interpolated in order to guarantee continuous and steady machining. However, because of the highly nonlinear relation between arc lengths and spline parameters, it is difficult to develop algorithms to simultaneously achieve real-time corner smoothing and interpolation with high-order continuity, although it is important to guarantee both high calculation efficiency and good dynamic performance of high-speed CNC machining. This paper develops a computationally efficient real-time corner smoothing and interpolation algorithm with C3 continuous feature. The corners at the junction of linear segments are smoothed by inserting Pythagorean-hodograph (PH) splines under the constraints of user-defined tolerance limits. Analytical solutions of the arc length and curvature of the smoothed tool path are obtained by evaluating a polynomial function of the spline parameter. The smoothed tool path is interpolated in real time with continuous and peak-constrained jerk. Simulations and experimental results show that the proposed tool path smoothing and interpolation algorithm can be executed in real time with 0.5 ms control period. Acceleration and jerk continuity of each axis are achieved along the tool path. Comparisons with existing corner smoothing algorithms show that the proposed method has lower jerk than existing C2 algorithms and the real-time interpolation algorithms based on the Taylor series expansion.
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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) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".