Synthesis of the Base Curves For N-Lobed Elliptical Gears
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
Motivated by the need to synthesize the tooth profiles of noncircular gears, we approach the synthesis of the tooth profile of circular spur gears using their pitch circle, rather than their base circle. We do this by means of envelope theory. The proposed formulation gives the involute tooth profile and its well-known base circle for any pitch radius and profile angle of the rack cutter, which coincides with the pressure angle for circular gears. Then, the foregoing approach applies to the synthesis of the base curves of noncircular gears with involute tooth profiles and of their rack. We do this by resorting to basic differential geometry using the Euler–Savary Theorem, rather than to envelope theory. In particular, the formulation of both base curves for the right and left involute tooth profiles is obtained, for the first time, for N-lobed elliptical gears and their rack through the formulation of the pitch curves and their evolutes. The proposed formulation is illustrated with numerical results.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 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 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it