Using a planar rack cutter with variable modulus to generate a spherical gear pair
Bibliographic record
Abstract
In this study, an imaginary planar rack cutter with variable modulus and discrete conical teeth was used to generate a spherical gear pair with double degree of freedom. First, a geometric method was used to design the mathematical model of the imaginary planar rack cutter with variable modulus and discrete conical teeth. Next, the relationship of coordinate systems between the generating and generated surfaces was established. Then, the family of the imaginary planar rack cutter surfaces was obtained by homogeneous coordinate transformation matrix. Further, two equations of meshing between the generating and generated surfaces were determined by the two-parameter envelope theory. The mathematical model of spherical gear pair with variable modulus and discrete ring-involute teeth can be created by using the two equations of meshing and the family of the imaginary planar rack cutter surfaces. The mathematical models of the spherical gear pair with double degree of freedom and tooth contact analysis method were used to investigate the assembly errors of the gear pair in four cases.
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How this classification was reachedexpand
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 | 0.000 | 0.000 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".