Singularity Equations of Gough–Stewart Platforms Using a Minimal Set of Geometric Parameters
Bibliographic record
Abstract
So far, in the derivation of the singularity equations of Gough–Stewart platforms, all researchers defined the mobile frame by making its origin coincide with the considered point on the platform. One problem can be that the obtained singularity equation contains too many geometric parameters and is not convenient for singularity analysis, especially not convenient for geometric optimization. Another problem can be that the obtained singularity equation cannot be used directly in practice. To solve these problems, this work presents a new approach to derive the singularity equation of the Gough–Stewart platform. The main point is that the origin of the mobile frame is separated from the considered point and chosen to coincide with a special point on the platform in order to minimize the geometric parameters defining the platform. Similarly, by defining a proper fixed frame, the geometric parameters defining the base can also be minimized. In this way, no matter which practical point of the platform is chosen as the considered point, the obtained singularity equation contains only a minimal set of geometric parameters and becomes a solid foundation for the geometric optimization based on singularity analysis.
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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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.002 |
| 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".