A Frame-Independent Vector Expression of the Singularity Locus of the Gough-Stewart Platform
Bibliographic record
Abstract
This paper presents a vector expression of the singularity locus of the Gough-Stewart platform. In order to obtain this expression, several algebraic operations are performed on the manipulator’s Jacobian matrix such as relocating the origin of the reference frame and linearly combining columns. The third-degree vector expression thus obtained does not contain a constant term, which allows the factorization of an instance of the position vector. An alternative notation that reduces the number of times that the position vector appears in the expression is then presented. It is also demonstrated that a simplified architecture such as that of the MSSM can significantly reduce the length of the expression. Finally, some numerical examples of singularity loci are presented, which were estimated by combining the proposed formulation with interval analysis in the cases of a generic Gough-Stewart platform and of an MSSM. The results obtained illustrate how the precision of interval analyses are influenced by the form of the symbolic expression of the singularity locus.
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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) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 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".