Singularity Analysis and Representation of the General Gough-Stewart Platform
Why is this work in the frame?
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Full frame distilled prediction
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.
- Candidate categories
- none
- Consensus categories
- none
- Domain
- Candidate signal: noneConsensus signal: none
- Study design
- Candidate signal: Simulation or modelingConsensus signal: Simulation or modeling
- Genre
- Candidate signal: EmpiricalConsensus signal: Empirical
- Teacher disagreement score
- 0.084
- Threshold uncertainty score
- 0.152
- Validation status
machine_predicted_unvalidated·codex-gemma-dda1882f352a
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 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 | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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.
- Teacher spread
- 0.297 · how far apart the two teachers sit on this one work
- Validation status
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
Abstract
In this paper, the singularity loci of the Gough-Stewart platform are studied and a graphical representation of these loci in the manipulator’s workspace is obtained. The algorithm presented is based on analytical expressions of the determinant of the Jacobian matrix, using two different approaches, namely, linear decomposition and cofactor expansion. The first approach is used to assess the effect of the architecture parameters on the nature of the singularity loci, while the second approach leads to a significant reduction of the computational complexity of the determinant. It is shown that, for a given orientation of the platform, the singularity locus in the Cartesian space is represented by a polynomial of degree three. Moreover, this polynomial equation is applied to several simplified Gough-Stewart architectures and it is shown that the expression is reduced when the base of the mechanism is coplanar and for other special geometries. A comparison with the results obtained using Grassmann geometry is then presented, which illustrates the advantages of using one single compact equation for the singularity loci. The generalization of Fichter’s singular configuration is also developed, and several observations are then made. Finally, a brief discussion on the architecture singularities is presented and a graphical representation of the singularity loci in the Cartesian workspace of the manipulator is obtained. Two examples clearly illustrate the usefulness of the results for the analysis and design of parallel manipulators.
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.
The record
- Venue
- The International Journal of Robotics Research
- Topic
- Robotic Mechanisms and Dynamics
- Field
- Engineering
- Canadian institutions
- Université Laval
- Funders
- Natural Sciences and Engineering Research Council of Canada
- Keywords
- SingularityJacobian matrix and determinantCartesian coordinate systemWorkspaceMathematicsParallel manipulatorStewart platformGravitational singularityRepresentation (politics)Locus (genetics)PolynomialGeneralizationExpression (computer science)AlgorithmComputer scienceGeometryApplied mathematicsAlgebra over a fieldMathematical analysisPure mathematicsRobotArtificial intelligenceKinematics
- Has abstract in OpenAlex
- yes