Singularity Loci of a Special Class of Spherical Three-degree-of-freedom Parallel Mechanisms with Revolute Actuators
Bibliographic record
Abstract
In this paper, we study the singularity loci of a special class of spherical three-degree-of-freedom parallel manipulators. The concise analytical expressions describing the singularity loci are obtained in the joint and in the Cartesian spaces by using the direct and inverse kinematic solutions of these manipulators, respectively. As mentioned elsewhere, there are three different types of singularities for parallel manipulators, each having a different physical interpretation. These types are considered and it is shown that, for the manipulators considered here, the three types of singularities coincide. Moreover, for the two types of manipulators studied here, there are only four singular configurations in the Cartesian space. In addition, the three-dimensional graphical representations of the singularity loci in the joint and in the Cartesian spaces are illustrated. The description of the singular configurations provided here has great significance for robot trajectory planning and control.
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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 | 0.001 | 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) | 0.002 | 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 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".