Bibliographic record
Abstract
As shown in this paper, when designing parallel manipulators for tasks involving less than six degrees of freedom, the topology can be laid out by resorting to qualitative reasoning. More specifically, the paper focuses on cases whereby the manipulation tasks pertain to displacements with the algebraic structure of a group. Besides the well-known planar and spherical displacements, this is the case of displacements involving: rotation about a given axis and translation in the direction of the same axis (cylindrical subgroup); translation in two and three dimensions (two- and three-dimensional translation subgroups); three independent translations and rotation about an axis of fixed direction, what is known as the Scho¨nflies subgroup; and similar to the Scho¨nflies subgroup, but with the rotation and the translation in the direction of the axis of rotation replaced by a screw displacement. For completeness, the fundamental concepts of motion representation and groups of displacements, as pertaining to rigid bodies, are first recalled. Finally, the concept of Π-joint, introduced elsewhere, is generalized to two and three degrees of freedom, thereby ending up with the Π2-and the Π3-joints, respectively.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 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".