Determination of the Uniqueness Domains of 3-RPR Planar Parallel Manipulators With Similar Platforms
Bibliographic record
Abstract
Abstract A uniqueness domain is a part of the Cartesian workspace corresponding to the same assembly mode of the 3-RPR (planar parallel) manipulator. This paper presents an efficient method to determine the uniqueness domains of the 3-RPR manipulators with similar platforms. The method is based on the singularity and forward displacement analysis (FDA) of the 3-RPR manipulator with similar platforms. The singularity analysis and the FDA of the 3-RPR manipulator with similar platforms is first performed. It is then proved that each of the solutions distributes into different singularity-free regions of the manipulator. Each singularity-free region corresponds to one uniqueness domain of the 3-RPR manipulator with similar platforms which can thus be determined in a direct way. At last, it is proved that the four solutions in analytic expression form to the forward displacement analysis correspond to different uniqueness domains for the 3-RPR manipulator with similar aligned platforms. This simplifies further the FDA in this case as the unique solution to the FDA can be found without the need to compute all the four solutions as long as the singularity-free region in which the manipulator works is given.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. 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.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 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 | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".