GEOMETRIC OPTIMIZATION OF PLANAR 3-<i>R<u>P</u>R</i> PARALLEL MECHANISMS
Bibliographic record
Abstract
To pursue the maximal singularity-free workspace of parallel mechanisms is a very important concern for robot designers. This paper focuses on the case of planar 3-RPR parallel mechanisms. First, a relatively simple singularity equation of any point on the platform is derived. The obtained singularity equation shows that the singularity locus of any point on the platform is a circle of the same size, as long as the base and the platform are similar triangles. Furthermore, the three centres of the workspace circles lie exactly on the singularity circle. With these useful observations, the singularity-free workspace as well as the maximal leg length ranges can be determined. For a base of unit area, it is found that robots with equilateral triangle base and platform can obtain the maximal singularity-free workspace. Three case studies demonstrate this observation. Finally, a procedure for this kind of robot geometric design is provided.
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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 | 0.001 |
| 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".