Some Special Cases of the Burmester Problem for Four and Five Poses
Bibliographic record
Abstract
The Burmester problem aims at finding the geometric parameters of a planar four-bar linkage for a prescribed set of finitely separated poses. The synthesis related to the Burmester problem deals with both revolute-revolute (RR) and prismatic-revolute (PR) dyads. A PR dyad is a special case of RR dyad, i.e., a dyad with one end-point at infinity. The special nature of PR dyads warrants a special treatment, outside of the general methods of four-bar linkage synthesis, which target mainly RR dyads. In this paper, we study the synthesis of planar four-bar linkages addressing the problem of the determination of PR dyads. The conditions for the presence of PR dyads with the prescribed poses are derived. A synthesis method is developed by resorting to the parallelism condition of the displacement vectors of the circle points of PR dyads. We show that the “circle” point of a PR dyad can be determined as one common intersection of three or four circles, depending on whether four or, correspondingly, five poses are prescribed.
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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".