The Synthesis of the Axodes of Spatial Four-Bar Linkages
Bibliographic record
Abstract
The paper introduces a procedure for the motion analysis of a four-bar linkage by means of dual algebra and the Principle of Transference. This procedure allows the mapping of the motion from the Euclidean to the spherical dual space. In particular, the position analysis of a spatial four-bar linkage is formulated by referring to a spherical four-bar linkage, which moves on the dual unit sphere. Moreover, both fixed and moving axodes of the coupler link are obtained, as traced by the spatial motion of the instant screw axis (ISA) with respect to the fixed and moving frames. These ruled surfaces reproduce the spatial motion of the coupler link upon relatively rolling and sliding around and along the ISA. Finally, the proposed procedure has been implemented in MatLab, in order to analyze the motion of the different types of four-bar linkages, including the Bennett mechanism and the Hooke joint. The motion is illustrated by means of animations of the four-bar linkages and their axodes.
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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".