A General Methodology for the Forward Kinematic Problem of Symmetrical Parallel Mechanisms and Application to 5-PRUR Parallel Mechanisms (3T2R)
Bibliographic record
Abstract
In this paper, a general methodology is introduced in order to formulate the FKP of symmetrical parallel mechanisms in a 7-dimensional projective space by the means of the so-called Study’s parameters. The main objective is to consider rigid-body displacement, and consequently the FKP, based on algebraic geometry, rather than rely on classical recipes, such as Euler angles, to assist in problem-solving. The state of the art presented in this paper is general and can be extended to other types of symmetrical mechanisms. In this paper, we limit the concept of kinematic mapping to topologically symmetrical mechanisms, i.e., mechanisms with limbs having identical kinematic arrangement. Exploring the FKP in a higher dimensional space is more challenging since it requires the use of a larger number of coordinates. There are, however, advantages in adopting a large set of coordinates, since this approach leads to expressions with lower degree that do not involve trigonometric functions.
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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 | 0.001 | 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".