A Unified Approach to Direct Kinematics of Some Reduced Motion Parallel Manipulators
Bibliographic record
Abstract
After discussing the Study point transformation operator, a unified way to formulate kinematic problems, using “points moving on planes or spheres” constraint equations, is introduced. Application to the direct kinematics problem solution of a number of different parallel Schönflies motion robots is then developed. Certain not widely used but useful tools of algebraic geometry are explained and applied for this purpose. These constraints and tools are also applied to some special parallel robots called “double triangular” to show that the approach is flexible and universally pertinent to manipulator kinematics in reducing the complexity of some previously achieved solutions. Finally a novel two-legged Schönflies architecture is revealed to emphasize that good design is not only essential to good performance but also to easily solve kinematic models. In this example architecture, with double basally actuated legs so as to minimize moving mass, the univariate polynomial solution turns out to be simplest, i.e., of degree 2.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
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 source (direct Gemma or distilled Codex), 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".