A direct kinematic computation algorithm for all planar 3-legged platforms /
Bibliographic record
Abstract
An analysis and comprehensive solution to the direct kinematics problem (DK) of all planar 3-legged platforms with lower pairs, called general planar Stewart-Gough platform (PSGP), is presented. There are 10 types of PSGP DK problem formulation including those with mixed leg architecture. Planar kinematic mapping expresses pole position and rotation angle of a planar displacement as a point in 3-dimensional projective space represented by 4 homogeneous coordinates. This provides a universal tool for kinematic analysis. Its application will be demonstrated in the derivation of a general algorithm for planar DK. For each type of PSGP, the problem is reduced to a 6th order univariate polynomial whose roots reveal all solutions. An example of a PSGP with 6 real assembly configurations is presented. Furthermore, this algorithm was implemented and tested exhaustively. A complete self-contained version, coded in C, is available at http://www.cim.mcgill.ca/~paul/. It should be easy to customize and adapt to any given real time micro-controller application.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.019 | 0.007 |
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".