FORCE-UNCONSTRAINED POSES OF THE 3-PRR AND 4-PRR PLANAR PARALLEL MANIPULATORS
Bibliographic record
Abstract
Force-unconstrained (singular) poses of the 3-PRR planar parallel manipulator (PPM), where the underscore indicates the actuated joint, and the 4-PRR, a redundant PPM with an additional actuated branch, are presented. The solution of these problems is based upon concepts of reciprocal screw quantities and kinematic analysis. In general, non-redundant PPMs such as the 3-PRR are known to have two orders of infinity of force-unconstrained poses, i.e., a three-variable polynomial in terms of the task-space variables (position and orientation of the mobile platform). The inclusion of redundant branches eliminates one order of infinity of force-unconstrained configurations for every actuated branch beyond three. The geometric identification of force-unconstrained poses is carried out by assuming one variable for each order of infinity. In order to simplify the algebraic procedure of these problems, the assumed or “free” variables are considered to be joint displacements. For both manipulators, an effective elimination technique is adopted. For the 3-PRR, the roots of a 6th-order polynomial determine the force-unconstrained poses, i.e., surfaces in a three dimensional space defined by the task-space variables. For the 4-PRR, a 64th-order polynomial determines curves of force-unconstrained poses in the same dimensional space.
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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) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 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) | 0.006 | 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".