Jacobian Matrix of General Parallel and Hybrid Mechanisms With Rigid and Flexible Links: A Software-Oriented Approach
Bibliographic record
Abstract
This paper first presents a procedure for the determination of the Jacobian matrix exact to the first order of general parallel manipulators (GPMs) with rigid and flexible links. The formulation is then extended to the class of general hybrid parallel manipulators (GHPMs) with rigid and flexible links. The acronym GHPM refers to as a parallel mechanism in which the base is connected to the platform by serial subchains and/or hybrid subchains containing closed-chain modules, and with an arbitrarily located subset of actuated joints. The model of each flexible link includes bending in two perpendicular directions as well as torsion around its longitudinal axis. The proposed procedures involve the symbolic generation of a set of augmented matrices combined with a numerical postprocessing and are believed to be especially dedicated to the automatic software generation of the instantaneous kinematic equations of most types of complex closed-chain mechanisms, including all types of in-parallel and hybrid parallel manipulators, cooperative robots, and multifingered hands. A hybrid manipulator, pertaining to the class of GHPMs, is finally considered as an example.
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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 | 0.001 |
| 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 | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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".