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 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 | 0.000 | 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".