A New Method for Dynamic Modeling of Flexible-Link Flexible-Joint Manipulators
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Bibliographic record
Abstract
In this article, by combining the assumed mode shape method and the Lagrange’s equations, a new and efficient method is introduced to obtain a closed-form finite dimensional dynamic model for planar Flexible-link Flexible-joint Manipulators (FFs). To derive the dynamic model, this new method separates (disassembles) a FF into two subsystems. The first subsystem is the counterpart of the FF but without joints’ flexibilities and rotors’ mass moment of inertias; this subsystem is referred to as a Flexible-link Rigid-joint manipulator (FR). The second subsystem has the joints’ flexibilities and rotors’ mass moment of inertias, which are excluded from the FR; this subsystem is called Flexible-Inertia entities (FI). While the method proposed here employs the Lagrange’s equations, it neither requires the derivation of the lengthy Lagrangian function nor its complex derivative calculations. This new method only requires the Lagrangain function evaluation and its derivative calculations for a Single Flexible link manipulator on a Moving base (SFM). By using the dynamic model of a SFM and the Lagrange multipliers, the dynamic model of the FR is first obtained in terms of the dependent generalized coordinates. This dynamic model is then projected into the tangent space of the constraint manifold by the use of the natural orthogonal complement of the Jacobian constraint matrix. Therefore, the dynamic model of the FR is obtained in terms of the independent generalized coordinates and without the Lagrange multipliers. Finally, the joints’ flexibilities and rotors’ mass moment of inertias, which are included in the FI, are added to the dynamic model of the FR and a closed-form dynamic model for the FF is derived. To verify this new method, the results of simulation examples, which are obtained from the proposed method, are compared with those of a full-nonlinear finite element analysis, where the comparisons indicate sound agreement
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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 it