A Constrained Lagrange Formulation of Multilink Planar Flexible Manipulator
Bibliographic record
Abstract
In this article, the closed-form dynamic equations of planar flexible link manipulators (FLMs), with revolute joints and constant cross sections, are derived combining Lagrange’s equations and the assumed mode shape method. To overcome the lengthy and complicated derivative calculation of the Lagrangian function of a FLM, these computations are done only once for a single flexible link manipulator with a moving base (SFLMB). Employing the Lagrange multipliers and the dynamic equations of the SFLMB, the equations of motion of the FLM are derived in terms of the dependent generalized coordinates. To obtain the closed-form dynamic equations of the FLM in terms of the independent generalized coordinates, the natural orthogonal complement of the Jacobian constraint matrix, which is associated with the velocity constraints in the linear homogeneous form, is used. To verify the proposed closed-form dynamic model, the simulation results obtained from the model were compared with the results of the full nonlinear finite element analysis. These comparisons showed sound agreement. One of the main advantages of this approach is that the derived dynamic model can be used for the model based end-effector control and the vibration suppression of planar FLMs.
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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 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 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".