Natural Frequencies of a Manipulator with Rigid Tip Mass: the Case of Flexural-Flexuraltorsional Coupling
Bibliographic record
Abstract
The characteristic (or frequency) equation of a flexible manipulator with a rigid tip mass is derived. The manipulator is modelled as an Euler-Bemoulli beam and it permits flexural (bending) deformation in two planes and torsional deformation. The position of the centroid of the tip mass may not necessarily be coincident with the elastic axis of the beam. This is represented by the use of offset coordinates. The natural frequencies of the manipulator are obtained by solving the characteristic equation. The results are compared to the results in the literature, where possible, and also to those obtained using a commercial finite element software ANSYS. The effects of the magnitude of the tip load, offset of the tip mass centre of gravity from its point of attachment, the length of the beam and slenderness ratio on the natural frequencies are examined.
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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) | 0.001 | 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 | 0.001 |
| 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".