Dynamic Balancing of Two-DOF Parallel Mechanisms Using a Counter-Mechanism
Bibliographic record
Abstract
Dynamic balancing generally involves the static balancing of a mechanism using countermasses followed by the dynamic balancing of the inertia using counter-rotations. This approach requires that the statically balanced mechanism have a constant inertia for any configuration. Two of the main drawbacks of dynamic balancing are a significant increase in mass and actuation inertia. In this paper, static balancing strategies are optimized regarding the addition of mass and actuation inertia using Lagrange multipliers. The results are optimal mass-inertia curves which are akin to Pareto curves. Optimal static balancing rules are obtained and a comparison of balancing strategies shows that relaxing the constant inertia constraint may significantly reduce the total mass and actuation inertia. Then, a counter-mechanism is introduced in order to dynamically balance a mechanism with variable inertia. The conditions for which the counter-mechanism matches the inertia of the main mechanism for any configuration are derived. The significant influence of the radius of gyration of the counter-inertias on the optimal mass-inertia curves is revealed. Additionally, the advantages of counter-mechanisms over counter-rotations are demonstrated. Finally, examples of dynamically balanced mechanisms and a prototype are presented in order to illustrate the concepts.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.000 |
| 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".