Continuous Approximate Kinematic Synthesis of Planar, Spherical, and Spatial Four-bar Function Generating Mechanisms
Bibliographic record
Abstract
The focus of this work is on synthesising kinematic input-output (IO) function generators, specifically in the context of single degree of freedom four-bar linkages.The synthesis process typically involves minimising two key metrics: design error and structural error.Design error minimisation aims to reduce the arithmetic residual of the synthesis equation for the four-bar linkage, while structural error minimisation focuses on minimising the difference between prescribed and generated output parameters.The latter is crucial for real-world performance evaluation as it directly impacts the physical performance of the linkage, albeit requiring computationally intensive non-linear optimisation algorithms.The objective of the research is to integrate the algebraic input-output equation across the input angle range to avoid explicit solution of the non-linear structural error optimisation problem.This approach, termed continuous approximate algebraic inputoutput synthesis, aims to expand the dataset used for kinematic synthesis to infinity by minimising the residual of the dot product of two arrays containing linkage geometry and desired input-output function information.Continuous approximate algebraic input-output synthesis effectively and simultaneously achieves both design and structural error minimisation by extending the dataset cardinality to infinitely many points, while still functioning as a linear least squares optimisation.Comparisons with traditional non-linear structural error synthesis techniques demonstrates that continuous approximate algebraic input-output synthesis generates structural error minimised linkages with reduced errors between desired and synthesised functions.In addition to its computational efficiency, continuous approximate algebraic input-output synthesis is capable of producing improved results compared with classical problems within function generator synthesis, while also enabling combined type and dimensional synthesis, eliminating the need to define the linkage type beforehand.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.000 |
| 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".