Optimization of a Four-bar Spherical Homokinetic Linkage with Minimum Design Error
Bibliographic record
Abstract
Motion transmission between two shafts with intersecting axes at right angles is a recurrent problem in machine design. The mechanism should be able to accom- modate the given layout of the driver and the driven shafts. Further, a constant velocity ratio, in our case 1:1, between the input and the output velocities is usually desired to eas e the control algorithm. In this paper, a four-bar spherical linkage is optimally designed to transmit motion between two orthogonal intersecting shafts with an approximately constant 1:1 velocity ratio through a120 ◦ rotation of its in- put link. This is done via minimizing the root-mean-square value of the design error at a sample of input-output values; the error is defined as the residue of synthesis equation at the prescribed set of input values. Optimization is reporte d here by means of a shifting of the zeros of the input and the output dials. To obtain the global minimum of this op- timization problem, its first-order normality conditions a re formulated. Eliminating all unknowns except for the two shift angles yields a set of two nonlinear equations in two unknowns, whose real solutions are found by a semigraph- ical approach.
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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 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".