Exact Path Synthesis of RCCC Linkages for a Maximum of Nine Prescribed Positions
Bibliographic record
Abstract
Abstract This article addresses the path synthesis of RCCC (revolute-cylindrical-cylindrical-cylindrical) linkages, a problem that has not received due attention in the literature. Compared with planar and spherical four-bar linkages, a RCCC linkage has many more design parameters, which lead to a complex formulation of the path synthesis problem and, consequently, to a quite challenging system of algebraic equations. In this article, the problem is solved with a novel formulation of path synthesis for visiting a number of prescribed positions. This is achieved by means of an alternative coordinate system, which allows point coordinates to be expressed with the aid of two vectors fixed to the same body. By this means, the rotation matrix used to represent the coupler link attitude is obviated. The synthesis equations are then formulated in a simple form. Our formulation confirms that path synthesis admits exact solutions for up to nine prescribed positions, which proves a landmark claim submitted by Burmester. Examples are included to demonstrate the path synthesis procedure with the method thus developed.
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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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 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".