Kinematic analysis of spherical double-triangular parallel manipulators
Bibliographic record
Abstract
Parallel mechanisms are being introduced as platforms for machine tools, where stiffness and vibration supression is vital. A novel parallel architecture, called double triangular (DeltaDelta), was proposed and studied in depth by Daniali in anticipation of applications which require fast and precise motion. However, Daniali failed to find the minimal solution to the spherical DeltaDelta parallel manipulator, which he suspected is quadratic. Here, projective geometry and Grassmannian incidence relationships are used to unify the method of direct kinematic analysis (DKP) of two types of three degree-of-freedom manipulators, viz., the planar and spherical versions of DeltaDeltaPM, while preserving the geometric meaning of the solution. This method was to demonstrate for the first time that SDeltaDeltaPM can have only two real assembly modes; however, the minimum solution is found to be of order eight. An example is included to show that SDeltaDeltaPM can actually possess eight real assembly modes. Only two of the eight real poses lie within the workspace, while the other six arise due to a quadruple triangular tesselation of the sphere. Furthermore, a method to solve the general three-points-on-three-lines problem along with application to statics and spatial parallel manipulators is presented.
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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 | 0.000 |
| 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 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.003 | 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 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".