Uncertainty Singularity Analysis of Parallel Manipulators Based on the Instability Analysis of Structures
Bibliographic record
Abstract
When all the inputs of a parallel manipulator (PM) are locked, the manipulator is usually turned into a structure. When an uncertainty singularity occurs for a PM, the latter structure is unstable or, in other words, it may undergo infinitesimal or finite motion. Hence, the investigation of the uncertainty singularities of a PM can be reduced to the instability analysis of its corresponding structure. PMs with a 3-XS structure cover a broad class of PMs. A 3-XS structure is composed of two platforms connected by three XS serial chains in parallel. Here, X and S denote a generalized joint with one degree of freedom (DOF) and a spherical joint, respectively. An X joint can take the form of any kinematic joint with one DOF, such as a revolute joint or a prismatic joint, or the form of any closed kinematic chain with one DOF, such as a parallelogram. In this paper, the instability condition of the 3-XS structure is derived by simply differentiating its constraint equations. The geometric interpretation of the instability condition is revealed using a method based on linear algebra. The uncertainty singularity analysis of the 6-3 Gough-Stewart PM is performed to illustrate the application and efficiency of the proposed approach. Several specific cases of the 6-3 Gough-Stewart PM with singularity surfaces of reduced degree are proposed. The geometric interpretation of the singularity conditions is also given for some of the specific cases.
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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 | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".