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 distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".