Kinematically Redundant Spatial Parallel Mechanisms for Singularity Avoidance and Large Orientational Workspace
Bibliographic record
Abstract
This paper introduces a novel architecture of kinematically redundant parallel mechanisms. This family of mechanisms is similar to the well-known Gough-Stewart platform, and it retains its advantages, i.e., the members connecting the base to the moving platform are only subjected to tensile/compressive loads. The proposed architecture exploits kinematic redundancy to avoid singularities and extend the rotational workspace. The novel kinematic architecture is described, and the associated kinematic relationships are developed. Based on the derivation of the Jacobian matrices, it is shown that the singularities of this type of mechanism are governed by the orientation of passive links connecting the redundant legs to the platform. Grassmann geometry is then used to demonstrate that, given some simple geometric assumptions on the architecture, all singularities can be avoided by exploiting the kinematic redundancy. The orientational workspace is then discussed, and a graphical representation is provided for an example architecture comprising nine actuators, whose orientational workspace is shown to be very large. The translational workspace is also studied. Example trajectories are given in order to illustrate the capabilities of the mechanism to produce very large rotation angles without encountering singularities. Computer animations of the trajectories are provided in a multimedia extension of the paper.
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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) | 0.001 | 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 | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| 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".