A closed-form solution to the direct kinematics of nearly general parallel manipulators with optimally located three linear extra sensors
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Bibliographic record
Abstract
This paper presents a new closed-form solution of the direct kinematic problem of nearly general parallel manipulators by using three linear extra sensors. The sensors are disposed at optimal location, connecting the planar base and the planar mobile platform at distinct points. The basic idea is to use the coordinates of the three distinct anchor points of the extra sensors on the mobile platform to represent the pose of the mobile platform. Thus, the extra sensory data enable one to reduce the problem to the solution of a system of six linear equations in six of the nine generalized coordinates. The other three coordinates are obtained directly from the extra sensory data. In addition, an optimal location of the extra sensors is sought by minimizing the condition number of the linear equations for the least sensitivity to sensor measurement errors. A numerical example is presented for optimal sensor location and the error behavior of the proposed solution scheme by computer simulation.
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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 | 0.000 | 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) | 0.000 | 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 it