Periodic Trajectory Planning Beyond the Static Workspace for 6-DOF Cable-Suspended Parallel Robots
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Bibliographic record
Abstract
This paper proposes a dynamic trajectory planning technique for six-degree-of-freedom (6-DOF) cable-suspended parallel robots (CSPRs). First, a passive mechanical system that is equivalent to the CSPR is introduced to provide insight and facilitate the design of trajectories that can extend beyond the robot's static workspace. The tilt-and-torsion angle convention is used to develop the mathematical model and impose restrictions for the rotational component of the trajectories. The dynamic differential equations that govern the translational component of the trajectories are shown to become linear under some conditions. Natural frequencies of an equivalent passive linear system of constant-stiffness springs are, thus, obtained and the set of linear differential equations associated with this system is integrated to produce a general solution for natural, periodic trajectories. This approach is used to produce pure translation trajectories and more complex motion that includes changes in position and orientation. An experimental implementation is also presented using a 6-DOF prototype and a supplementary video file is included to demonstrate the results.
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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 | 0.001 | 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