Periodic Trajectory Planning Beyond the Static Workspace for 6-DOF Cable-Suspended Parallel Robots
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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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 | 0.000 |
| 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) | 0.002 | 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".