Solving the Forward Kinematic Problem of 4-DOF Parallel Mechanisms (3T1R) With Identical Limb Structures and Revolute Actuators Using the Linear Implicitization Algorithm
Bibliographic record
Abstract
This paper investigates the forward kinematic problem of 4-DOF parallel mechanisms with revolute actuators and identical limb structures and performing a three translations and one rotation motion pattern. The general architecture of all the mechanisms under study in this paper originates from the type synthesis performed for 4-DOF parallel mechanisms with identical limb structures. The mathematical framework used in this paper is based on algebraic geometry where the forward kinematics and constraint expressions are explored in a seven-dimensional kinematic space by means of the so-called Study parameters (dual quaternions). In this paper, the algorithm applied for obtaining the forward kinematic and constraint expressions is based on a recent and novel approach, called linear implicitization algorithm, which is based on solving systematically a system of linear equations to determine the coefficients of the non-linear constraint equations. This paper presents also an example of a 4-DOF parallel mechanism.
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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 | 0.000 | 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 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".