NUMERICAL ANALYSIS OF DISPLACEMENTS IN SPATIAL MECHANISMS WITH SPHERICAL JOINTS UTILIZING AN EXTENDED D-H NOTATION
Bibliographic record
Abstract
Spherical joints consist of a pair of concave and convex spherical surfaces engaged in such a way as to prevent translational motion of the ball and socket whilst simultaneously allowing three degrees of rotational freedom. The kinematics of spatial mechanisms comprising links and joints are commonly analyzed using the Denavit-Hartenberg (D-H) notation. However, whilst this method allows the kinematics of mechanisms containing prismatic, revolute, helical and cylindrical joints to be explicitly defined, it cannot be directly applied to mechanical systems containing spherical pairs. Accordingly, this paper proposes an extended D-H notation which allows the independent parameters of any spatial mechanism, including one with spherical pairs, to be derived for analysis and synthesis purposes. The validity of the proposed notation is demonstrated via its application to the analysis of mechanisms containing revolute (R), spherical (S), cylindrical (C) and prismatic (P) joints. The results confirm the viability of the extended D-H notation as a means of analyzing the displacements of mechanical systems containing kinematic chains such as RSCR, RSCP, CSSR and CSSP.
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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 | 0.001 |
| 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".