The dynamics of parallel Schönflies motion generators: The case of a two-limb system
Bibliographic record
Abstract
The formulation of the mathematical model governing the dynamics of parallel Schönflies motion generators (SMGs) is the subject of this paper. These are robotic systems intended to produce motions that entail displacements of the Schönflies subgroup of rigid-body displacements. Such motions are representative of those produced by the serial robots termed SCARA, which involve three independent translations and one rotation about an axis of fixed direction. The main features of SMGs are illustrated with the aid of the McGill Schönflies motion generator. This robot is composed of two limbs, each being a four-joint RΠΠR - R representing a revolute, Π a Π joint, or a parallelogram linkage - kinematic chain, with only two joints actuated. One important feature of the McGill SMG is its mass distribution, as its moving parts account for about 10 per cent of the mass of its drive units, which are (a) fixed to the robot frame and (b) the only steel parts of the whole robot. Moreover, its joints account for roughly 10 per cent of the total mass of its moving parts, fabricated from aluminium, which justifies neglecting the joint inertia in the mathematical model. This feature calls for a formulation of the model in question in terms of the motor displacements, rather than the joint displacements, as the generalized coordinates of the model. Furthermore, in order to derive the model, the robot is decomposed into two subsystems, the drive and the linkage, the drive being decomposed, in turn, into two subsubsystems, the epicyclic gear train and the right-angled gearbox. The robot kinematics is first derived and then the dynamics model is formulated by means of the natural orthogonal complement. In the framework of this methodology, the inertia and what are called the Coriolis matrices of the mathematical model are additive, in the sense that they can be computed as the sum of the contributions of the different subsystems and subsubsystems of a given mechanical system. The contributions of the subsystems and subsubsystems, in turn, can be computed as the sum of the contributions of the individual moving parts of these. Some general results applicable to all SMGs are derived, which leads to the simplification of the mathematical model of such systems.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
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".