Quantitative Dexterous Workspace Comparison of Serial and Parallel Planar Mechanisms
Bibliographic record
Abstract
Through either method of obtaining a constrained dimensionally homogeneous Jacobian matrix (proposed by (Gosselin, 1992) or by (Pond & Carretero, 2006)) for planar mechanisms, a choice exists on which of the potential six Cartesian velocity components on the end effector be used to define the task space velocity variables. The choice has an influence on the resulting Jacobian matrix and therefore its condition number and singular values. Without constraining the Jacobian matrix, the condition number was demonstrated to be essentially meaningless, as in (Kim & Ryu, 2003). In terms of measuring dexterity, the constrained dimensionally homogeneous Jacobian matrices (J'P) are superior to the screw based Jacobian matrix (J) in that they are dimensionally consistent. Furthermore, the six matrices (J'P) are superior to the 3 ? 6 dimensionally homogeneous matrix (J') in that they are constrained, and therefore provide true dexterous information. The condition number and singular values of each of the six matrices (J'P) are different for any given pose. Therefore, dexterity measures involving only one of the six (J'P) matrices are potentially bias. Four potential strategies for dexterity measurement have been proposed based on the condition number and/or singular values of the Jacobian matrices obtained in all six cases. Each measure has a distinct physical meaning, as discussed. In sum, the Jacobian matrix formulation presented in this chapter allows, for the first time, to quantitatively compare different mechanism architectures with complex degrees of freedom in terms of dexterity. Moreover, as illustrated in this chapter, the formulation is not limited to parallel manipulators as it can also be used to quantitatively compare the dexterity of different architectures as long as the end effector is represented by an equivalent set of points. Quantitative dexterity comparisons will allow robot designers to better select proper mechanisms for specific tasks.
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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 | 0.003 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.003 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.003 | 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".