Kinematics and Singularity Analysis of a Novel Type of 3-CRR 3-DOF Translational Parallel Manipulator
Bibliographic record
Abstract
A new three-degrees-of-freedom (3-DOF) translational parallel manipulator (TPM) with linear actuators, i.e., 3-CRR TPM, is first proposed. The rotation singularity analysis, the inverse kinematics, the forward kinematics, and the kinematic singularity analysis of the 3-CRR TPM are then performed. The analysis shows that the proposed TPM has the following kinematic merits over previous TPMs. (1) The forward displacement analysis can be performed by solving a set of linear equations. (2) The Jacobian matrix of the TPM is constant. The inverse of the Jacobian matrix can be pre-calculated, and there is no need to calculate repeatedly the inverse of the Jacobian matrix in performing the forward displacement analysis and forward velocity analysis. (3) There is no rotation singularity. (4) There is no uncertainty singularity. (5) The TPM has a fewer number of links or joints. The geometric condition for a 3-CRR TPM to be isotropic is also revealed. Two additional kinematic merits exist for the isotropic 3-CRR TPM. The first is that an isotropic 3-CRR TPM is isotropic in its whole workspace. The second is that no calculation is needed in order to pre-determine the inverse of the Jacobian matrix. Finally, preliminary design considerations are presented.
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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) | 0.000 | 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 | 0.001 |
| Open science | 0.001 | 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".