Numerical Versus Analytical Direct Kinematics in a Novel 4-DOF Parallel Robot Designed for Digital Metrology
Bibliographic record
Abstract
Direct (forward) kinematic solution of the parallel robots is a challenging task for pure pose determination of the movable platform, which is crucial either in designing of the robot or its controlling. The availability of this solution is more critical especially in the case of using robot as a coordinate measuring machine (CMM). Solving direct kinematics (DK) problem of parallel robots is complicated as it is engaged with highly coupled nonlinear equations that are difficult to solve analytically to obtain exact answer. Hence in order to solve the mentioned problem, various approaches including empirical solutions e.g. using auxiliary sensors on the robot, neural network, and numerical methods are utilized. Meanwhile, numerical methods as the most cost-effective approach can acquire one unique accurate answer in a reasonable time. The aim of this article is to solve DK of a novel CMM parallel robot, which has three translational motions and a rotational around horizontal axis, using both analytical and numerical (Newton-Raphson scheme) approach along with comparing the results. After explaining the implementation procedure of methods according to the configuration of this robot, the results of simulations for both methods are presented and compared to each other. Moreover, inverse kinematics and direct kinematics are analyzed for the mentioned mechanism thoroughly. Results show that although analytical method gives more accurate answer especially for horizontal positions, numerical method solves the problem faster and also with acceptable accuracy.
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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 | 0.000 |
| 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) | 0.001 | 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".