A Real-Time Method for Solving the Forward Kinematics of a Tripod With Fixed-Length Legs
Bibliographic record
Abstract
This paper presents a real-time method for solving the forward kinematics of a tripod with fixed-length legs. The basic idea is to model the problem at hand based on a spatial four-bar linkage through which three sliding legs can be interrelated by choosing one link as a driving variable and other two links as driven variables. As a result, the original multivariable nonlinear problem with three variables can be reduced to one variable problem. A complete approach is provided to solve the unitary nonlinear programing problem. This includes a method for solving the implicit functions in terms of the driving and driven variables, and an approximation method for selecting an initial value leading to a fast solution. The simulation results show that (i) the method is effective, (ii) can reach very accurate results within five iterations for an error bound of 10−10, and (iii) numerically very stable. The experiment results show that the proposed forward kinematic method is fast enough to be implemented in real time to provide an accurate prediction of the tool pose from the joint encoder measurement.
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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) | 0.000 | 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 | 0.001 | 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".