Discrete Kinematic Geometry in Testing Axes of Rotation of Spindles
Bibliographic record
Abstract
The accuracy of actual motion of the spindle of a machine tool, a key performance index, is measured at a series of positions, and evaluated using a discrete kinematic geometry model. The kinematic geometry model, or more precisely a novel mechanism, is presented for the first time in this paper and validated using an apparatus consisting of a spindle, an artifact with double master ball and five displacement sensors as per ASME codes and standards [1]. The six kinematic parameters of the spindle with a single rotor — three translations and three rotations are obtained using the novel mechanism and the measurements. The theory of discrete kinematic geometry is employed to reveal the intrinsic properties of the trajectories traced by the characteristic lines of the rotor. In order to avoid the influences caused by the locations and directions of the measuring coordinate systems, the invariants of a discrete line-trajectory, particularly the spherical image curve and the striction curve [2], are introduced to deal with the discrete measurements. The global invariants, the approximated moving axis and the approximated fixed axis of the rotor in the error motion, independent of the assembling position of the double master balls on the rotor, are proposed to evaluate the rotational accuracy of spindles. The discrete kinematic geometry provides a new perspective and a theoretical base for assessing the accuracy of the spindle motion.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| 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) | 0.000 | 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 teacher head, 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".