Effect of Virtual Mass and Time Delay on the Stability of Haptic Rendering
Bibliographic record
Abstract
Virtual mass simulation is one of the recent topics in the field of haptic devices (HDs), which can alter the apparent mass of the HD. Simulating negative values of virtual mass leads to a decrease in the apparent effective mass, improving transparency but weakening stability. Positive virtual mass rendering increases the apparent mass, reduces transparency, and enhances stability. This paper analyzes the stability of a haptic device while simulating a virtual environment consisting of a mass, spring, and damper in the presence of a constant time delay. The results are closed-form equations that can predict the stability boundary for small and even large values of virtual damping and time delay. These closed-form equations demonstrate that the maximum renderable virtual mass is twice the physical mass of the HD, and the minimum value equals its negative; both occur in the case of zero time delay. Increasing the time delay reduces both the minimum and maximum values of the renderable virtual mass. The study also shows that using virtual mass can improve the maximum value of a renderable virtual spring. The equations show that, in the absence of delay, properly tuning the virtual mass and virtual damping can enlarge the maximum renderable stiffness by up to 5.8 times in theory. In the experiments under time delay, the stiffness increased by a factor of 3.5, compared to the theoretical prediction of 4.1 times. The results further reveal situations where a nonzero minimum stiffness is required for stability. All findings are validated via simulations and experiments on a dedicated test bed.
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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 | 0.004 |
| 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 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| 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".