Mechanism Metrics
After an optimization run completes, deFlex computes a set of metrics that characterize the mechanism's structural performance. These metrics appear in the Mechanism Metrics panel (from qualification analysis) and the Test Result panel (from manual tests). This page explains what each metric means, how it is computed, and what values to look for.
Factor of safety
Definition: The ratio of the material's yield stress to the maximum Von Mises stress in the mechanism.
Factor of Safety = sigma_yield / sigma_max_von_mises
This is the single most important metric for determining whether a mechanism can safely operate at a given load. It is displayed as a prominent color-coded card in both the Mechanism Metrics and Test Result panels.
Thresholds
| FoS Value | Color | Interpretation |
|---|---|---|
| >= 1.5 | Green | Safe. The mechanism operates well within elastic limits. Comfortable margin for manufacturing variability and load uncertainty. |
| >= 1.0, < 1.5 | Orange | Marginal. The mechanism is near yield. Acceptable for prototyping or controlled environments but consider increasing FoS for production. |
| < 1.0 | Red | Unsafe. The mechanism is predicted to yield (permanently deform) at this load. Reduce the load or redesign. |
Practical guidance
- A factor of safety of 2.0 or higher is typical for mechanical components in production use.
- For compliant mechanisms that intentionally operate near yield (e.g., bistable designs), values close to 1.0 may be acceptable, but verify with nonlinear analysis.
- The metric uses Von Mises stress, which combines all stress components into a single scalar. It is the standard failure criterion for ductile metals. For brittle materials, maximum principal stress may be more relevant -- check the Stress Details section of the test results.
Mechanical advantage
Definition: The ratio of the output (grip) force to the input (applied) force.
Mechanical Advantage = F_grip / F_applied
Mechanical advantage tells you how much the mechanism amplifies or reduces force between input and output. It is computed from the analysis results by comparing the reaction force at the workpiece spring to the applied input force.
Interpretation
| Value | Meaning |
|---|---|
| > 1.0 | Force amplification. The mechanism multiplies the input force. |
| = 1.0 | No amplification. Force is transmitted without change. |
| < 1.0, > 0 | Force reduction. The mechanism trades force for displacement. |
| < 0 | Inverted output. The output moves in the opposite direction from a simple lever. |
The mechanical advantage is set as a target (J*) in the analysis settings and then measured in the analysis results. The achieved value may differ from the target depending on how well the optimizer converged.
Design limits (operating envelope)
The design limits define the safe operating range of the mechanism -- the maximum force and displacement at input and output before the material reaches yield stress.
Metrics
| Metric | Description |
|---|---|
| Max Input Displacement | Maximum displacement at the input before yield stress is reached |
| Max Output Displacement | Maximum displacement at the output before yield |
| Max Input Force | Maximum force at the input before yield |
| Max Output Force | Maximum force at the output (grip force) before yield |
How they are computed
Qualification analysis runs two simulations with incrementally increasing prescribed displacement:
- Free motion -- The mechanism deforms without a workpiece. Displacement is increased step by step until the effective stress (Von Mises) reaches the material's yield stress.
- Grip block -- The mechanism grips a rigid block. The same incremental loading is applied.
The maximum values from these two simulations define the design limits. Limits from qualification analysis are exact. If qualification analysis has not completed, estimated limits from the operating envelope analysis are shown, marked with "(est.)".
Qualification analysis status
Each phase reports a convergence status:
| Status | Meaning |
|---|---|
| Converged | Analysis completed normally |
| Yield Found | Yield stress was reached within the analysis steps |
| Yield Reached | Yield was detected but may be at a coarse step |
| Yield (Est.) | Yield was extrapolated from the available data |
| Low Confidence | Results are available but confidence is limited |
| Failed | Analysis did not converge |
| Diverged | Solver diverged (numerical instability) |
| Max Steps | Maximum number of incremental steps reached without finding yield |
| No Yield | Yield was never reached within the analysis range |
| Skipped | Qualification analysis was not run |
Stress metrics
Stress metrics come from the structural analysis and describe the internal force distribution in the mechanism.
Peak stress values
| Metric | Description |
|---|---|
| Max Von Mises | Peak equivalent stress combining all components. Primary failure criterion for ductile materials. |
| Max Principal (sigma_1) | Maximum tensile principal stress. Relevant for brittle fracture. |
| Min Principal (sigma_2) | Maximum compressive principal stress. Negative values indicate compression. |
| Max Shear (tau_max) | Maximum shear stress. Relevant for shear-dominated failure modes. |
Stress percentiles (test results only)
| Metric | Description |
|---|---|
| P50 | Median stress across all elements. Indicates typical stress level. |
| P90 | 90th percentile. Most of the mechanism is below this stress. |
| P99 | 99th percentile. Only 1% of elements exceed this. Useful for identifying if peak stress is a localized hot spot or widespread. |
If P99 is close to the maximum Von Mises stress, the peak is an isolated stress concentration. If P90 is close to the max, stress is widespread and the design may be understrength.
Strain metrics (test results only)
| Metric | Description |
|---|---|
| Max Von Mises Strain | Peak equivalent strain (dimensionless) |
| Max Principal Strain | Maximum tensile strain |
| Min Principal Strain | Maximum compressive strain (can be negative) |
| Strain Safety Factor | Yield strain divided by max Von Mises strain. Analogous to the stress-based factor of safety. |
Fatigue metrics (test results, Goodman criterion)
Fatigue metrics appear when the material has an endurance limit defined and the analysis produces cyclic loading data.
| Metric | Description |
|---|---|
| Goodman Safety Factor | Ratio indicating distance from the Goodman failure line. Values > 1 predict survival. |
| Assessment | Infinite life = safe for unlimited load cycles. Finite life = will eventually fail under repeated loading. |
| Stress Amplitude | The alternating (cyclic) component of stress at the critical element. |
| Mean Stress | The static (average) component of stress at the critical element. |
The Goodman criterion combines mean and alternating stress to predict fatigue failure. A safety factor above 1.0 means the loading point falls inside the safe region of the Goodman diagram.
Qualification analysis chart
The qualification analysis chart is an inline SVG visualization with two stacked subplots:
- Force vs. Displacement (top) -- Plots input force against prescribed displacement for both free motion and grip block phases. The slope of these curves represents the mechanism's stiffness in each mode.
- Stress vs. Displacement (bottom) -- Plots effective stress (Von Mises) against prescribed displacement. A horizontal dashed line marks the material yield stress. Where the stress curve crosses this line is the onset of yielding.
Both subplots share the same displacement axis (horizontal). The free motion curve and grip block curve are shown in different colors with a legend.
Related pages
- Test a Mechanism -- How to run tests and interpret results
- Configure Analysis Settings -- Stress constraint and mechanical advantage settings
- Select a Material -- Material properties drive factor of safety calculations
- Solver Parameters -- Complete parameter reference
- Materials Reference -- Built-in material catalog