Actuator Backlash and Position Error Budget
Estimate worst-case position error, RSS random error, and bidirectional deadband from backlash, lead error, feedback resolution, and compliance shift. The result is a preliminary engineering estimate, not a product rating or safety approval.
Calculate position error from backlash
Enter the measured or assumed inputs in one unit system. The calculator converts to SI internally, evaluates the stated model, and displays the result in the selected unit system.
Engineering visualizer
Schematic, not to scale. The drawing updates from the production calculation engine and labels the main outputs.
Calculator by FIRGELLI Automations.
Embed this calculator
When embedded on another page, the calculator shows only the working tool. FIRGELLI attribution, the visualizer, and the calculation-error report remain available.
b = 0.20 mm, lead error 0.10 mm, feedback resolution 0.05 mm, compliance shift 0.15 mm. E_wc = 0.50 mm. E_rss = 0.187 mm (page model: RSS of lead error, resolution, and compliance only). Deadband D = 0.40 mm. RSS is not worst-case; 0.50 mm is not a product rating.
Related checks: open-loop drift and skew calculator, Super Duty actuators, and micro actuators.
What This Calculator Calculates
What does actuator backlash and position error budget mean? This quantity describes one specific part of the actuator design problem. It should be read as a model output, not as a complete product selection rule.
When Not To Use This Calculator
When should I not use the actuator backlash and position error budget model? Do not use this model when the inputs are unknown, the mechanism is outside the stated boundary, or the decision depends on manufacturer ratings, fatigue, shock, compliance, or regulated safety approval.
Engineering model and calculation details
Estimate worst-case position error, RSS random error, and bidirectional deadband from backlash, lead error, feedback resolution, and compliance shift.
The page separates the calculator result from product selection. It explains the inputs, limitations, interpretation, and next design checks so the result is not mistaken for a complete actuator rating.
Governing equations
| Quantity | Equation | Model meaning |
|---|---|---|
| Worst-case position error estimate | E_wc = b + e_l + r + c |
Calculates worst-case position error estimate for the stated simplified model. |
| RSS random-position error estimate | E_rss = sqrt(e_l^2 + r^2 + c^2) |
Calculates rss random-position error estimate for the stated simplified model. |
| Bidirectional backlash deadband | D = 2b |
Calculates bidirectional backlash deadband for the stated simplified model. |
Variables and canonical units
| Symbol | Variable | SI unit | Domain |
|---|---|---|---|
backlash |
Measured backlash | m | finite engineering value in the documented model domain |
lead_error |
Lead error allowance | m | finite engineering value in the documented model domain |
feedback_resolution |
Feedback resolution | m | finite engineering value in the documented model domain |
compliance_shift |
Mounting compliance shift | m | finite engineering value in the documented model domain |
worst_case_error |
Worst-case position error estimate | m | finite result from valid inputs |
rss_random_error |
RSS random-position error estimate | m | finite result from valid inputs |
bidirectional_deadband |
Bidirectional backlash deadband | m | finite result from valid inputs |
Assumptions and boundary conditions
- Inputs represent one consistent operating condition.
- The model uses the simplified boundary stated on the page.
- The model begins and ends at the user-defined actuator or mechanism boundary.
Limitations and omitted checks
- The result depends on user-entered values and simplified boundary conditions.
- The model does not replace FIRGELLI product data, installation review, endurance testing, or a qualified engineering review.
- Shock, fatigue, misalignment, mounting strength, and controller behavior may govern before the calculated value.
Worked example
b = 0.20 mm, lead error 0.10 mm, feedback resolution 0.05 mm, compliance shift 0.15 mm. E_wc = 0.50 mm. E_rss = 0.187 mm (page model: RSS of lead error, resolution, and compliance only). Deadband D = 0.40 mm. RSS is not worst-case; 0.50 mm is not a product rating.
Related checks: open-loop drift and skew calculator, Super Duty actuators, and micro actuators.
What this model evaluates
| Mode or effect | Status | Disclosure |
|---|---|---|
| calculated quantity | evaluated | The named output is evaluated for the stated model. |
| manufacturer rating | not evaluated | The result is not a manufacturer product rating. |
| installation detail | not evaluated | Mounting, alignment, shock, fatigue, and environment require separate review. |
Common mistakes
- Treating a simplified estimate as a manufacturer rating.
- Mixing units or entering values measured at a different operating point.
- Ignoring mounting, alignment, shock, duty cycle, or controller limitations.
- Failing to compare the result with the next logical FIRGELLI design check.
Engineering references
- Barry N. Taylor and Chris E. Kuyatt. Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results. National Institute of Standards and Technology, NIST Technical Note 1297. Supports: Root-sum-square treatment of independent standard uncertainty components.. Accessed 2026-07-28. Source.
- National Institute of Standards and Technology. NIST Guide to the SI. National Institute of Standards and Technology, Accessed 2026. Supports: SI unit definitions and unit-consistent engineering calculation display.. Accessed 2026-07-28. Source.
Author, validation, and review status
Author: Robbie Dickson
Author profile: Robbie Dickson prepares FIRGELLI actuator education and calculator content for product users and engineering teams.
Engineering model type: Backlash-centered actuator position error budget
Validation: The production JavaScript engine is compared with a separately written Python oracle across known-answer, SI/imperial-equivalent, boundary, invalid-input, and randomized cases.
Questions about this calculator or found an error? Message our engineering team.
