Robot Repeatability Estimate Calculator

Work out robot repeatability estimate instantly with clear inputs, formula shown and shareable results.

About Robot Repeatability Estimate Calculator

Repeatability is dominated by transmission lost motion, not encoder resolution. Combining the independent error sources in quadrature (root sum of squares) is the standard approach, and it usually shows that halving the encoder count changes almost nothing while eliminating backlash changes everything.

Formula

Error budget

total = sqrt(encoder^2 + lost motion^2 + drift^2), each converted to a tool-point distance

Worked example

With the default values below, Robot Repeatability Estimate Calculator returns Estimated repeatability of 0.3515. Change any input above and every figure here is recalculated in your browser.

Inputs used

Encoder resolution at the joint: 0.002 °
Arm length: 800 mm
Transmission lost motion: 1.5 arcmin
Thermal and structural drift: 0.03 mm

Results

Estimated repeatability: 0.3515 mm
Encoder contribution: 0.02793 mm
Lost motion contribution: 0.34907 mm
Precision class: Coarse handling only

Step by step

1Values used
2Error budget
3Estimated repeatability= 0.3515 mm
4Encoder contribution= 0.02793 mm
5Lost motion contribution= 0.34907 mm
6Precision class= Coarse handling only

Assumptions and limits

The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 5 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Why combine errors in quadrature rather than adding them?

Independent random errors rarely peak together, so root sum of squares gives a realistic figure while simple addition gives a worst case that is far too pessimistic.

Is repeatability the same as accuracy?

No. Repeatability is returning to the same place; accuracy is reaching the commanded place. Accuracy is typically several times worse and can be improved by calibration.