Accuracy, Repeatability & ISO 230-2

Stage Building Axioms

Ultimate Truths

  • A Stage Can Never Be Stiff Enough
  • Servo & Mechanical Tune Must Match
  • Below 1 Micron, Everything Turns to Rubber
  • Positioning Problems Are Never What They Appear to Be


Total Sum of Errors in Multi-axis Systems Is Always Greater Than the Addition of Errors in Each Axis.

“Point of Interest” Is Never on One Plane Only.

Demystifying Terminology of Specifications

  • Accuracy
  • Repeatability
  • Resolution
  • Orthogonality

Axis Diagram

Position Accuracy   

Maximum Observed Difference in Distance Between Move Instruction and Actual Position - Measured by the Laser Interferometer.

positional accuracy


Range of Difference in Position Observed When Returning to a Targeted Position.

With All External Conditions Equal, to What Degree Does the Positioner Provide the Same Result for a Fixed Input. a.k.a. Precision

unidirectional accuracybidirectional accuracyprecisin

Straightness, Flatness

Bandwidth of Transversal Movement Observed Deviating From Ideal Linear Trajectory.

Perfect Stage Would Have 0.0 μm (nm) Flatness/Straightness Error.

The Transverse Position Deviations Along an Axis, Which Fall Between Two Imaginary Parallel Planes That Run Along This Axis.


Angular Errors

Measures the Ability of the Moving Component to Change Orientation Around The 3 Cartesian Coordinate Axes.

Angular Errors Reported in Arc-Second , milli-radians or micro-radians.

Angular Errors (YPR)

  • Yaw
  • Pitch
  • Roll

angular errors

YPR impact on Straightness/Flatness

Because We Are Positioning Extended Bodies YPR Errors Are a Component of Observed Straightness and Flatness Performance.

YPR Also Manifests as “Apparent Error” in Orthogonality.

ypr impact


Cartesian Systems (XYZ),  Orthogonality Describes “Squareness” Between Architectural Axes Is a Major Component in “Point-of-interest” Positioning.

Reported by Angular Deviation, From Ideal in Degrees, Micro-radians  or Arc Seconds.

Arc seconds Degrees ø Linear Deviation (µm) = L * Sin ø
100mm 150mm 200mm 300mm
5 0.001389 2.4 3.6 4.8 7.3
10 0.002777 4.8 7.2 9.6 14.6
15 0.004167 7.2 10.9 14.5 21.8
20 0.005556 9.7 14.5 19.4 29.1
25 0.006944 12.1 18.2 24.2 36.4


The Measure of Deformation (Elastic) in the Translator under the Effect of Gravity, Payload or Inertia.


  • Bearing Stiffness – Ball, Needle, Cross Roller, Air
  • Pre-load Level
  • Structural Deformation
  • Shifting Payloads & Changing Force Vectors

Other Mechanical Considerations


  • Load
  • Moments
  • Inertia

Temperature & Environment

  • Temp Gradient
  • Air Flow
  • Noise (Acoustic, Electric)

Offset (Abbé) Error

  • Distance From Bearing Plane or Encoder Head to Point of Interest (POI)

Structural Errors

  • Integrity of Parts & Components
  • Precision
  • Mechanical Junctions

Control Error

Encoder Linearity Resolution

  • Correction
  • Linear Vs. Angular

Controller Frequency (Counter Clock)

  • Resolution Vs. Velocity
  • Servo Update Rate


  • Move & Settle
  • Jitter
  • CV
  • Error Bandwidth

Error Mapping - LIBEC

  • Measure Coordinate Based  Errors
  • Create “Look-up Table” for the Motion Controller
  • Controller Makes Correction by Adding or Subtracting lut-values at Each Position Position


ISO-230-2 Aspects

All tests must be performed in a temperature controlled environment (20°C, 68°F). This provides a standard reference temperature. Changing the environmental temperature causes thermal expansion and contraction, which can cause significant positioning errors (approximately ± 11.7 microns per meter per degree C).

All tests must include a full warm up cycle that simulates actual operating conditions prior to testing. Some manufacturers purposely omit a warm up cycle to overstate the accuracy of their systems because omitting a warm up cycle prevents the thermal expansion of the drive train caused by frictional heating.

All tests clearly specify unidirectional (approaching target points from one direction only) and bi-directional approaching target points from both directions) positioning performance with statistical error bands.

Linear axes require at least 5 target points per meter. It should be measured at random intervals to avoid masking periodic errors (e.g. a metric drive system has target points spaced in inches).
Rotary axes require at least 3 target points per 90 degrees.

Each test requires at least 5 trials per target point per direction of approach. Utilizing multiple trials per target point allows statistical error bands to be calculated. According to the current ISO 230-2 standard, the typical error band is ± 2 times the statistical estimator (standard deviation).

Application vs. Specification


  • Straightness, Flatness, YPR
  • Velocity Jitter
  • Repeatability


  • Accuracy, Repeatability
  • Move & Settle
  • Accel l- Decel


  • Stiffness
  • Repeatability


  • In-position Stability
  • Fidelity
  • No Dead Band
  • No Hysterisis

About Us

NUTEC Mechatronic Systems' positioning is based on perfection. Engineering and design are focused on details and balanced design, flawless fabrication and precision machining to exacting standards and consistent quality.

Nutec Components
81 Jefryn Boulevard East
Deer Park, NY 11729

Working Hours

Call us or email us for formal quotations. We can be reached during the week at these times.

  1. Monday-Friday: 7:30am to 4:00pm
  2. Weekends: Closed

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