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Calibration Curves: Linear Least Squares01:20

Calibration Curves: Linear Least Squares

A calibration curve is a plot of the instrument's response against a series of known concentrations of a substance. This curve is used to set the instrument response levels, using the substance and its concentrations as standards. Alternatively, or additionally, an equation is fitted to the calibration curve plot and subsequently used to calculate the unknown concentrations of other samples reliably.
For data that follow a straight line, the standard method for fitting is the linear...
Design Example: Measuring Distance Between Two Points with Obstructions01:10

Design Example: Measuring Distance Between Two Points with Obstructions

When measuring distances in areas with physical obstructions, such as a lake in a field, surveyors must employ techniques to calculate accurate lengths without direct line measurements. One effective method is the offset technique, which allows for precise distance estimation over inaccessible stretches.In this scenario, a surveyor must measure a side of an area that crosses a lake. Since the measuring tape cannot span the lake, the surveyor begins by establishing a baseline that aligns with...
Distance Corrections01:15

Distance Corrections

To achieve precise distance measurements, especially in surveying and construction, certain corrections must be applied to account for potential sources of error like the standardization errors, temperature variations, and slope adjustments.Standardization error emerges when measurement equipment undergoes changes, such as wear, repairs, or weather impacts. To address this, surveyors compare the equipment’s readings to a standard. This process identifies any deviation that might lead to...
Calibration Curves: Correlation Coefficient01:10

Calibration Curves: Correlation Coefficient

In a linear calibration curve, there is a value called the calibration coefficient, denoted by 'r,' which measures the strength and the direction of association between two variables. The correlation coefficient value ranges from −1 to +1. A value of +1 indicates a perfect positive linear correlation, −1 denotes a perfect negative correlation, and 0 implies no correlation between the two variables. A positive correlation value establishes that as one variable increases, the other increases, and...

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Related Experiment Video

Updated: May 10, 2026

Automatic Laser-based Geometry Capture for Finite Element Analysis of Weld Beads
07:58

Automatic Laser-based Geometry Capture for Finite Element Analysis of Weld Beads

Published on: July 25, 2025

An innovative method for coordinate measuring machine one-dimensional self-calibration with simplified experimental

Cheng Fang1, David Lee Butler

  • 1School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore. CHENGFANG@ntu.edu.sg

The Review of Scientific Instruments
|June 8, 2013
PubMed
Summary

This study introduces a novel Coordinate Measuring Machine (CMM) self-calibration method using affordable ball bearings. This approach simplifies calibration and reduces measurement uncertainty by 50%.

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Area of Science:

  • Metrology
  • Mechanical Engineering
  • Instrumentation

Background:

  • Coordinate Measuring Machines (CMMs) require precise calibration for accurate measurements.
  • Traditional CMM calibration often relies on expensive reference standards like laser interferometers.
  • There is a need for cost-effective and simplified CMM calibration methods.

Purpose of the Study:

  • To propose an innovative and low-cost self-calibration method for Coordinate Measuring Machines (CMMs).
  • To simplify the CMM calibration process and data analysis.
  • To reduce the measurement uncertainty of CMMs.

Main Methods:

  • Developed a self-calibration method using a low-cost artefact made of precision ball bearings.
  • Optimized the mathematical model and data sampling positions to minimize experimental complexity.
  • Supplemented a simplified equation set by calibrating single-point error with a laser interferometer.
  • Utilized spline interpolation to determine the error compensation curve.

Main Results:

  • Successfully implemented a simple calibration system on a commercial CMM.
  • Demonstrated a significant reduction in measurement uncertainty.
  • Achieved a reduction in measurement uncertainty by up to 50% with the proposed error compensation curve.

Conclusions:

  • The proposed CMM self-calibration method is effective and cost-efficient.
  • The method simplifies the calibration process compared to traditional approaches.
  • The technique significantly enhances CMM measurement accuracy and reduces uncertainty.