Related Experiment Video
Updated: Jul 31, 2026
09:36
Measurement of Spatial Stability in Precision Grip
Published on: June 4, 2020
Geometrical error compensation of machines with significant random errors.
1Department of Electrical and Computer Engineering, National University of Singapore, Singapore, Singapore.
ISA Transactions
|February 3, 2005
Summary
This study introduces a statistical method to compensate for machine errors by analyzing random error probabilities. This approach effectively reduces random error impacts on systematic error compensation, improving machine accuracy.
Area of Science:
- Metrology
- Statistical Analysis
- Mechanical Engineering
Background:
- Machine accuracy is crucial for precision manufacturing.
- Significant geometrical errors can arise from systematic and random sources.
- Existing compensation methods may struggle with substantial random errors.
Purpose of the Study:
- To develop a statistical approach for soft geometrical error compensation.
- To mitigate the influence of random errors on systematic error compensation.
- To enhance the accuracy of machines with significant geometrical errors.
Main Methods:
- Defining error classes based on calibration error bands.
- Computing the probability of random error magnitudes within each class.
- Statistically deducing the most probable systematic error component.
- Implementing geometrical error compensation based on the deduced systematic error.
Main Results:
- Experimental validation of the statistical approach.
- Successful linear error compensation for a single-axis piezo-ceramic motion system.
- Demonstrated reduction in adverse effects of random errors on compensation.
Conclusions:
- The proposed statistical method offers an effective solution for soft geometrical error compensation.
- The approach enhances machine accuracy by statistically addressing random error influences.
- This methodology is particularly beneficial for systems with significant geometrical errors.
Related Concept Videos
03:37Uncertainty in Measurement: Accuracy and Precision
Scientists typically make repeated measurements of a quantity to ensure the quality of their findings and to evaluate both the precision and the accuracy of their results. Measurements are said to be precise if they yield very similar results when repeated in the same manner. A measurement is considered accurate if it yields a result that is very close to the true or the accepted value. Precise values agree with each other; accurate values agree with a true value.
01:20Random and Systematic Errors
Scientists always try their best to record measurements with the utmost accuracy and precision. However, sometimes errors do occur. These errors can be random or systematic. Random errors are observed due to the inconsistency or fluctuation in the measurement process, or variations in the quantity itself that is being measured. Such errors fluctuate from being greater than or less than the true value in repeated measurements. Consider a scientist measuring the length of an earthworm using a...
01:12Types of Errors: Detection and Minimization
Error is the deviation of the obtained result from the true, expected value or the estimated central value. Errors are expressed in absolute or relative terms.
Absolute error in a measurement is the numerical difference from the true or central value. Relative error is the ratio between absolute error and the true or central value, expressed as a percentage.
Errors can be classified by source, magnitude, and sign. There are three types of errors: systematic, random, and gross.
Systematic or...
Absolute error in a measurement is the numerical difference from the true or central value. Relative error is the ratio between absolute error and the true or central value, expressed as a percentage.
Errors can be classified by source, magnitude, and sign. There are three types of errors: systematic, random, and gross.
Systematic or...
01:04Random Error
Random or indeterminate errors originate from various uncontrollable variables, such as variations in environmental conditions, instrument imperfections, or the inherent variability of the phenomena being measured. Usually, these errors cannot be predicted, estimated, or characterized because their direction and magnitude often vary in magnitude and direction even during consecutive measurements. As a result, they are difficult to eliminate. However, the aggregate effect of these errors can be...
01:20Random and Systematic Errors
Scientists always try their best to record measurements with the utmost accuracy and precision. However, sometimes errors do occur. These errors can be random or systematic. Random errors are observed due to the inconsistency or fluctuation in the measurement process, or variations in the quantity itself that is being measured. Such errors fluctuate from being greater than or less than the true value in repeated measurements. Consider a scientist measuring the length of an earthworm using a...
01:15Distance 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...