Use of coordinate measuring machines and digital optical machines for the geometric characterization of circumference arcs using the minimum zone method (original) (raw)

This paper presents an optimised method for the characterization of circular features of any amplitude, which includes the capture of geometric data, by means of the use of three-coordinate measuring machine or digital optical machines with a CCD camera, and its subsequent mathematical processing. The proposed model determines the radius and the circularity error, based on the minimum zone method, and to this end it uses linear programming techniques, the Simplex programming principles and the limaçon approximation. An experimental study on ring gauges and reference disks is provided, including a comparative analysis using the Chauvenet and Grubbs filtering procedures. Last of all, an uncertainty estimation method is proposed by means of the Monte Carlo simulation. The experimental analysis carried out on ring gauges and reference disks accredit that the algorithm developed, implemented in a Matlab Ò environment, gives reliable results for any circumference arc considered, regardless of its amplitude.

Effect of CMM point coordinate uncertainty on uncertainties in determination of circular features

Measurement, 2006

Coordinate measuring machines (CMM) are commonly used to determine the parameters of a circular feature using different criteria like minimum zone, least squares, minimum circumscribed or maximum inscribed. For these criteria, the uncertainties in the evaluated parameters have been determined using Monte Carlo simulation. It has been assumed that the uncertainties in the point coordinates obtained from the CMM are independent, identical and normally distributed. The effect of varying CMM standard uncertainty on the mean and uncertainty interval width of all parameters has been shown graphically. The complete numerical results are provided for one case, which can serve as reference data. The results show that the nominal values of circularity error calculated from the measurement results may not represent the best estimates of the true value considering the measurement uncertainty.

Uncertainty analysis for angle calibrations using circle closure

Journal of Research of the National Institute of Standards and Technology

We analyze two types of full-circle angle calibrations: a simple closure in which a single set of unknown angular segments is sequentially compared with an unknown reference angle, and a dual closure in which two divided circles are simultaneously calibrated by intercomparison. In each case, the constraint of circle closure provides auxiliary information that (1) enables a complete calibration process without reference to separately calibrated reference artifacts, and (2) serves to reduce measurement uncertainty. We derive closed-form expressions for the combined standard uncertainties of angle calibrations, following guidelines published by the International Organization for Standardization (ISO) and NIST. The analysis includes methods for the quantitative evaluation of the standard uncertainty of small angle measurement using electronic autocollimators, including the effects of calibration uncertainty and air turbulence.

Computational metrology of the circle

Proceedings. Computer Graphics International (Cat. No.98EX149), 1998

Fitting a circle to a set of data points arranged in a circular pattern is a common problem in many fields of science and engineering. Specific applications in metrology include center position and circularity measurements. The fitting criteria usually depends on the application and varies with the statistical error model. Chebyshev fits, also known as MinMax or Least L-Infinity fits, are of particular interest in metrology where they quantify the form error in addition to yielding an allegedly more objective position assessment. This paper offers further empirical evidence to support this conjecture.

Evaluation of Circularity from Coordinate data using Maximum Distance Point Strategy (MDPS)

Measurement of cylindrical features using Coordinate Measuring Machine (CMM) is one of the important operations in precision engineering industries. The operation necessitates use of efficient computational algorithms as it has to determine radius/diameter of cylindrical features from measured point coordinates. One of the most widely used algorithm for such application is Least-Square Method (LSM) which fits a circle to the points measured using CMM. This paper proposes a new approach termed as Maximum Distance Point Strategy (MDPS) to determine radius/diameter of cylindrical feature for minimizing circularity from measured data-points. The results of MDPS are compared to that of LSM. Moreover, the results of MDPS are also compared with other methods available in literature and it has been found that the results are comparable with the same. It is also demonstrated that the developed methodology offers simplicity in understanding and ease of implementation in computational algorithms.

Digital method of automatically determining errors in the diameters of graduated circles

Measurement Techniques, 1982

A method [i] has been developed for finding the errors of graduated circles, dials, or scales based on apparatus designed so that the circle being tested and the standard circle occupy the same axis and are directly rotated by a drive. The devices used for reading the circle, two photoelectric microscopes per circle, determine the instants at which the calibration marks of the dials pass the observation point [2].

Geometric calibration of the circle-plus-arc trajectory

2007

In this paper, a novel calibration method for C-arm cone-beam (CB) scanners is presented which allows the calibration of the circle-plus-arc trajectory. The circle-plus-arc trajectory has been investigated recently for exact image reconstruction and is especially well suited for C-arm systems. The main idea is the separation of the trajectory into two segments (circle segment and arc segment) which are calibrated independently. For each trajectory segment, a calibration phantom is placed in an optimal way. The calibration results are then combined by computing the transformation the phantom experienced inbetween the independent runs. This combination can be done in a postprocessing step by using the Singular Value Decomposition (SVD). The method works for any calibration procedure in which the phantom has a favored orientation with respect to a trajectory segment. Results are presented for both, simulated as well as real data acquired with a Siemens AXIOM Artis C-arm system.

Study on Inspection of Circular Parts Used in Mechatronics

International Journal of Mechatronics and Applied Mechanics

Classical methods for the inspection on a production line of circular profiles are characterized by a reduced flexibility, making them extremely expensive. This work provides a study on vision systems used for determining deviation from circularity of components used in mechatronics. The paper present a vision system that analyzes and processes the captured image of circular parts in an automatic mode in order to undertake the dimensional inspection. The proposed system has been tested for MR522ZEZO class miniature bearings. The inner diameter of MR522ZEZO bearing is 2 mm, which makes it unavailable for dimensional control by conventional methods. Experimental results show that the proposed system is able to perform an accurate dimensional control in automatic mode while ensuring high flexibility for distinct types and sizes of mechatronic components with circular profiles.

Circumference imaging for optical-based identification of cylindrical and conical objects

SPIE Proceedings, 1997

Inspection and identification of cylindrical or conical shaped objects presents a unique challenge for a machine vision system. Due to the circular nature of the objects it is difficult to image the whole object using traditional area cameras and image capture methods. This work describes a unique technique to acquire a two dimensional image of the entire surface circumference of a cylindricalkonical shaped object. The specific application of this method is the identification of large caliber (155 mm) ammunition rounds in the field as they are transported between or within vehicles. The proposed method utilizes a line scan camera in combination with high speed image acquisition and processing hardware to acquire images from multiple cameras and generate a single, geometrically accurate, surface image. The primary steps involved are the capture of multiple images as the ammunition moves by on the conveyor followed by warping to correct for the distortion induced by the curved projectile surface. The individual images are then tiled together to form one two-dimensional hiage of the complete circumference. Once this image has been formed an automatic identification algorithm begins the feature extraction and classification process.

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