Machine vision-based relative-angle measurement system between circular holes

Abstract

In this study, the machine-vision technique is employed to measure the angle between two circular holes for the derailleur parts of a bicycle. A delta robot equipped with a motorized zoom lens is constructed as an automatic measurement device. In this way, we can detect the normal vectors of circular holes with different positions and sizes by using only one camera. By calculating the plane normal vectors of two circular holes within the camera coordinate system and performing the cross-product operation, the angle between the two circular holes is obtained. Simulation experiments reveal that the measurement method is influenced by the projection eccentricity error, and the error can be reduced by increasing the focal length and employing the virtual-center alignment method. The results show that the average error for measuring the derailleur parts is approximately 0.061°, and the standard deviation is 0.112°. Experimental analysis indicates that while the magnification of the image is larger, the average error of the measurement result is reduced, and the standard deviation is reduced as well. When the magnification is 0.4×, the measurement average error is 0.04°, and standard deviation is 0.101°. When the distance between the center of the circle and the center of the image is increased, the error in the angle calculation is also increased. A significant improvement is obtained by setting the fitting center position to the optical central position, which omits the influence of the error amplification caused by the distance of the circular hole from the optical axis.