Submitted to: Transactions of the ASABE
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 7/15/2008
Publication Date: 8/12/2008
Citation: Narayanan, P., Lefcourt, A.M., Tasch, U., Rostamian, R., Grinblat, A., Kim, M.S. 2008. Theoretical analysis of stability of axially symmetric objects with regard to orienting apples. Transactions of the ASABE. 51(4):1353-1364. Interpretive Summary: Theoretical analysis of the stability of rotating fruit indicated that fruit is most stable when rotating about the stem/calyx axis. Commonly, fruit are manually inspected for bruises and contamination before they are sent to market. Scientists have developed imaging systems for the automated inspection of fruits; however, these imaging systems frequently identify the stem and the calyx region of fruit as a problem area. A solution to this problem would be to orient all fruit so that the location of the stem/calyx region is known before taking pictures. Various mechanical systems have been developed to orient fruit, but they have not been commercially successful due to mechanical complexity, cost or error. Preliminary tests showed that apples could be oriented along the stem/calyx axis by rolling them down a test track; it was observed that as the apples gained speed, they moved to a configuration where the stem/calyx axis was perpendicular to the direction of travel. In this study, two theoretical methods are used to determine the stability characteristic of a spheroid-object with an axis of axial symmetry. Results from the first method indicated that fruit would be more stable when they rotate about the stem/calyx axis. The second method based on the concept of action integral indicated that the distance traveled down the test track prior to orientation would vary depending on the characteristics such as mass and shape of the apple. These results support the preliminary observations, and provide justification for efforts to develop a simple system for orienting fruit based-on rotational stability. An inexpensive system that allows fruit to be oriented would result in the development of commercial systems for the automated inspection of fruit for quality and contamination. In addition, this study introduces a novel use of action integrals to examine stability.
Technical Abstract: Described is the potential use of stability properties to orient fruit along the stem/calyx axis. Inspection using machine vision offers the potential for improved food safety and quality. However, effectiveness of fruit inspection has been limited by the difficulty of appropriately orienting fruit for imaging. Commercial orientation systems have had only limited impact due to mechanical complexity, cost, error, or some combination thereof. Preliminary tests demonstrated that apples could be oriented along the stem/calyx axis using inertial properties. Apples were rolled down two parallel tracks. When sufficient angular velocity was achieved, the apples moved to an orientation where the stem/calyx axis was perpendicular to the direction of travel and parallel to the plane of the tracks. The purpose of the current study was to examine stability characteristics of axially-symmetric objects. Rotation of a free body around an axis of axially symmetry was found to stable, while rotation around a perpendicular axis was not. Furthermore, comparisons of action values for ellipsoid models of apples indicate that inertial characteristics can be used to orient apples, but that the distance traveled down the test track prior to orientation will vary depending on characteristics such as mass and shape. The critical assumption for this analysis was that for the same object traveling the same path with different initial orientations, lower action values represent preferred motions. This study introduces a novel use of action integrals to examine stability and provides justification for efforts to develop a simple system for orienting fruit based-on rotational stability.