Submitted to: ASABE Annual International Meeting
Publication Type: Proceedings
Publication Acceptance Date: 7/12/2006
Publication Date: 7/12/2006
Citation: Narayanan, P., Lefcourt, A.M., Tasch, U., Rostamian, R., Grinblat, A., Kim, M.S. 2006. Theoretical aspects of orienting fruit using stability properties during rotation [abstract]. ASABE Annual International Meeting. Paper No. 061144. Interpretive Summary:
Technical Abstract: Described is the potential use of a stability property of fruit to allow fruit to be oriented along the stem/calyx axis. Inspection using machine vision offers the potential for improved safety and quality of foods. However, effectiveness of fruit inspection has been limited by the difficulty of differentiating stem and calyx regions from problem sites. It is possible to orient fruit prior to imaging; however, commercial systems have had only limited impact due to mechanical complexity, cost, error, or some combination thereof. Preliminary tests using inertial properties demonstrated that apples could be oriented along the stem/calyx axis. Apples were rolled down a ramp consisting of two parallel tracks. When sufficient angular velocity was achieved, the apples moved to a configuration where the stem/calyx axis was perpendicular to the direction of travel. For this study, the theoretically stability of an ellipsoid-object subject to rotation was examined using the small perturbation method and the analysis using the action integral. For the small perturbation method, perturbations were assumed to be sufficiently small so that the associated nonlinear Euler equations could be linearized. Theoretical derivations, and a practical demonstration using Maple software, indicated that an object rotating at constant velocity was stable only when the object rotated around the axis of radial symmetry, e.g. the stem/calyx axis. Action is defined as the integral of kinetic energy minus potential energy over some time period. Ellipsoids were constructed by rotating an ellipse (x2/a2 + y2/b2 = 1) around the x-axis. Lower action values were assumed to indicate greater stability. Relative action values were generally lower (for a > b) for rotation around the x-axis (the axis of radial symmetry) compared to rotation around the y-axis, and the difference increased as a/b increased. These results justify efforts to develop a simple system for orienting fruit based-on rotational stability.