Part feeders take an unsorted bulk of identical parts and output them in a uniform orientation. Common feeders sort out those items that settle initially on one specific face, and further reorient them as desired. Quick estimators of the probability of settling on a given face facilitate the design of parts for efficient feeding and of the feeding lines themselves. Nevertheless, the evaluation and the development of such estimators have been hindered by the lack of data. Here, I create and analyze a large, simulated dataset; evaluate estimators available in the literature by comparing their predictions to simulation results with the help of a custom-made metric; and propose new estimation algorithms. The new estimators offer viable alternative to the direct dynamic simulation of parts due to their low average errors.

We investigate the local motion of a planar rigid body with unilateral constraints in the neighborhood of a two-contact frictional equilibrium configuration on a slope. A new sufficient condition of Lyapunov stability is developed in the presence of arbitrary external forces. Additionally, we construct an example, which is stable against perturbations by infinitesimal forces, but does not possess Lyapunov stability against infinitesimal displacements or impulses. The great difference between previous stability criteria and ours leads to further questions about the nature of the exact stability condition.