Analysing the natural resting aspect of a prism on a hard surface for automated assembly

Abstract

This paper introduces a new approach for predicting the natural resting behaviour of a square prism and a rectangular prism on a hard surface. The methods proposed in [1] involve the use of empirical factors. Considering the complex formulae and computation required, the authors have decided to employ the centroid solid angle concept to predict the natural resting behaviour of a part. The method presented here is the centroid angle concept which assumes that the probability of any surface of a part on which it comes to rest, is directly proportional to the difference between the centroid solid angle of that aspect and the average of the critical solid angles of the neighbouring aspects, and inversely proportional to the height of the centre of gravity of that aspect. The results showed that the predicted data agree well with both the experimental data obtained in [1] and the authors. This is the first successful attempt at the analysis of the natural behaviour of a part on a hard surface without resorting to empirical factors.