Modelling the Natural Resting Aspect of Small Regular Shaped Parts

This paper presents a mathematical model for predicting the natural resting aspect of parts of regular shapes but of different sizes based on stability considerations. The objective of this model is to facilitate the design of effective and efficient orientating devices for vibratory bowl feeders. The results from the mathematical modelling were compared with the theoretical models and experimental results of other investigators. Good agreement was obtained.

Analysing the natural resting aspect of a complex shaped part on a hard surface for automated parts feeding

This paper presents a new approach to analysing the natural resting behaviour of a non-regular prism on a hard surface. The methods proposed by Boothroyd, Redford, Poli and Murch (1) involve the use of empirical factors. Considering the complex formulae and computations 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 the part coming 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 is inversely proportional to the height of the centre of gravity of that aspect. The results showed that the predicted data agreed well with the experimental data obtained by the authors. This is the first successful attempt to analyse the natural behaviour of complex shaped parts on a hard surface without resorting to empirical factors.

Analysing the Natural Resting Aspects of a Component for Automated Assembly

This paper proposes the construction of an energy envelope that can be used to advantage with the energy barrier method to analyse the natural resting aspect of engineering parts destined for automatic assembly. Unlike the energy barrier method, the energy envelope does not require any visualization of the projection of the energy barrier on the aspect of interest. The energy envelope is the three-dimensional topology of the changes in height of the centroid, as the part attempts changes of aspect. The paper describes how it may be computed in a CAD (computer aided design) solid modeller. The results of applying the energy envelope to prisms of square and cylindrical cross-sections are the same as those predicted by the energy barrier method. When extended to the analysis of a rectangular prism, the results were consistent with Boothroyd's dynamic solution and Boothroyd's experimental data. This conclusion is encouraging as there is no irrefutable evidence that the energy barrier method may be applied to the analysis of the rectangular prism.