Analysing the probabilities of the natural resting aspects of a component with a displaced centre of gravity

Abstract

This paper presents a new approach in the analysis of the natural resting behaviour of a component with a displaced centre of gravity. The methods proposed by Boothroyd et al. (1972), and Boothroyd and Ho (1977), can analyse parts with the centre of gravity located al their geometric centre. Hitherto, the only attempt at analysing pans with displaced centres of gravity entailed the use of empirical factors (Boothroyd et al. 1972). The hypothesis presented herein makes use of the centroid solid angle concept to analyse a component with a displaced centre of gravity. The proposed hypothesis postulates that the probability of a part coming to rest in its various natural resting aspects is directly proportional to the magnitude of the centroid solid angle and inversely proportional to the height of the centre of gravity from that aspect. The experimental results of drop tests conducted on a test specimen corroborate the hypothesis within a maximum deviation of 4%. This is the first successful attempt in the a...