ANALYZING THE PROBABILITIES OF THE NATURAL RESTING ASPECTS OF A COMPONENT WITH A DISPLACED CENTER OF GRAVITY

This paper presents a new approach in the analysis of the natural rest ing behaviour of a component with a displaced centre of gravity. The m ethods proposed by Boothroyd et al. (1972), and Boothroyd and Ho (1977 ), can analyse parts with the centre of gravity located at their geome tric centre. Hitherto, the only attempt at analysing parts with displa ced centres of gravity entailed the use of empirical factors (Boothroy d et al. 1972). The hypothesis presented herein makes use of the centr oid solid angle concept to analyse a component with a displaced centre of gravity. The proposed hypothesis postulates that the probability o f a part coming to rest in its various natural resting aspects is dire ctly proportional to the magnitude of the centroid solid angle and inv ersely proportional to the height of the centre of gravity from that a spect. The experimental results of drop tests conducted on a test spec imen corroborate the hypothesis within a maximum deviation of 4%. This is the first successful attempt in the analysis of the natural behavi our of components with displaced centres of gravity that does not rely on empirical factors.