ANALYZING THE NATURAL RESTING ASPECTS OF A COMPLEX PART

This papers introduces a new approach to predicting the natural restin g behaviour of a prismatic part of irregular cross-section. The method s proposed by Boothroyd et al. (1972) and Boothroyd and Ho (1977) were successful in analyzing parts with geometrically simple configuration s, although empirical factors were used in the former case. For the pa st 16 years or so, however, no attempt has been made to analyze parts with complex shapes. Up to now, the study of the natural resting behav iour of complex shapes was conducted by approximating or simplifying t he two stated methods. Considering the fact that most parts encountere d in industry are not geometrically simple, this practice is the norm rather than the exception. The hypothesis presented in this paper prop oses that the probability of a part coming to rest on any of its many feasible resting surfaces is directly proportional to the centroid sol id angle and inversely proportional to the height of the centroid from that surface. No empirical factors are needed or assumed. Complex com ponents, such as those with a displaced centre of gravity, can be anal yzed thus. The proposed hypothesis is compared with Boothroyd's Energy Barrier Method'. The predictions of the hypothesis and the empirical results of drop tests conducted on non-symmetrical (oblong) and symmet rical (T-shaped) prisms are consistent to within 7%. This is the first successful attempt in the analysis of the natural behaviour of compon ents with a complex shape.