Abstract
In a previous paper, for a variety of structures extracted from a machine, a hierarchical representation sheme was introduced, in which s-structures(s=1, 2, ···, 5)were identified as the machine structures essential to analyzing the phenomena of interference among parts of a machine in motion. In this paper, the properties of the structures are mathematically treated in terms of interference. By using a topological link of closed curves, a theorem is proved which states a sufficient condition for the following proposition:A given 3- or 4-structure with closed loops of members is Σ3-interferential with regard to a closed motion. This proposition means that the 3- or 4-structure causes every machine derived from it to produce interference during the motion;hence the theorem enables one to filter out unsuitable design plans of 3- or 4-structures from the point of view of interference avoidance.
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