機械の運動における部材干渉の研究 : 第2報,閉路を持つ構造の閉運動に関する干渉性の位相幾何学的解析

抄録

In a previous paper, for a variety of structures extracted from a machine, a hierarchical representation scheme was introduced, in which s-structure (s=1, 2, …, 5) were identified as the machine structures essential to analysing the phenomena of interference among parts of a machine in a motion. In this paper, the properties of the structures are mathematically treated in terms of interference. By means of a topological link of knots, 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 record to a closed motion. This proposition means that the 3- or 4-structure causes every machine derived from it to raise interference during the motion, and the theorem hence enables one to filter out unsuitable design plans of 3- or 4-structures from the point of view of interference avoidance.