A Study of Interference among Parts of a Machine in Motion. 3rd Report. Graph-Based Judgment of Interferential Characteristics of Multi-Loop Structure.

Abstract

This study deals with the problem of analyzing the phenomena of interference among parts of a machine in motion. Some machines cause interference because of their basic structure as well as of their superficial form. A previous report demonstrated that a machine causes interference in a motion when its basic structure realizes a certain relationship among the torsion numbers, that is, the numbers of relative revolutions to occur between links in kinematic pairs in the motion. This report presents a graph-based method of judging the realization of the relationship for multi loop structures. First, the basic structure and the torsion numbers are represented in a graph. Next, this graph is transformed through a series of several graphs into a graph, called the fourth pair graph, each arc of which corresponds to a set of kinematic pairs in the structure and has a weight: the sum of all the torsion numbers that are each related to a kinematic pair in the Set. It is graph theoretically shown that when the weight of an arc in the fourth pair graph is not zero, the above-mentioned relationship is realized. Hence, by calculating the weights, one can easily judge the interferential characteristics of the structure.