ワイヤロープの微分幾何学的考察

概要

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Wire ropes are analyzed by assuming that the central lines of these wires are threedemensional spatial curves, and their surfaces are canal surfaces. These central lines are also curves on other inner canal surfaces. To study them it is very important to use the most suitable frame as a basis. In general, for the treatment of the curve Frenet frame is used, and for the surface Gauss' frame is used. However, it will be found that two other new frames should be set up and used to analyze the curves on surfaces and other surfaces such as wire rope. Then the analysis of these surfaces and curves are devided in several steps. At first, being set the frame of central line, more complicated canal surfaces will be achieved step by step. In this paper, the above mentioned theoretical development of analysis in wire rope will be described, the principal geometrical quantities calculated and then the projection of configuration of wires will be made for the case that the central line of the rope is straight or circular for example.
日本応用数理学会の論文
1993-12-15