ヒト前腕骨の形態と機能 : 単一の幾何学的概念(円錐面上の測地線)を用いて行った,生物の形態および機能設計

Abstract

In human forearms, the radius and the ulna are geometrically regarded as a combination of two spirals arranged in parallel, which rotate in opposite directions. I assume that the optimal curves for these spirals are geodesic curves on a surface of a cone, expressed as a formula as follows: [numerical formula] [numerical formula] [numerical formula] γ: the shortest distance from the vertex of the cone to the geodesic curve. [numerical formula], where φ is the vertex angle in developed plane of the cone. When two geodesic curves exist on a corn, the curve which is obtained by proper prolongation or reduction of one curve proves to be homothetic to the other. And all geodesic curves on a corn are symmetrical when they are prolonged to the proper extent. It is interesting that this symmetric formula is a common characteristic of hard tissues of animals. Furthermore, it seems that these geodesic curves exist in several hard tissues of many animals, as well as in humans. When two geodesic curves rotate with rolling contact at one point and at a constant angle between tangent planes of two-geodesic curves, the distance between the vertexes of two cones is kept constant. Using this geometric concept of geodesic curves on the cone, I designed a model of forearm movement. In this model, the humeral capitulum and the mid-point of the axis of the humeral trochlea are regarded as the vertexes of two cones. The above-mentioned hypothesis proposed the novel concept that morphology and functions can be generalized under the identical geometric theory with the geodesic curves on the cone.