ねじれ面の三角形展開と組立て^*

抄録

Since the warped surfaces are always developed by triangulation on flat planes, the surfaces constructed by rolling the developments without folding become single-curved surfaces. In the present paper, we report the results of the estimation of approximation in these procedures, i.e., the development by triangulation and construction of warped surfaces. Comparison has been made between the warped surfaces and single-curved surfaces whose restriction conditions are similar to each other. The principale results are as follows.
1. Warped transition surfaces
In the parameter range used in usual design, the area of the development of a 4-branched warped transition becomes nearly equal to that of the convolute surface whose directrices are identical to those of the warped transition. It shows that it is possible to construct convolute-like surfaces by rolling smoothly the developments of 4-branched warped transitions. Similar results have been obtained for 2-branched warped transitions.
2. Helicoids
In the parameter range R₂L/R₁²≤3, the area of the development of the helicoid becomes nearly equal to that of the convolute surface whose directrix is the inner helix of the helicoid. It shows that it is possible to construct convolute-like surfaces by rolling the developments of the helicoids smoothly. It is, however, impossible to construct surfaces similar to the original helicoids for large R₂L/R₁².