Sweeping Surfaces in theThree-Dimensional Lie Group

This paper investigated the rotation minimizing frames that are related to the space curves and the sweeping surfaces that are traced by these frames in the three-dimensional Lie group. Then, the sufficient and necessary conditions for the sweeping surface to be a developable ruled surface were obta...

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Bibliographic Details
Published inSymmetry (Basel) Vol. 14; no. 4; p. 698
Main Authors Nazra, Sahar H., Abdel-Baky, Rashad A.
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 29.03.2022
Subjects
Geometry
Industrial design
Lie groups
local singularities
Sweeping
sweeping surface
Velocity
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Summary:This paper investigated the rotation minimizing frames that are related to the space curves and the sweeping surfaces that are traced by these frames in the three-dimensional Lie group. Then, the sufficient and necessary conditions for the sweeping surface to be a developable ruled surface were obtained. In particular, we mostly focused on the study of the resulting developable surface is a cylinder, cone, or tangent surface. Meanwhile, to support the results in the paper, some illustrative examples are presented.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym14040698