Representation of generalized circular surfaces as rigid body motions

Selahattin Aslan; Murat Bekar; Yusuf Yaylı;


In this paper, we introduce generalized circular surfaces, which is a new kind of surfaces, as generalization of generalized tube surfaces and circular surfaces. Moreover, we define a dual quaternion using apparatus frame of the spine curve of the generalized circular surface. We prove that screw motion obtained by using dual quaternion generates a generalized circular surface (i.e., a tube surface, a genaralized tube surface or a circular surface) in three dimensional real vector space. These kind of surfaces are also expressed as homothetic motions of one of the apparatus frame vectors of these surfaces. Finally, we give examples of these kind of surfaces.

Vol. 25 (2024), No. 1, pp. 79-91

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