Cumali Ekici

ON THE PARALLEL SURFACES IN GALILEAN SPACE

In this paper, first of all, the definition of parallel surfaces in Galileanspace is given. Then, the relationship between the curvatures of theparallel surfaces in Galilean space is determined. Moreover, the firstand second fundamental forms of parallel surfaces are found in Galileanspace. Consequently, we obtained Gauss curvature and mean curvatureof parallel surface in terms of those curvatures of the base surface.

On Darboux rotation axis of lightlike curves

In this paper, by used Frenet trihedron for a lightlike curve, the motion of Darboux rotation axis is seperated to two simultaneous rotation motions. These rotation motions are that tangent and normal vectors of lightlike curve rotate around each other. But, the angular speeds of them are different. Then, by doing the similar operations, we obtain that Darboux axis rotates around spacelike vector of Frenet trihedron of the lightlike curve and this spacelike vector rotates around Darboux axis. Consequently, we obtain the series of Darboux vectors by this way. So, simple mechanisms can be formed.

On Motion of Robot End-Effector Using the Curvature Theory of Timelike Ruled Surfaces with Timelike Rulings

The trajectory of a robot end-effector is described by a ruled surface and a spin angle about the ruling of the ruled surface. In this way, the differential properties of motion of the end-effector are obtained from the well-known curvature theory of a ruled surface. The curvature theory of a ruled surface generated by a line fixed in the end-effector referred to as the tool line is used for more accurate motion of a robot end-effector. In the present paper, we first defined tool trihedron in which tool line is contained for timelike ruled surface with timelike ruling, and transition relations among surface trihedron: tool trihedron, generator trihedron, natural trihedron, and Darboux vectors for each trihedron, were found. Then differential properties of robot end-effectors motion were obtained by using the curvature theory of timelike ruled surfaces with timelike ruling.