Browsing by Author "Ugurlu H.H."

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    Integral characterizations for timelike and spacelike curves on the Lorentzian sphere S13
    (Shiraz University, 2008) Kazaz M.; Ugurlu H.H.; Ozdemir A.
    V. Dannon showed that spherical curves in E4 can be given by Frenet-like equations, and he then gave an integral characterization for spherical curves in E4. In this paper, Lorentzian spherical timelike and spacelike curves in the space time R14 are shown to be given by Frenet-like equations of timelike and spacelike curves in the Euclidean space E3 and the Minkowski 3-space R1 3. Thus, finding an integral characterization for a Lorentzian spherical R14 -timelike and spacelike curve is identical to finding it for E3 curves and R13 -timelike and spacelike curves. In the case of E3 curves, the integral characterization coincides with Dannon's. Let {T, N, B} be the moving Frenet frame along the curve α(s) in the Minkowski space R1 3 . Let α(s) be a unit speed C4-timelike (or spacelike) curve in R13 so that α'(s) = T . Then, α(s) is a Frenet curve with curvature κ(S) and torsion τ(S) if and only if there are constant vectors a and b so that (i) T′(s) = κ(s){a cosξ(s)+b sinξ(s) + ∫0s cos[ξ(s)-ξ(δ)]T(δ)κ(δ)doδ}, T is timelike, (ii) T′(s) = κ(S){ aeξ+ ∫0 scosh((ξ(s)-ξ(δ))T(δ)κ(δ)dδ}, N is timelike, where ξ(s)= ∫0s(δ)dδ. © Shiraz University.
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    A study on motion of a robot end-effector using the curvature theory of dual unit hyperbolic spherical curves
    (University of Nis, 2016) Sahiner B.; Kazaz M.; Ugurlu H.H.
    In this paper we study the motion of a robot end-effector by using the curvature theory of a dual unit hyperbolic spherical curve which corresponds to a timelike ruled surface with timelike ruling generated by a line fixed in the end-effector. In this way, the linear and angular differential properties of the motion of a robot end-effector such as velocities and accelerations which are important information in robot trajectory planning are determined. Moreover, the motion of a robot end-effector which moves on the surface of a right circular hyperboloid of one sheet is examined as a practical example. © 2016, University of Nis. All rights reserved.