Sahiner, BKazaz, MUgurlu, HH2024-07-182024-07-18http://akademikarsiv.cbu.edu.tr:4000/handle/123456789/6703UNIV NIS, FAC SCI MATHArticle; Proceedings PaperIn 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.