A Study on Motion of a Robot End-Effector Using the Curvature Theory of Dual Unit Hyperbolic Spherical Curves

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Sahiner B., KAZAZ M., UĞURLU H. H.

FILOMAT, vol.30, no.3, pp.791-802, 2016 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 30 Issue: 3
  • Publication Date: 2016
  • Doi Number: 10.2298/fil1603791s
  • Journal Name: FILOMAT
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.791-802
  • Keywords: Curvature theory, dual Darboux frame, dual tool frame, dual velocity vector, robot end-effector, ruled surface, trajectory planning


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.