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

ŞAHİNER B., KAZAZ M., UĞURLU H. H.

FILOMAT, vol.30, no.3, pp.791-802, 2016 (SCI-Expanded, Scopus) 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 (SCI-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
  • Manisa Celal Bayar University Affiliated: Yes

Abstract

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.