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

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 the 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 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.