Examining motion of a robot end-effector via the curvature theory of dual Lorentzian curves

Abstract

In this paper, we study the motion of a robot end-effector using the curvature theory of a dual Lorentzian unit spherical spacelike curve which corresponds to a timelike ruled surface with spacelike ruling generated by a line fixed in the end-effector. In this way, we determine linear and angular time dependent differential properties of motion such as velocities and accelerations which are important information in kinematics and robot trajectory planning. Moreover, motion of a robot end-effector in Lorentzian space whose generating surface is a helicoid is examined as a practical example.